Make the Switch to Blackjack Switch

            Over the years, numerous inventors have attempted to tinker with the game of Blackjack.  I warn them to tread very carefully when doing this.  Of all the games in the casino, blackjack strategy has probably become the best learnt strategy.  With the proliferation of computer generated strategies, you see far less splitting of 10's/faces and far less awful choices by the average Player.  You'll still occasionally find the novice who isn't happy until their own hand is 17 or better, even if that means busting it, but you'll now get a collective groan out of the remaining Players instead of several following suit.

            This is where the trouble started for creating a blackjack variant.  Players knew that original Blackjack had a payback of 99.5% (give or take) and they had learned the strategy fairly well.  When someone created some form of blackjack with a twist, they guessed it meant a lower payback (otherwise, why would the casinos offer it?) and it meant a new strategy.  Just like in video poker, if you don't adapt your strategy for the rules of the game, you can't earn the top payback. 

            So, once in a while a new game would hit the floor, Players would give it a try, but, without the right strategy, the theory on payback turned into a self-fulfilling prophecy - and the Player invariably lost more playing the new version than the original.  The new game might have been a bit more exciting than Blackjack, but not enough to overcome the extra losses the Player had to endure.

            As well all know, over the years a few blackjack variants have stuck.  Spanish 21 is likely the most successful of these variants.  It removes the 10's (not the face cards) from the deck.  As this hurts the Players, it returns this missing payback to the Player by offering more liberal rules and some bonus payouts for some novel hands.  This added more excitement to the game and offered the Player some opportunities for something other than mostly even money payouts.   While Spanish 21 is past its prime, it continues to boast a significant presence in the casinos.   It's payback is actually quite comparable to blackjack, but the need to learn a new strategy has kept the casinos happy by having Player error contribute to the hold of the game.

            More recently, Blackjack Switch has also entered the market.  It has roughly 100 tables in the marketplace.  Blackjack Switch uses a unique method to alter the game.  If the Dealer busts with a 22, all Player non-busted hands (except a natural Blackjack) are a push.  This costs the Player several percentage points.  But, to make up for this, Blackjack Switch allows the Player to 'switch' the 2nd card dealt in each of his two hands.  So, if dealt a 5-10 and a 10-6, the 10 and 6 can be swapped to turn the hands into an 11 and a 20.  From two stiffs to two strong hands.  The payback again is comparable to regular blackjack, albeit you must play two hands at a time.

            Blackjack Switch requires not only learning the strategy for the 'Push 22' rule, but you must also learn when to switch cards.  Much of the time it will be fairly obvious as in my earlier example.  In others, less so.  Imagine being dealt a 10-7 and an 8-10 vs a Dealer face card.  What is the right play?  You have two pat hands or you can 'switch' and have a total bust (15) and one strong hand (20).  When we look at the expected values of each of these hands, there is not much of a choice.  17's and 18's against a Dealer 10 are sitting ducks in any blackjack game.  We do the swap and the combined expected value of our hands goes from 1.3 to 1.97.  If you never switched cards, you'd take a 7-8% hit in payback.  No one would ever (hopefully) play this bad, but if you go by the seat of your pants, you're likely to take a 2-3% hit.  Throw in not knowing how to alter your strategy for the Push 22 rule and you could easily take Switch down to a 97% payback from its 99.5+% payback.
            Just like in video poker, there is a simple solution for this.  LEARN THE STRATEGY.  To help you with this, my booklet Expert Strategy for Blackjack Switch comes with a full-color pocket-sized strategy card that you can bring with you into the casino.  One side has the expected values for every hand to help you decide when to switch.  The other contains the hit/stick strategy for Push 22.  The retail price is $6.95 for the booklet and the card, but for a limited time, I'll offer them to GT readers for only $5.95.  You can also order ADDITIONAL strategy cards for $1.00 each.  If you would like to order, please send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

Giving Thanks

            I apologize to those of you who have been looking for my column the past couple of weeks and couldn't find it.  As some of you may have heard by now, my mother (and wife of Lenny Frome), passed away two weeks ago.  After the funeral, my brother recounted a story to me that I had never heard before.

            When my father passed away in 1998, my brother was the first one who headed out to Las Vegas to be with our mom.  It took a day or two before all the arrangements were made for them to come back East for my dad's funeral.  Yet, of course, they still had to eat.  My brother asked my mom where she wanted to go to dinner and she responded with Hugo's Cellar at the Four Queens.  My family had already made that a regular dinner spot when anyone came to town - and it is a tradition that carries through until today. 

            As they walked through the casino from the parking garage to the restaurant, they passed by two women playing video poker.  They were each holding a copy of one of my dad's books.  My brother said he could not have staged it any better if he tried.  This was clearly a sign.  My father's impact to the industry would continue long after he was gone.

            My father was informally called "the Godfather of Video Poker" by many in the industry.  To be sure, he played NO part in the invention of the game.  At the same time, no one can deny the impact he had on popularizing it.  Even if you are not a video poker expert or even a regular, I can't help but imagine that your play isn't just a tiny bit better from having read his articles - or any of the numerous writers who came after him - including me!  Would video poker have had the staying power if there wasn't someone telling the early Players how to play it?  Would video poker have eaten up as large a percentage of the casino floor as it does today?

            Of course, my father could just have easily been called "the Godfather of Proprietary Table Games".  He had a hand in the development of Let It Ride, Three Card Poker, Spanish 21 and Caribbean Stud Poker.  At their respective peaks, there must have been a combined 2500-3000 of these tables.  As I consider myself an extension of my father's work, we can add on Ultimate Texas Hold'em, Mississippi Stud and a host of smaller games to the total.  This brings the total to perhaps as high as 4000 proprietary tables that my father directly or indirectly had a hand in.  Imagine the casino floor without any of these games.

            While my father was the public face of everything that went on, everyone that knew them (both personally and professionally) knew that my parents were always together.  My dad brought my mom to business meetings to size up the potential client.  My mother was the proofreader for all of my dad's books and booklets.  She was responsible for shipping orders and for the accounting.  In fact, it was my mother who was always listed as the "President" of their company. 

            With the help of Catherine Jaeger, the editor of Midwest Gaming and Travel, we have launched a campaign to get my father into the American Gaming Association's (AGA) Gaming Hall of Fame in 2012.  No disrespect to Blue Man Group (one of the inductees for this past year), but I truly believe Lenny Frome's impact on the industry has been far greater.  To this end, we are asking people to write to the AGA and urge them to induct my father into the Hall of Fame in 2012.

            There are a number of ways to make your voice heard.  You can copy the sentence below or use your own experience to explain why you believe the time has come for Lenny Frome to be inducted into the Gaming Hall of Fame. "Because of his many significant contributions to casino gaming, I respectfully request your consideration of Lenny Frome for induction into the Gaming Hall of Fame."

Mail it to:
American Gaming Association
Frank J. Fahrenkopf, Jr., President/CEO
1299 Pennsylvania Avenue, NW, Suite 1175
Washington, DC 20004

E-mail to:
Brian Lehman/Communications Manager-AGA

            Over this Thanksgiving weekend, my family and I one again dined at Hugo's Cellar.  This time, for the first time we toasted the memory of both my father and my mother.  My dad may have been the "Godfather of Video Poker", but most importantly, they were the "Father/Mother and Grandfather/Grandmother of the Frome family."  Once again, they are "always together."

Don't Be Foolish!

            It was almost a year ago that I launched this blog (  I was very nervous about launching it.  If there is one thing I've learned about the internet over the years is that pretty much any idiot can have a blog - and quite frankly, I didn't want to be 'any idiot.'  I'd like to think that the name "Frome" is the gold standard in the industry where math analysis is concerned.  To our credit, we have Three Card Poker, Let It Ride, Caribbean Stud Poker, Spanish 21, Ultimate Texas Hold'em, Mississippi Stud, Imperial Pai Gow and countless sidebets.  That's a lot of the casino floor whose math was done by Leonard Frome or Elliot Frome. 

            So, I was quite surprised this past week when I came across a financial blog that was very unimpressed this year's G2E where table games were concerned.  Admittedly, I did write a column last year that called on more inventors to display their ideas at the G2E.  I recognize that the cost of even a small booth can be rather prohibitive for the individual inventor, but what a great opportunity to show your game to people in the industry.  I was pleasantly surprised to see at least two new inventors displaying their games and larger booths from some of the more established companies.

            What I found amazing about this financial blog, however, was not that the writer looked over every game and found none of them to his liking.  That would've been one thing.  Instead he essentially takes table game companies to task for "designing games that the gambler has no hope of beating, but they force the gambler to take the time to learn how to play them!"  This blew me away!  Does he truly expect the casino to introduce games that the Player can easily beat?  That's not going to happen.  The only game that has ever been put on the floor that can readily be beaten are certain variations of video poker. 

            Further, our blogger is annoyed that you have to take time to learn how to play them.  The only game which requires ZERO time to learn how to play them is perhaps slot machines.  As I've recounted in my column many times, I can't even figure out when I've won or lost anymore in today's video slots, but since all you need to do is press the 'spin' button and we can assume that the machine will properly tally your win or loss, I assume this meets the requirement of not needing to take time to learn how to play them.

            Thus, we can conclude from our blogger that what he is looking for is a slot machine with a 100%+ payback.  Perhaps he should've read my column from two weeks ago where I talked about a company that provides the payback information for their slot machines.  This WOULD necessitate learning how to use the smartphone 'app', so I don't know if this meets his strict criteria.

            A couple of days after this first column appeared, our blogger was back with more information for us.  First, he repeats some of his thoughts from the previous column, decrying the lack of innovation from table game companies and then stating, "how the gaming industry has not seen a blockbuster table game since blackjack, and how the industry may not see one until somebody steps up and creates a game that is theoretically beatable."

            That is quite a statement.  According to Wikipedia, blackjack's origins may be as much as 400 years old.  The game as it is played in most jurisdictions is hardly beatable - or at least not easily.  Yes, we're all aware of the MIT team that did it, but this took a rather significant effort on the part of a focused group of individuals. 

            In 1991, the table half of the casino floor consisted of nothing but blackjack, craps and roulette.  Twenty years later, it is estimated that as much as 15-20% of the tables in the U.S. market may be those that were invented AFTER blackjack.  Twenty years from now, I have little doubt that blackjack will make up an even smaller percent of that floor.   Let's not forget that a blackjack table is essentially FREE to the casino while they have to pay to put a proprietary table game on their floor.

            As a gaming analyst - and one that focuses mostly on table games - I am keenly aware of the math of the games.  Most of the newer games that are being introduced have paybacks in the higher 98% to low 99% range.  Yes, they do require that you 'learn' how to play them to achieve these paybacks.  No one, not myself, not the inventors nor the casinos will try and let you believe that the games are beatable in the long run.  That does NOT, however mean that you cannot have winning sessions in the short run and enjoy the entertainment value that they can provide.  Most table games are developed to have the Player win about 35-45% of the time over a 3-hour session - assuming you are willing to 'take the time to learn how to play them'

            Best of all, I won't "force" you to do this, but I'll give you the opportunity to!  There are now 7 books in the Expert Strategy series for table games (Let It Ride, Three Card Poker, Four Card Poker, Spanish 21, Caribbean Stud Poker, Mississippi Stud and Blackjack Switch) and for a limited time, you can order the entire set for $20 which includes postage and handling.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

Coming Soon to a Casino Near You?

           Every inventor thinks their new game is going to be a sure-fire hit.  It's taken Three Card Poker about 15 years to get to 1500 or so tables.  Everyone else is sure they can do it in 2 to 3 years.  So what, if so far, no other game has even come close.  I believe the record for fastest game to 100 tables belongs to Ultimate Texas Hold'em and that took just over a year.

            So, in reality, I can't say with any certainty that any of the games I'm going to discuss today will make it to a casino any time soon.  They will, however, be on display at the Global Gaming Expo (G2E) next week, at the Shuffle Master booth.  I didn't work on these games, so I can't give much insight into the strategy or the math (yet).  If you're going to the show this year, make sure to check these games out.  Next week, for the G2E edition, I'll review a couple of games I did the math on and be able to go more in depth on each.

Cincinnati 7 Card Stud

The base game is a simple game going head-to-head against the Dealer.  You make an Ante and Blind wager.  You get to look at the first 6 cards of what will eventually be a 7-card hand.  After reviewing your 6-cards, you can Fold or Play 1x or 2x your Ante.  The Dealer reveals his 7-cards and you get to see your 7th card.  If the Dealer beats you (best 5 out of 7 cards), you lose all your wagers.  If you beat the Dealer, the Ante and Play pay even money and the Blind pays according to the paytable.  There is also a bonus sidebet that pays if your 7-card hand is Three of a Kind or better.

The twist in Cincinnati 7 is the second optional sidebet.  Here, you are playing against all the other Players as well.  Top hand takes the enitre pot - as long as it at least a Two Pair or Better.   The Dealer participates just like every other Player - including putting up a wager each hand.  If nobody has Two Pair or better, all the wagers carry over to the next round.  Obviously, you can't jump into the middle of a pot.  If you skip a round, you're out until someone wins the pot.  Get a mini hot streak and you can increase your bankroll quickly.  It should also be noted that this sidebet has NO house advantage.  You're playing true odds against everyone.

Six-Card Poker

Another relatively simple to understand game against the Dealer.  Player makes an Ante Wager and is dealt 6 cards.  The Dealer is dealt 6 cards as well and turns over three of them, face up.  Player can now Fold or Play, making another wager equal to the Ante.  The Dealer reveals the rest of his hand.  If the Dealer does not have an A-K or better, the Ante pushes and the Play wager is won or lost depending on who has the best hand (best 5 out of 6 cards).  If the Dealer does have an A-K or better, then both Ante and Play wagers are won or lost depending on who has the best hand.

There is also an Aces Up sidebet that pays if the Player's hand is a Pair of Aces or better.  This sidebet pays even if the Player folds.  Yes, you will Fold with a Pair of Aces if the Dealer's three upcards are Three of a Kind.

Money Market

This one is a bit more complex and a little reminiscent of Mississippi Stud.  To begin Play, you make an Ante Wager and get 4 cards.  You must now either Fold or discard 1 card AND make a wager of 1-4x your Ante.  The Dealer will now expose the 1st of 3 community cards.  You must now either Fold or make a wager of 1-3x your Ante.  Dealer will expose the 2nd of 3 community cards and you will either Fold or make a wager 1-2x your Ante.

The Dealer will expose the final community card and then expose his 3 cards.  Best 5 out of 6 cards wins.  The Ante will pay according to the paytable.  All other wagers pay even money.

The betting structure on this one means you'll be wagering at least 4 units if you stay in until the end and might wager as much 10 units.  Unlike Mississippi Stud, you might have a likely winner, but you will rarely have a guaranteed winner.

There is also a one-way bad beat sidebet.  If you lose with a Pair of Jacks or Better, you win this sidebet.  This wager stays in action even if you Fold your base wager.

If you make it to the show and get to check out these games, feel free to let me know your thoughts about any or all of them.  You can reach me at or on my blog at

Don't Try These in the Casino!

            We are all familiar with the phrase that “nothing is certain but death and taxes.”  This quote is quite important to the world of gambling.  As I discussed in last week’s column, even when the Player has an advantage over the casino in a particular game, it does NOT mean that he will always walk away a winner.  In similar fashion, not every bad gambling idea leads to an immediate loss.  Even if you choose to hit a 20 while playing blackjack, every so often you WILL hit an Ace and it will help you win when you would otherwise lose (well technically it can only help you push when you would have lost or win when you would have pushed).  But, the bottom line is, even if it works out once in a while – it still doesn’t make it a good idea.

            This week, I’m going to look at a few “common” bad ideas that you will see when you walk into a casino.

1.  Splitting 10’s into a bust card
            The Dealer has a 4, 5 or 6 up and you’ve got a pair of 10’s.  The dealer is going to bust anyhow, so why not split up your 10’s and draw two more 10’s and crush the house.  Well, first of all, if you split the first two 10’s and you draw two more, you’d split again!  If it’s a good idea the first time, it must be a good idea the 2nd time too! 

            What makes this one so dangerous is that in the end, it IS a winning proposition.  The problem is, relative to just holding the 20, it is a TERRIBLE decision.  If you were dealt 100,000 Pair of 10’s (against a 6) and were to just stick as you are supposed to, you would win 67,600 units.  This means you win the hand almost 84% of the time.  If you decide to get split happy and just keep splitting 10’s, you’ll win a total of about 30,700 units or less than half as much – all while risking more than 3 times as much money.  So, it might feel the good the once in a while when the Dealer busts and you win 3 or 4 hands at once.  But when the Dealer winds up with a 17, 18 or 19 and you realize you just below a good hand for 2 or 3 or 4 lousy ones, the euphoria will quickly disappear.  No matter how you slice it, your bankroll will suffer in the long run.

2.  Playing a Jack High hand in Three Card Poker
            Several years ago, I was sitting out a Three Card Poker table when a woman told another Player that generally she plays only a Queen High, but once in a while you can beat the Dealer with a Jack High hand.  Actually, NO, you can’t.  If you have a Jack high hand, the only way you ‘win’ is if the Dealer does not Qualify.   In this case, your Play wager will push and your Ante wager will win.  This will happen 5,277 of the 18,424 possible Dealer hands.  You will be wagering 2 units in the hopes of winning one and it will occur far less than 30% of the time.

            With 18,424 possible Dealer hands, if you fold, you will lose 18,424 units.  If you Play, you will risk 36,848 units and win back only 15,831 for a net loss of just over 21,000 units.  It may be painful to Fold and if you do Fold, you will NEVER get paid any ‘winners’ for a Jack High hand, but your bankroll WILL thank you because it will last that much longer.

3.   Betting 4x only on Pairs when Playing Ultimate Texas Hold’em (UTH)
            Proper strategy for UTH calls for betting 4x on a significant number of hands.  The strategy DOES include Pairs of 3’s or better, but also includes any hand with an Ace and a variety of Suited and Unsuited Hands with a Jack or better (full full list, go to my website  I’ve heard of Players playing properly while Dealers tell them they are playing too aggressively.   The payback of UTH is 99.25% when you use Expert Strategy.  If you choose to bet 4x ONLY when you are dealt a Pair of 3’s or better, the payback goes down about 3% to 96.25%.  Put another way, the house advantage increases 400%!

            One could say that casino games are developed with these types of ‘traps’.  But the reality is that they are only traps if you fall into them.  The proper strategy is readily found for virtually every casino game.  You can either choose to learn them or follow your own bad idea. 

            Check out my website at for tips on how to play many table games.

As Plain as the Nose on my Face!

            I have frequently stated in my column that the biggest difference between slots and video poker is that in video poker ‘everything is known’.  What does this mean?  Well, it DOES NOT mean that anyone knows exactly which cards are about to be dealt or drawn.  What it DOES mean is that because the cards are random, we know what will happen over the long run and we know the probability of winning hands forming.  Thus, we are able to create a strategy that maximizes the amount of money we can win by using these probabilities and the payouts of these winning hands.

            When you walk up to a Roulette Wheel, everything is known also – and fairly simplistic.  If you bet a single number (and assuming a single zero wheel), you have a 1 in 37 chance of winning.  If you bet ‘Odd’ or ‘Black’, you have an 18 in 37 chance of winning.  If you sit down at a Blackjack table you know that the probability of you getting a blackjack is about 4.75%.  This information is all known because you’re dealing with real life objects that have a clear probability and are completely random.

            The same is true of video poker.  The fact that it is a digital deck does not change the randomness.  Everything about the game would be the same if you could somehow play it with a real deck of cards.  The overall math is a bit more complex than figuring out the probability of a single number in Roulette or of getting a blackjack, but the concepts are the same.  Let’s start with a simple example.  Let’s say you are dealt the following:

3♥        4♦        5♣       6♠        10♥

            The play is fairly obvious.  Discard the 10 and go for the Straight.  What is the probability of drawing the Straight?  There are 8 cards that will complete it, with 47 possible cards to be drawn.  Thus, the probability is 8/47 or about 0.17.  With a payout of 4, we multiply this by the probability to arrive at the Expected Value (EV) of this hand of 0.68.

            What if we make the hand a bit more complex?  What if the 10 was another 6?  Now there are two possible plays.  We can do as we did before and go for the Straight or we can discard the 3-4-5 and hold the Low Pair.  We don’t have to guess what the right play is.  While the specific result for a single hand will be determined by the Random Number Generator of the machine, we can look at every possible outcome of each situation and determine which results in the higher Expected Value.  When we look at all the possible draws or use some combinatorial math, we find that starting from a Low Pair and drawing 3 cards (16,215 possible outcomes) will result in 45 Quads, 165 Full Houses, 1854 Trips, 2592 Two Pairs and 11,559 losing hands.  When we multiply each of these by the payouts of each hand, and divide the total by the total possibilities, we come up with our EV of a Low Pair, which is 0.82.

            This is considerably higher than the EV of the 4-Card Straight (0.68).  Thus, the proper play is to hold the Low Pair.  By looking at every possible (2,598,960), every possible way of playing each one (32) and every possible draw for each of these ways (varying depending on how many cards are drawn), we can figure out the probability of absolutely everything that can happen in video poker.  In total, we have to look at more than 675 BILLION combinations of Deals/Draws.  Fortunately, with the help of today’s computers, this really isn’t all that daunting of a task (and there are some shortcuts to help!).

            The important thing to realize is that there is no guesswork here.  There is hard, cold and very precise math based on a 52-card deck and the idea that the probability of any card appearing is the same as every other card.  A long time ago, I saw someone suggest that the way to tell if a slot machine is a ‘good one’ is to play 20 times and count the number of winners.  A machine set to pay more will have a higher win frequency than one set lower (I can’t even verify this much!), so based on how many winning hands you have in the 20 times gives you an idea of if the machine is a good payer or not!  HUH??

            Show me a video poker machine’s paytable and I’ll tell you the win frequency and the payback in a matter of minutes (okay, if it’s something new, it might take a bit longer!)  This can be done because there is nothing hidden in video poker.  The payback is known.  The hit frequency is known.  The strategy is known.  Everything is known!

            If you’d like to know more, one of the best ways to learn more about video poker is from my father’s book Video Poker: America’s National Game of Chance.  It is 200 pages of dozens of some of my father’s best articles about video poker, all geared to teaching you how to play in a more laid back way.  It retails for $19.95, but for a limited time, I’m making it available for ONLY $6 each or 2 for $10, which includes 1st class shipping and handling.  Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

Blurry Lines

            Recently, one of my ‘friends’ on my Gambatria Facebook page posted up a poll.  They asked people what they play when they go into the casino – table games, slots or other.  I wasn’t sure what to answer.  I tend to split most of my time between blackjack and video poker.  In the end, I decided that video poker was probably the most appropriate answer for me, though.  So, my first reaction was to check the ‘other’ box, but then I began to wonder if maybe the creator of the poll may have included video poker in the choice for ‘slots’.

            If you’ve read my column over the years, you know how much I hate it when people consider video poker to be slots.  They’ve been frequently categorized as such because of the physical similarity of the machines.  Once upon a time, slot machines meant mechanical reels in a wooden box, while video poker was a computer monitor in an identical wooden box.  Then slot machines went digital too and now both are essentially computers in a box.

            But, is this REALLY how we categorize casino games?  By physical characteristics?  It is ironic that originally video poker machines were put into slot-machine boxes and then over time, slot machines were put onto video poker computers in those same boxes.  While they are not so easy to find anymore, if a Player plays a stand-alone video blackjack machine are they playing slots because of the hardware?  Not in my book!

            As the technology of the casino has evolved, the lines have become even more blurred if we look only at the technology and/or hardware that the game is being played on.  Some jurisdictions don’t allow live dealers and/or actual cards, so they only allow some of the newer hardware in – fully electronic tables, where chips and cards are digital and there is either no dealer to speak of or perhaps just a moving image of one.  If you play blackjack on one of these machines are you still playing slots?  Or, are you only playing slots if the machine looks like a slot machine and you’re playing in a non-social environment?  On the other hand, if you’re sitting at something that looks like a blackjack table (or does it look like a set of new fangled slots all hooked together?) then you’re deemed to be playing a table game?

            These new electronic tables have proven the folly of considering a video poker machine to be a slot machine.  We can’t categorize games by the technology that they are played on.  A mistake was made a long time ago to not consider video poker machines as their very own category.   In most ways, they are actually far more like table games than they are slot machines. 
So, perhaps the real mistake was not considering video poker machines to be slots, but to not recognize that slot machines are like nothing else in the casino industry.  They are truly what their long nickname implies – one-armed bandits (only they no longer even have the one-arm!)

            When you sit down at a table game or a video poker machine, I can tell you the exact payback of every wager on the table.  Some of the wagers require learning a complex strategy, others are simple and yet others require no strategy at all.  But, even this last category has known probabilities for each of the paying hands.  When you play Pair Plus (of Three Card Poker) you have nothing to do, but you know exactly what the odds of getting a Three of a Kind is.
            Video poker fits this mold perfectly.  In fact, the strategy required to play video poker is on the complex end of the scale.  It could be argued that this is the exact reason why it was created for a digital platform.  In theory, a casino could put out a blackjack table and deal a paytable version of draw poker.  Each Player could get five cards face down and discard as few or as many as they want.  The payback of this game would be identical to that of a video poker game with the same paytable.  Voila!  ‘Video poker’ is now a table game!

            None of this is true for slots.  Not only is there no strategy whatsoever, you also have absolutely no way of knowing what the payback of a machine.  Two machines sitting side by side appearing to be identical could be set to pay either identical paybacks or paybacks differing by 10% or more!  A machine could be changed overnight to pay 10% less than it was set to the day before and there’s no way of you knowing this.  Absolutely NOTHING is know about the probabilities of a slot machine by the Player and there is no way to get this information. 

            Saying that video poker is slots would be like saying the Space Shuttle and a coffee maker are the same thing because they are both machines.  It just doesn’t add up.  To help you better understand video poker machines and to break the slot habit, our special for June continues.  You can get Expert Video Poker for Las Vegas for just $7.95 (reg $9.95) by sending a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.  

Don't Be Timid when Playing Ultimate Texas Hold'em

             This may come as a surprise to some of you, but Texas Hold’em has been played in poker rooms for a very long time.  However, it was not the primary game until recently.  When you said you were going to play Poker, it mostly mean 7-card Stud.  Secondary to that were the Texas Hold’em and Omaha tables.  I’m not really sure what got the Texas Hold’em craze going, but I’ve long suspected it was a few famous people who started playing it and all of a sudden, a game barely heard of became the game you had to play.

            Once Texas Hold’em became popular, it was no surprise that table games for the casino floor would try and capitalize on this popularity.  There have been several attempts to create a game that somehow captures the essence of Texas Hold’em.   The most successful, but not the first out, has been Shuffle Master’s Ultimate Texas Hold’em (UTH).  UTH was one of the first truly successful games that I personally worked on, and hopefully aided in its creation. 

            What makes UTH so unique is its betting structure.  You basically get one chance to make a wager beyond your initial wager.  But, you can make this wager at three different points.  The earlier you make the wager, the more you can bet.  Another relatively unique feature about UTH is that you don’t have to decide if you want to Fold until you’ve seen all your cards.  To begin play, the Player makes an Ante and an equal-sized Blind wager.  The Player also has the option to make an paytable sidebet wager.  The Player is then dealt 2 cards faced down.  He can now check or wager 4x his Ante.  The Dealer will then expose 3 community cards.  At this point, if the Player has already wagered 4x, he is done.  If he checked, he many now check again or wager 2x his Ante.  The Dealer exposes the final 2 community cards.  The Player who has already wagered is done.  The Player who checked twice must now either Fold or make a bet equal to 1x his Ante.

            The Dealer will expose his two cards.  If the Dealer does not have at least a Pair, the Ante pushes.  If the Dealer’s best 5-card hand beats the Player’s best 5-card hand, the Player loses all wagers (except the Ante as just described).  If the Player’s hand beats the Dealer’s hand, the Player wins even money on the Ante (unless the Dealer’s hand did not qualify, in which case it pushes).  The Blind bet pushes, unless the Player won with a Straight or Better, in which case it will pay according to the paytable in use.  The Play bet (1x – 4x) will pay even money. 

            UTH hit the casinos about 5 years ago and now has over 500 tables, making it one of the most successful proprietary table games of all time.  The full strategy for the game is extremely complex and somewhat fuzzy.  The unique betting structure makes it difficult to determine in all cases whether your are better off betting more now or waiting for more information and betting less.  Also, any game that uses community cards in a head-to-head game creates challenges in determining when to wager.  Stating to ‘bet’ when you have a Pair of Aces becomes impossible because it might be the community cards that has the Pair, while you’re left holding a 2 and 6 in your hand!  Your hand is quite worthless at that point!

            Ironically, it is the first decision point (to check or bet 4x) that was the easiest one to analyze.  With only your pocket cards as your guide, the decision becomes a relatively simple yes or no answer.  From talking to many Players, one thing has also become very clear.  Most Players are playing FAR TOO TIMIDLY than they should.  Proper strategy for the first wager dictates that you should bet 4x a whopping 38% of the time.   UTH boasts a payback of at least 99.25%, but if you shy away from betting 4x, you’re going to cut into this significantly.

            If there ever was a game where discipline is needed, this is it.  Between the Ante, Blind, Play and sidebet, you could easily have 7 units on the table – 38% of the time.  This is not the game to bring $100 to a $5 table and think you are properly bankrolled.  But, the math is the math and if you choose to wait to see how things play out, you might win more hands, but win less money.  Most Texas Hold’em players know that the secret to winning is that you don’t win a lot of hands, but you win a lot of money when you do.  The same can be said for UTH.

            So, without further ado, here is the strategy for the first decision point of UTH:

q  If you are dealt a Pair of 3’s or higher, bet 4x.
q  If you are dealt an Ace, bet 4x.
q  If you are dealt a suited K-X, where X is any card of the same suit, bet 4x.
q  If you are dealt a suited Q-X, where X is greater than a 4, bet 4x.
q  If you are dealt a suited J-X, where X is greater than a 7, bet 4x.
q  If you are dealt an unsuited K-X, where X is greater than a 4, bet 4x.
q  If you are dealt an unsuited Q-X, where X is greater than a 7, bet 4x.
q  If you are deal an unsuited J-10, bet 4x

I know I’ve promised for a long time that I’m working on a booklet for UTH and I have finally started the work.  Hopefully, I’ll get it done by the end of the summer.

For more information on UTH and other games, head over to my website at 

Multi-Play Video Poker Primer

            This past week, I received an e-mail from a reader who had some questions about Multi-Play video poker.  For those who are not familiar with it, Multi-Play allows Players to play out the result of a draw multiple times.  The Player is dealt five cards as per normal video poker.  He then decides which cards to hold/discard.  The draw is then played out from 2 to 100 times depending on which version he is playing and how many hands he chooses to play.  Generally speaking, the casinos offer 3-Play, 5-Play, 10-Play, 50-Play and 100-Play.  The underlying video poker game may be any of the ones offered on a regular video poker machine – jacks or better, Bonus, Double Bonus, Deuces Wild, etc…

            The game was invented about 15 years ago by Ernie Moody of Action Gaming.  If you’ve never heard of Mr. Moody, well, I guess multi-play didn’t make him a household name, but it sure did make him a lot of money.  There are thousand, if not tens of thousands of these games across the casinos of the world.  While it seems that the game may be off its peak (in terms of popularity, not necessarily total machines), it is still an immensely popular game.

            The good part about Multi-Play is that you don’t need to learn any new strategies.  It does not matter if you are playing 1 hand, 2 hands, 100 hands or theoretically a million hands at a time.  The proper strategy is still Expert Strategy which will look at the expected values of each possible way you can play the hand.  The number of times the draw is played out does NOT change this one bit.  The payback of Multi-Play is NOT dependent on the number of hands being played, but rather is based on the underlying video poker variation being played and the paytable being used.

            The bad news about Multi-Play is that you had best be prepared to bring a larger bankroll or to lower the denomination that you are used to playing, which can have its problems too.  Ideally, you want to keep playing max-coin to help ensure being paid 800 for 1, instead of 250 for 1 if you hit a Royal.  Assuming you do this, then the amount you are wagering per game is multiplied by the number of hands you are playing.  If you play Five Play then you are going to have to wager 5 coins (for max-coin) times 5 hands or 25 units.  If you’re a Quarter Player, you just went from wagering $1.25 per game to $6.00 per game.  This does not necessarily mean you need to have 5 times the bankroll (for reasons I’ll get to shortly), but you will need something close to this.

            To help with the bankroll issue, you could lower the denomination you normally play at.  If you go from Quarters to Nickels, you’ll still be wagering $1.25 even though you will now be playing five hands instead of one.  The only thing you need to watch out for is that sometimes the paytable for Nickels will be different (i.e. lower) than the one for Quarters.  This is true even when you are on the same physical machine but merely switch denomination.  You’ll get away with a lesser bankroll by switching to nickels, but if the payback is cut by 1% (or more), you’ll pay for it in other ways.

            So, how does playing multiple hands effect our bankroll requirements?  The more hands you play simultaneously (in the manner of Multi-Play), the less volatile the game can be.  When you play a single hand and are dealt a Low Pair, the number of possible outcomes is relatively small.  You might lose, get a Two Pair, Trips, Full House or Quads.  Your payout will be exactly equal to zero (losing) or one of the payouts of a winning hand.  None of these are very close to the actual expected value.  However, as you play more hands at the same time, you’ll find that you’ll approximate the actual expected value far more often.  This is especially true if you play 50-Play or 100-Play.  It is amazing how many times you’re dealt a Low Pair in 100-Play only to find that you win 80-85 coins back (per unit wagered) and that this hand has an EV of 0.82.  In essence you bring the long run to your game much quicker.   This is why I said earlier that you don’t necessarily need 5 times the bankroll.  But, don’t be fooled into thinking that you don’t need a larger bankroll if you’re playing 5 times the amount of money per game.

            So, one of the questions my reader asked is, “Is there a "best" number of multiple hands to play out of: Triple, Five Play, Ten Play Video Poker?”  The answer is not really.  As always you have to play the one you feel most comfortable playing based on bankroll, paytable and enjoyment.

A Slot Upgrade?

             This past weekend, we had some friends over for lunch.  Invariably, the conversation winds up on my relatively unique profession.  Somewhat ironic in this case as one of the other guys is a hedge fund manager who counts as one of his clients one of the top poker players in the world.  Then again, some would argue that we’re both in the same general profession – casino gambling!

            I got asked the usual question of what the best games to play are and how I got started in the profession.  At one point, the subject turned to slot machines.  There was both good news and bad news to report here.  On one hand everyone seemed to agree that these were amongst the worst payers in the casino.  On the other hand, not everyone admitted that they would never play one.  For those whom are intimidated by the table games, the slots still are the mainstay – no matter how bad they pay.

            I remarked how I had just read an article talking about a comeback that is being made by ‘old fashioned’ mechanical slots.  Everyone in the room agreed that the older slots were better than the newer ones.  A few reasons were cited.  One was that they actually had a handle to ‘pull’.  Another was the clinking of the coins coming out when you won.  I actually commented that I wasn’t sure if the machines making the comeback are ticket-in/ticket-out or truly old-fashioned in that they accept and pay out real coins. 

            One of the reasons I cited for the popularity of the mechanical machines was that you could actually tell when you won or lost.   As I’ve written many times in my column in Gaming Today, I have occasionally put a $5 machine into a penny or nickel video slot machine in order to kill some time.  I then press a button that says “Play max lines” and press another that says “Spin”.  When the reels are done ‘spinning’, the machine then tells me that I either won some number of coins or that I lost.  No matter how many times I try to figure it out, I can’t tell on my own WHY I’ve won when I do!

            I’ll see several identical symbols on the same line only to find that’s not really a line to this 5 ‘reel’, 27-line machine!  Someone should tell some of the slot manufacturers that a ‘line’ usually denotes a STRAIGHT line between two points, not an up and down line that looks more like a heart monitor!  Is it any wonder that people are not having fun playing slots anymore?  It wasn’t good enough when the casinos were essentially taking the Player’s money with 92-93% slot machines, now they have to do it in a way that most Players have absolutely no idea what is going on?  For anyone reading this, please tell me – are you really having fun playing the newer video slots?  I’m sure it’s a lot of fun when you get to a Bonus Round on something like Wheel of Fortune, but do you even know why you got there? 

            I remember playing one slot machine that put me into some sort of Bonus Round.  I won about $25 (on a nickel machine) in under 5 minutes.  I couldn’t tell you why I wound up in the Bonus Round or what I was trying to do while in it!  It just kept telling me to pick boxes and I did.  Each time it opened one, I won more coins.  Hey, I was very happy to win $25 in a few minutes, but I have to be honest.  I can’t really say I had any fun doing it.  I could’ve just as easily lost my bankroll (okay, it was only $5 for the slot machine) and been just as clueless.

            As I raised this point to my guests, there was universal agreement.  While some of them admitted to still playing them, none said they had fun while doing it.  My hedge fund manager friend does all he can to dissuade his wife from playing the slots at all – just based on their horrible paybacks.

            Of course, I have mixed emotions about a comeback for the mechanical slots.  They still have the worst paybacks in the casinos and I would much prefer that slot machines go the way of the dodo bird.  There are SO many better games to play in the casino with better paybacks and that are more fun.  I know that one of the reasons people avoid them is sometimes they are intimidated to play new games that they don’t know how to play.  So, we try to make it a bit easier with our books and booklets.

            Today, May 12th, 2011 would have been my father’s (Lenny Frome’s) 85th birthday.  So, for the rest of May, we’re offering some special prices on our titles:
  •         Winning Strategies for Video Poker and Video Poker: America’s National Game of Chance (both books) for $19.26 (his birth year)
  •          Expert Video Poker for Las Vegas or Expert Video Poker for Las Vegas for just $5.12 each.
  •          Any of the Expert Strategy series books (Three Card Poker, Four Card Poker, Let It Ride, Spanish 21, Caribbean Stud Poker, Mississippi Stud or Blackjack Switch)  - 1 for $4.85, 2 for $8.85, 3 for $11.85 or all 7 for $19.26

            To learn more about any of these titles, go to my website at and click on the “Products” tab.  If you would like to order any products, just send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

Coming Up Aces

            When it comes to video poker, I think there is no doubt that the Ace is by far the most enigmatic card in the deck.  In the old days when we only had jacks or better video poker, the Ace was actually worth far less than most people gave it credit for.  In video poker an Ace High Flush or Ace High Straight has no more value than a 7-High hand of the same rank.  Whereas a Full House with three Aces is nearly unbeatable in table poker, it has no more value than 3’s over 2’s in video poker.

            The only additional value an Ace has is as a High Card.  In this regard, it has the same value as a Jack, Queen or King.  These four cards give extra weight to the expected value of our partial hands because of the opportunity to pick up a High Pair.  Once you have a High Pair or better, they provide no additional value.  This is where the irony starts to build.  A single Ace actually has the lowest expected value of any single High Card (tied with a King).  This is because an Ace inherently creates only INSIDE Straights.  With a single Ace you still have two shots at a Straight (10 – A or A-5), but if you add an Ace to any other High Card (i.e. J-A) you leave yourself only once chance to make a Straight.  Whereas, if you hold a J-Q, you can make a Straight multiple ways (8-9-10, 9-10-K, 10-K-A). 

            We overlook this weakness when we have an opportunity to hold two suited High Cards (i.e. a 2-Card Royal).  We would rather hold a suited J-A then an off-suit J-Q.  However, when we have three unsuited High Cards and one of them is an Ace, we do NOT keep the Ace.  Thus, if dealt J-Q-A, J-K-A or Q-K-A (offsuit), we keep the two NON-Ace cards.  The reduction in our chances of grabbing a Straight by keeping the Ace is greater than the benefit of keeping the third High Card.

            Thus, we see from all this that the almighty Ace is really not so almighty.  From an expected value perspective it is the weakest of all the single High Cards.  Fortunately for the Ace, someone invented the Bonus Poker variations of video poker restoring it to its full glory.

            The Bonus Poker variations turned the values of cards a bit upside down.  Pairs of Jacks or Better still paid 1 so this kept the extra value of the single High Card.  However, the 2nd tier of Bonus Payouts for Quads went to 2’s – 5’s.  This gave extra weight to these cards as they started to Pair up.  No one discards three of a kind so that wasn’t an issue, but all of a sudden ‘Low Pairs’ had to be split between ‘very’ low (2’s – 5’s) and just low (6’s – 10’s).  The top Tier (Aces) is what restored the Ace to the top of the pecking order.  Not only did it have value as a singleton above the low cards, it now had the top value as it began to Pair up and Players hoped to collect all four of them. 

            In reality, the paytable of the original bonus poker doesn’t do much for the Aces.  Obviously a Pair of Aces has a higher expected value, as does that of the single Ace – but not enough to really change how we play our hands.  However, as we move up the ladder of bonus games, this begins to change.  In Double Bonus Poker, a Pair of Aces outranks a 3-Card Royal, but a Pair of J-Q-K’s does not outrank all of them.  If you’ve got Trip Aces with another Pair (i.e. a Full House), you’ll throw away the Pair to go for the fourth Ace.  Don’t do that with any other Three of a Kind!

            If we move up to Double Double Bonus, we now find that if we’re dealt a Pair of Aces with another Pair (Two Pair) that we discard the other Pair hoping to get dealt the remaining two Aces.  The power of the Ace is complete!

            The most important lesson in all of this is that you need to learn the strategy table for whatever game you are playing.  You also need to discard your pre-conceived notions about cards and their values.  In table poker an Ace is a very powerful card.  In most versions of video poker, it is just another High Card and not even the most valuable of them.  Video poker is not about kickers and eking out a better hand.  It’s a game about cold calculated math.  

Take A Stroll Through the Casino

It has been more than 20 years since my father, Lenny Frome, began writing about video poker. I think he had two goals when he started. The first was to tell people about this relatively new casino game which had paybacks about as high as any in the casino – and in some cases over 100%. The second goal was to get people away from slots which have arguably the absolute worst paybacks in the casino. Two decades later, it would appear that while much good work has been done, much more is needed.

The most common question I’m asked by friends is “what is the ‘best’ game to play in the casino?” In this case, ‘best’ means having the highest payback. Usually, most people start to answer the question before I can and start with blackjack – which is essentially a correct answer. With a payback of 99.5% (give or take, depending on the rules), blackjack must be described as being one of the ‘best’ games to play. Of course, the original version is a bit slow and requires a significant degree of strategy, but that really isn’t part of the equation at the moment.

Frequently, the next answer that comes up is Craps. This is a bit tougher to size up. Craps is really dozens of different independent wagers so determining the ‘payback’ of Craps is not only difficult (if not impossible), it is also meaningless. Avoid all the proposition wagers with horrible paybacks and you’ll have a much higher payback than the guy constantly buying ‘hard ways’ bets. Craps can be a really fun game with a lively table and when a shooter gets hot. Playing with just a couple of Players and/or during only cold or slightly warm streaks and it I prefer games where you can sit down!

After blackjack and Craps, the person who asked the question finally goes silent. It is almost as if the casino still only has about 4 options – blackjack, Craps, Roulette and slots. Well, I guess the good news is that the silence means the most people have figured out that you’re not going to win money playing slots. As for Roulette, well, it is a bit like Craps, but almost every wager has the same so-so payback. But what about the rest of the casino? Over the past 20 years, the casino floor has changed tremendously. Many of the people who ask me the question do go to the casino. Have they not noticed all the other games?

I don’t know who is more surprised. The person I’m talking to when I say “video poker” or me when they respond “what’s that?” I guess if you’ve always been a table game person maybe you haven’t noticed that not all the ‘slot machines’ look alike. Of course, this was truer when slot machines still had handles and video poker machines didn’t. With the advent of video slots, the casual observer may just see lots of lights and colors on a computer screen and think they are all the same. I’ve spent many columns explaining the vast differences between slots and video poker to need to do so again today.

Once I explain what video poker is to the person who asked the original question, they are even more surprised to find out that a ‘routine’ payback can be about the same as blackjack and that there are still a fair number that can be found that have paybacks over 100%. This, of course leads to an explanation of what it takes to exploit such a Player advantage. Yes, you can probably make 30k-40K a year playing quarter video poker, but it would take playing 40 hours a week in a smoky casino, playing very disciplined and it would be a lot like having a very streaky commission job. You might earn nothing one year and earn 50-60K the next. This is not necessarily an easy job or one suited for anyone. The ultimate irony comes when I find out the person I’m talking to is an attorney, here in the NYC area, who is probably pulling down at least a few hundred thousand a year. I don’t think he’s giving up his day job!

So, I guess after more than 20 years of trying to get people to break the slot habit, we can confidently say we have achieved some success. I think the number of people who think that they have a shot at the slots has gone way down. At the same time, the campaign to keep teaching people about all the other games in the casino goes on. From video poker to blackjack to many of the newer table games that offer higher paybacks than the traditional casino games – many while offering a good deal more excitement too. The next time you head out to the casino, before you sit down to play, just walk the casino floor and check out all the games you may not have known existed. Then, to learn more about it, head over to my website and there’s a good chance I already have written about it. If not, feel free to drop me a line and I’ll do my best to cover it in the near future.

Bankroll Considerations

            Recently, I answered a question from a reader about what to do when you win ‘big’ early in your session.  Of course, both ‘big’ and ‘early’ are rather subjective terms.  Ironically, the definition of big probably has less to do with the denomination you are playing and more to do with the size of your bankroll.  If you showed up with $20 and you hit a $100 hand, you’re more likely to stop than if you came to the casino with $1000 and hit a $100 hand.  In the first case, the Player was probably bankrolled too small and in the latter case, it was overkill.  But it is just a normal human reaction to place the size of the winnings next to the amount of money we show up with to determine what ‘big’ is.

            This, of course, leads to an important question - and one that I’m frequently asked.  What is the right size bankroll for video poker?  To answer that, we need to define some things.  First – what is bankroll?  I’m going to drive my English teachers nuts by telling you what it isn’t.  It isn’t the amount of money you put into the machine.  It’s not the amount of money you head off to the casino with.  It (hopefully) is NOT your life savings.  Bankroll is the amount of money that is the maximum you are willing to lose before calling it quits over some period of time.  So, if you go to the casino with $100 in your pocket, but know full well that if you lose it, you’re going to head to the ATM to get more – then $100 is NOT your bankroll.  Conversely, if you’ve got $1000 in your pocket and if you drop $200 you are heading for your hotel room, then the $200 is your real bankroll and not the $1000.

            So, what does this bankroll really do for us?  Well, it sets a maximum that we can lose over some defined period of time.  Maybe it is a single session over a single day/night.  Or, maybe it is the amount we are willing to lose over a week-long vacation.  Why is it important?  Well, besides setting some limits for ourselves, it is also tells us that at the point we’ve lost that much, we are done.  There is no coming back from that loss with a hot streak.  So, if we were to sit at a $5 blackjack table with $5, we have to realize that if we lose that very first hand, we’re done.  If we sit down with $20, then we have to lose 4 more hand than we win (ignoring doubling and splits) to be ‘broke’.  If we sit down with $1000 then we’d have to lose 200 more hands than we won.  With a $5 bankroll, you have a greater than 50% chance of going bust just on the first hand.  With a $1000 bankroll, you might be able to play weeks or months before going bust.

            While we assign a payback to every game, and we can calculate the anticipated loss over a period of time for that game, this is just a theoretical average over time.  Most casino games are fairly volatile which is simple terms means STREAKY.  So, if you play an hour of $5 blackjack, you can realistically expect to lose about $8.  If you start with $100, you’re almost guaranteed to get thru that hour.  If, however you start with $10, your chances of playing the entire hour go down considerably, which ironically means that you would lose MORE than the ‘average’.  By not allowing yourself a reasonable opportunity to come back from a cold streak, you in essence do yourself a grave disservice.  This is why showing up with the right size bankroll is so important.

            One could thus argue that the right size bankroll is one that makes sure that you have ZERO chance of going bust before you are done playing the amount of time you want to play.  There is a certain amount of truth to this notion, but it removes the human element.  It is too easy for us ‘greedy’ human to decide to play longer or up our wager if we have too much cash on hand.  Also, sometimes it is not so practical to do this.  To play an hour at $5 blackjack, we would merely need to show up with $150-$175.  If, however, we wish to play 3 hours of video poker – max-coin quarters – we would need almost $2000 (assuming 500 hands per hour).  This is probably overkill if you’re playing a full-pay jacks or better machine.

            I created a program that simulated video poker.  It started with different bankroll amounts.  If at any point in the 1500-hand session the Player lost more than his bankroll, he was considered to have ‘busted’ and the session ended.  For the moment, I just focused on the percentage of busts and did not bother keeping track of how far into the session the Player was or how he would’ve done had he decided to go beyond his bankroll (i.e. how often does he recover his initial bankroll by using yet more money).

            If the Player starts with 200 wagers ($250 for a max-coin quarter machine), he went bust only 1.39% of the sessions.  If we cut our bankroll down to 120 wagers ($150), our Player went bust just a smidge under 20% of the time.  If the bankroll is reduced to 80 wagers ($100), we find that the bust rate goes up to over 43%.  If the Player tries to get away with a mere $50 bankroll, he’ll find that he’ll lose it all about 73% of the time.  Try and get away with only $25 and you’ll lose the entire bankroll more than 87% of the time.

            So, what’s the right amount of bankroll?  There is no absolute right answer for that.  You have to decide how much you’re willing to risk that your session ends prematurely.  But, if you’re looking for some advice, based on the numbers presented here, I’d go with 120 wagers ($150).   You’ll go bust only 20% of the time, and if you’re night is going that bad, you might just be best off calling it a night.

What To Do When You Win Early

            A couple of weeks ago, a reader sent me a note asking what he should do when he finds himself up significantly very early in a session when he expected to play 4-5 hours.  This is not an easy question to answer as it is really isn’t a math question.  The bottom line is that if you are playing a game with a payback below 100% (you can choose to throw in comps and cashback if you want) then you are playing a game in which you will lose over the long run.  The more you play, the greater the likelihood that you will lose and the amount you are likely to lose (from the beginning of time) continues to go up. 

            Of course, using this logic, you should never play any game with a payback below 100%.  So, if your only reason for playing is winning then you should stop now unless you are playing some of the video poker machines that pay over 100%.  However, as I have long surmised, most of you play in the casino for entertainment purposes.  We all want to win when we play, and the games are created to allow you to win some of the time over short sessions.  So, what is the answer when we’re up $100-$200 after 20 minutes of play after taking a long drive to the casino and expecting to play deep into the night?

            I’ve already explained the mathematical answer, but I don’t think that’s the one my reader was looking for.  So, the question has to be answered more from an emotional standpoint.  First of all, it is good for the psyche to win some of our sessions.  So, it might not be a bad idea to just walk away for the evening.  If you make these trips on a regular basis, giving up the few extra hours of play and driving home may be one solution.  Another possibility is to take your winnings and find something else to do in/around the casino.  Most have some other form of entertainment available.  Go see a show or a movie.  Go bowling.  Head to the video arcade (Pac-man, not video poker!).  This latter one is one of my personal favorites.  I can make a dollar last pretty long on a pinball machine! 

            Another possibility is to take it down in denomination.  If you’ve been playing quarters, maybe you want to try nickels for a little while.  If you’ve been playing multi-play, go back to playing a single hand.  The simple fact is that the math is against you and you can’t change that.  The key is to not allow yourself to lose your psychological edge.  You hold in your hand the casino’s money.  There is no reason to give it back. 

            The last thing you want to do is losing your composure.  It is human nature to get frustrated when the winning streak stops.  We start losing some of what we won and we want to get it back.  So, we start increasing our wager or taking bigger chances in the hopes of recovering some of what we started to give back.  If we were already on a downswing, our bankroll may be dwindling which limits the downside.  Or the credits may almost be gone from the machine so it will give us a reason to stretch our legs.  If, however, we just had a big win, these braking mechanisms won’t be there. 

            At the very least, I advocate hitting the “Cash Out” and taking your ticket out and going to cash it in.  Start with a new $20 after taking a little breather.  We’ve all seen the little disclaimer on advertising (when talking about stocks and the like) that past performance is not necessarily and indication of future gains.  Nothing could be more true for gambling.  In fact, it may be even more true for gambling.  What happened in the past is meaningless.  The game you are playing has a particular payback and that is what you can expect to happen over the long run going forward.  You simply cannot change this.  But, you CAN change how you let it effect you.


Who Isn't Crazy 4 Poker?

             Shortly after  Four Card Poker was being launched, another similar, yet different, game hit the marketplace.  It was called Crazy 4 Poker.  In a recent conversation with Roger Snow, Executive Vice President at Shuffle Master, he revealed that Crazy 4 Poker was invented on January 28, 2002.  How does he remember the specific day?  It was the same day that Four Card Poker went live at Jackson Rancheria in California.  Fearful that Four Card Poker was going to flop, he immediately went to work on its successor game.  As it turns out, he got them both right.

            For reasons not fully known, the game was a big hit in Nevada.  There are currently about 100 Crazy 4 Poker tables, of which 40 are in Nevada.  Virtually every major casino in Las Vegas has one.  Crazy 4 Poker is an important piece in the history of table games.  It introduced the concept of a ‘Super Bonus’ (now more commonly referred to as the “Blind” wager) in Shuffle Master games.  This has become a staple of their more recent games.

            Crazy 4 Poker is broken down into two separate wagers.  The first is called Queens Up is like Pair Plus.  If the Player is dealt a Pair of Queens or better he wins according to the paytable in use.  The second portion of the game is like Ante/Play.  It requires that the Player make both an Ante wager and a Super Bonus wager.  The Player and the Dealer are each dealt FIVE cards to make their best FOUR card hand.

            Once the Player has reviewed his hand, he can either Fold, forfeiting his Ante and Super Bonus wagers, or he can Play.  If the Player has a Pair of Aces or better, he may Play 3 times his Ante wager.  If he has less than a Pair of Aces, he can only wager 1 times his Ante.  Thus, when the Player has a strong hand, he can really sock it to the casino. 

            After all Players have decided what they want to do, the Dealer reveals his hand.  If the Dealer does not have at least a King High, his hand does not qualify.  In this case, the Ante wager is pushed and the Play wager is paid even money.  This means that if you have a strong hand and Play 3x you will still win even money on this when the Dealer does not qualify.  If the Dealer’s hand IS a King High or better, his hand qualifies.  In this case, if the Player’s hand outranks the Dealer’s hand, he will be paid even money on both his Ante and Play wagers.  If the Dealer’s hand outranks the Player’s hand, the Player will lose his Ante and Play wagers.

            The payouts on the Super Bonus wager are a bit more complex.  If the Player has a Straight or better (keep in mind with a 4-card hand, Trips outrank Straights and Flushes), he is paid according to the paytable regardless of the Dealer’s hand.  If the Player beats the Dealer, but with a hand less than a Straight, the wager pushes.  If the Player loses to the Dealer with a hand less than a Straight, the wager loses.

            The strategy for Crazy 4 Poker is rather similar to that of Three Card Poker.  The Player must remember only a single strategy to master the game – K-Q-8.  If the Player’s hand is K-Q-8 or higher, he should Play.  Technically, he must also remember to Play 3x if he has a Pair of Aces or better, but I consider this part of the strategy to be more than a little obvious.  The Player will win 90% of these hands.  It should be noted that K-Q-8 is not actually ‘perfect strategy’.  There are a handful of hands which should be Folded above K-Q-8 and a few that should be Played below.  However, these require taking into account the specific suit makeup of the hand and are more likely to cause errors by the Players than they are worth.  The difference between ‘perfect’ and ‘expert’ strategy is a mere 0.01% of payback.

            Speaking of payback, if you follow the simple strategy provided here, you’ll find Crazy 4 Poker affords a 98.91% payback on the Ante/Play portion of the game.  Given the relatively easy strategy, this is a very strong payback to offer.   As a side note to those that like to play games like this and never Fold.  Never folding in Crazy 4 Poker will take the payback down to 96.5%.  Considering an average wager of more than 3 units per hand, a $5 Player will be throwing away about $15 per hour more by following this wayward strategy.

            Stick to the K-Q-8 and before you know it, you’ll be Crazy 4 Poker too!  You can read more about Crazy 4 Poker and many other games at my website –

Don't Call It Spanish Blackjack

Until the recent emergence of Blackjack Switch, Spanish 21 was the only blackjack variant to make a significant impact to the casino floor. The trash heap is filled with the names of games using only numbers (i.e. 7, 11, 31, 41 and probably everything in between).
Spanish 21 (NEVER call it Spanish Blackjack!) is owned by Masque Publishing, a company you’ve probably never heard of. They are predominately a software company ( and license numerous variations of casino software. For fair disclosure, they have two titles (Video Poker Strategy Pro and Caribbean Stud Knowledge Pro) that were done in concert with my father’s strategies.
Spanish 21 is essentially a very liberal form of Blackjack. Here are some of the highlights of these rules:
Player Blackjack beats a Dealer Blackjack (and is still paid 3 to 2)
Player 21 beats a Dealer 21 (all other ties are pushes)
Player may Double Down on ANY number of cards
Player may Double Down after splitting
Late Surrender is allowed
Numerous Bonus 21 payoffs – 5-plus card 21, 6-7-8 and 7-7-7
‘Free’ Super Jackpot Bonus of $1,000 if player has suited 7-7-7 and dealer has 7 upcard.
As is always the case with table games, rules may vary a bit from one casino to the next, so keep your eyes open for the specific set of rules you’re playing.
So, how does Spanish 21 manage to give the player such a liberal game? Very easily. It uses a big shoe (six to eight decks) and removes the 10’s (NOT the face cards) from the shoe. For anyone who plays blackjack regularly, you know the big cards are good for the player and the little cards are good for the dealer. So, removing 24-32 10’s from a shoe can’t be good for the player.
The rule and deck changes combine to make significant shifts in how we play many hands. The removal of the 10’s causes the dealer to bust far less frequently. Thus, we find the player hits much more frequently against traditional "bust" upcards.
The 5-plus card 21 bonus causes us to hit some very ugly hands, IF we have 4-plus cards, in attempt to secure one of these bonuses. It should be noted, however, that we NEVER hit a hard 17 or greater to go for one of these bonuses. The payouts are simply not compelling enough in these cases.
The removal of the 10’s also causes us to re-think some of our double down situations. We don’t double on a 10 vs. 8 or 9 as we would in regular blackjack. At the same time, we have to be alert to the cases where we have three or more cards and get to a 10 or 11. In Spanish 21, you get to double in these cases.
The bottom line is you have to take your strategy for regular blackjack and throw it out the window.
 While there are, of course, similarities, the differences are significant. They affect every part of the game – when to hit, when to stick, when to double down and when to split.
 Spanish 21 offers the player a livelier version of the game at about the same payback as regular blackjack (99 percent-plus depending on the exact rules) but only if you learn the proper strategy. Fortunately, we’ve already done the hard part!
Availability: For $4.95 you can order Expert Strategy for Spanish 21 with a full-color pocket-sized strategy card. Send check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

How About That Strategy? It Works!

            This pretty much speaks for itself:

             Someone playing a $2 full-pay max-coin Double Double Bonus Poker hits an $8000 Royal Flush starting from a 2-Card Royal!  Without knowing who hit it (and I don’t), we really don’t know to what extent this Player follows Expert Strategy.  For all I know, he discarded a Pair of Jacks to go for the 2-Card Royal.  But, lacking this information, I’m going to use this picture to demonstrate some key components of Expert Strategy.

            Play the right machine – Well, Double Double Bonus isn’t exactly the ideal machine to play with its 98.8% payback.  However, it multiple jackpots (Royal and 4 Aces w/kicker) has made it immensely popular.  From the picture we can see that the Player chose to play one that is full-pay (1/1/3/4/6/9).  Before the payout on this hand, the Player had about $535 remaining in their bankroll.  If they play a short-pay machine, perhaps the bankroll is exhausted before they have the opportunity to win the $8000!

            Know the right strategy – This is really the crux of this column.  We don’t know what hand the Player was dealt, but we do know that he held the suited J-A.  2-Card Royals make up about 7-8% of our playable hands.  Misplaying them can be rather dangerous to your bankroll.  When my father, Lenny Frome, developed his first strategies for video poker, one of things that surprised him was that most 2-Card Royals outranked 3 High Cards.  Given the unlikely odds of hitting a Royal, intuitively, one might think that you’re better off having 3 High Cards increasing your chances of a Jacks or Better or a Straight.  But by holding 3 off-suited cards, you eliminate all chances of a Flush, reduce the likelihood of Trips and eliminate Quads and the Royal.

            ‘Unlikely’ is also a relative term.  The actual odds of hitting a Royal from a 2-Card Royal is ‘only’ 16,215 to 1.  In the grand scheme of the casino, this isn’t really all that rare.  If one out of 13 hands is a 2-Card Royal and 1 in 16,215 of these will result in a Royal Flush, then we’re talking about 1 in 210,000 hands will have this ‘fate’.  At 700 hands per hour, this means about 300 hours of play.  Depending on how serious of a Player you are, this might take weeks or months, but in a casino with hundreds of video poker machines being played 10-15 hours day each, it’s happening every day all over the place.  So, why not you?

            Of course, you increase your chances of it being you if you play your 2-Card Royals correctly.  This will, of course, depend on the specific game and paytable you are playing.  In the case of Double Double, here are some key pointers:

            -  A 10-A 2-Card Royal is NOT playable.  We hold only the Ace if we have no alternatives.
            -  We Play J-Q-K-A (off suit) over a 2-Card Royal
            -  Pay attention to all of your cards and don’t just focus on the 2-Card Royal.  You might be dealt 4-5-6 of one suit and a J-Q of another.  The 3-Card Straight Flush outranks the 2-Card Royal by a considerable margin.
            -   Do NOT discard any Pairs to go for a 2-Card Royal

            This list is hardly meant to be comprehensive.  If while reading it you realized that you didn’t know these things, you might want to brush up on your game before you spend real money.  As always, it is important to learn the strategy table of the game you intend to play and stick to it. 

            This way, maybe next time I post up a picture of a big jackpot, you can sit back and say “That’s MINE!”

Lenny Frome Left a Legacy to Casino Gambling World

(the following is a re-print of my column in this week's edition of Gaming Today)  

            There are days in our lives that we all have burned into our memories – weddings, births of our children and regrettably, the passing of someone dear.  As this article goes to print in Gaming Today, I will be remembering one of those days – the 13th anniversary of my father’s passing.  I will never forget my brother telling me that my dad had had a heart attack.  When I asked him how he was doing, he responded “he isn’t.”

            I could fill up this entire edition of stories about my dad as a dad.  I’m not sure exactly how long he wrote for Gaming Today, but I believe it was 8 or 9 years, which means we could fill this edition with the hundreds of articles he wrote.  But, why think small?  If one wants to see the legacy my father left to the casino world, one only needs to walk into virtually any casino in the world.

            A good gaming analyst doesn’t just crunch the numbers.  He works with the inventors to create the game.  You need the creative side to envision the cards and the betting, but the math is the glue that holds it all together.  So, the analyst may not have his name on the patent and he may not get technical credit for inventing the game, but there is no doubt that a good analyst helps to invent each game he works on.  So, try to walk into a casino and not see Lenny Frome’s handiwork. 

            You see some Let It Ride tables?  He worked with the founders of Shuffle Master to save that one from a horrible fate (a math error).  How about some Caribbean Stud tables?  Yep, his name is on the math for that one too.  Three Card Poker?  Yes, he worked with Derek Webb to refine the math and rules of the game.  He worked on Boston 5 from New Vision Gaming.  He worked on Spanish 21 with Masque Publishing.  He worked on dozens of other games that hit the casino floor but didn’t quite make it to success.  But even these failures opened up the doors to dozens more.  Imagine walking into a casino and having none of these games be there?  It would be like Las Vegas circa 1980!

            Of course, on the other half of the floor, we’d all be stuck with nothing but slot machines!  Oh, the horror!  Where would the casino of 2011 be without Lenny Frome’s contributions to video poker?  I don’t know who first called him the ‘godfather of video poker’ but it’s a nickname that has stuck through the years.  You can even find this on his Wikipedia page ( – which, by the way, I DID NOT create!

            Despite the accolades, when it came time for my father to choose an e-mail address – he didn’t choose “vpgodfather”, “vpguru” or “vpexpert”.  He chose “Playerspal”.  He tried very hard to create games that while they obviously had house advantages, at least gave the Player a fighting chance.  What he loved about table games and video poker was that everything was known and could be calculated using finite math.  He hated the slots because everything about them was a deep dark secret.  He called himself Playerspal because that’s how he saw himself.  He was there to educate the Players about how to play the games.

            Well, so far this has been about my father as a gaming analyst.  As I said earlier, I could fill up this entire edition of Gaming Today with stories about my dad as a dad.  Of course, there would be some similarities.  Education was very important to my father.  It didn’t really matter what the topic was.  Shortly after arriving in Las Vegas, he wound up teaching at UNLV.  Here was a guy who could ace my AP Physics tests at the dinner table without a calculator and he was teaching a relatively low level algebra course in college.  Still, he had the patience to teach the kids to the best of his ability and he took it far more seriously than many full-time professors I had in college.  It meant so much to him.  This is one of the reasons why my family started the Leonard Frome Memorial Scholarship at UNLV after he died. 

            Another thing very important to my father was his family.  He adored his children and grandchildren.  So, in an attempt to put together two very important things in my father’s life – children and education, I’m asking my readers to help me with a little project.  I found out via twitter (@gambatria) that my friends at Shuffle Master are having a book drive to help a Las Vegas based organization called “Spread the Word Nevada” which promotes literacy by distributing books to elementary schools throughout Nevada.   My wife and I will be shipping to them a few dozen gently-used books  from my kids’ home library.  I’m asking my readers to check out their website and if you are so inclined to assist them in any way you can – whether via a monetary donation, donating books or volunteering. 

            I’ll get back to gaming tips next week.  

Is that Harry Potter playing Blackjack?!

            A couple of months ago, my son, who is a college freshman , and I were walking through a local mall when he was telling me about some of the interesting people on his campus.  Apparently, there is one young man who wears ‘wizard’ clothing every day.  My son remarked “maybe if you’re buying all your clothes at Party City, you need to change your wardrobe.”  Maybe the kid was just hoping to land the job as official spokesman of the new game Blackjack Switch.

            We’ve all sat down at a Blackjack table at some point and watched as we are dealt a series of bad hands.  After a while, we notice the person next to us is being dealt hands just as bad, but like a mirror image.  We’re getting 5-10, he’s getting face-6.  Sooner or later, one of you joke how you wish you could switch your 2nd cards with each other.  Geoff Hall decided to do something about it.  He invented Blackjack Switch.

            It’s a very simple concept.  You play two Blackjack hands (equal wagers).  The Dealer deals you your regular 2 cards for each hand.  When it is your turn, you can ask him to switch the 2nd cards of the two hands.  So, if you’re dealt a 5-10 and a face-6, you now have a 5-6 and a 10-Face.  Two really lousy hands just became two killer hands!  So, what’s the catch?

            Well, being able to switch your cards like this is a pretty big advantage for the Player, so the house has to take a few things back.  First, a Natural Blackjack pays only even money.  A switched Blackjack only counts as a regular 21.  The ‘biggie’ is that a Dealer 22 (i.e. a busted hand) will PUSH against all Player non-busted hands EXCEPT a Player Natural Blackjack.  Other than that, the rules are pretty standard and moderately liberal.  The Player can double down on any two cards.  He can split until 4 hands.  (It should be noted that you should verify these rules before sitting down to play as casinos can sometimes choose to tighten up the rules a bit).

            Blackjack Switch gives the Player the opportunity to spend a lot more time playing good hands.  In order to get to this position, however, you’ll need to learn a whole new layer of strategy dealing with WHEN to switch cards.  Unfortunately, there is no simple strategy I can provide you.  The only way to know when to switch is by comparing the expected values (EV) of your initially dealt hands with the expected values of your potentially switched hands.  On a positive note, I’ve already done the hard part – calculating these expected values.  So, you just need to look up your hands on a simple chart.

            The second part of the strategy is knowing when to hit, stick, double and split.  The bad news is that if you attempt to use standard Blackjack strategy for Blackjack Switch, you’ll DOUBLE the house advantage even if you switch at all the right times.  The Dealer pushing on 22s greatly alters our strategy.  Doubling on soft hands is nearly nonexistent.  A Dealer upcard of a ‘2’ is transformed from a so-so upcard into a rather powerful one for the Dealer.  The bottom line is you need to throw out everything you learned about regular Blackjack strategy and replace it with a new Blackjack Switch strategy.  Again, I’ve done the hard part and figured out when to hit, stick, etc…

            When all is said and done, if you learn when to switch and you learn the right strategy, Blackjack Switch will afford you a payback right up there with regular Blackjack (about 99.4+%).  At the same time, you’ll be playing a more entertaining version of the game that keeps you involved in the play because you will be busting less often as you will have much better hands on average.

            Shuffle Master is the worldwide distributor of Blackjack Switch and from what I’m told you can now find more than 100 tables in the marketplace, and it is growing monthly.  You can read more about the game and where to find it on their Blackjack Switch Facebook page (

            I just picked up from the printer my brand new booklet Expert Strategy for Blackjack Switch.  It comes with a full-color 4-panel double sided strategy card which has both the expected values to help you decide when to switch AND the hit/stick strategy.  It will also go into far more detail on how the strategy was developed (and why it is mathematically sound!) and what to expect from this new Blackjack variant.  The booklet and strategy card sell for $6.95, but I’m running an introductory special for the month of March of just $5.95.  Additional strategy cards can be ordered for just $1.50 if you order the booklet or for $2.95 alone.  Head on over to my website at and download the order form to order or just send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603

You can be a Three Card Poker expert too!

            This past week, I posted something on the Facebook page for Three Card Poker.  Shuffle Master asked people to relate their best story about Three Card Poker.  So, to get the ball rolling, I posted the following true story:

I'll get the ball rolling: A few years ago, my wife and I sat down at a Three Card Poker table (I think we were at Sunset Station). It was the first time my wife ever sat a casino table game. We had covered the basics of how to play the game (strategy-wise), but after the Dealer gave her her chips, she looked at me and said "now what do I do" - meaning just where to put the wagers. The woman to her right struck up a conversation by telling my wife exactly where to put the chips and how to play. She told my wife that you "'usually play with Queen or better, but sometimes you 'Play' with a Jack and can beat the Dealer." It took all my wife's strength to not respond to the woman, "Do you have any idea who my husband is? He WROTE THE BOOK on Three Card Poker!" (literally). This is an absolutely true story, and unless someone recognizes me - I don't tell anyone who I am in the casino so that's why my wife didn't say anything.

            In response, another reader, posted the following:

‎^^^ little cocky huh? 

By the way Q-6-4 is a great strategy - if you work for Shuffle Master.

Q-J, Q-10 isn't even a good one. King high only, but you did write a book on it so you must know what you're talking about.

            I couldn’t really argue with the ‘cocky’ part.  When it comes to gaming math, I am one of the experts.  Nearly every successful proprietary table game in the casino has had either my father’s work or my work behind it.  The rest of this person’s response had me a bit befuddled.  Queen – Six – Four is not a great strategy if you work for Shuffle Master.  It’s a great strategy (and the best strategy) if you play Three Card Poker.  In fact, it really is ALL you need to know to be an expert at the game.

            This poster seems to have it backwards.  It is not because I wrote a book about Three Card Poker that I know what I’m talking about.  It is because I know what I’m talking about that I wrote the book Expert Strategy for Three Card Poker.  My father worked with the inventor of Three Card Poker.  Several years ago, when Shuffle Master had a Three Card Poker tournament, they came to me to write a strategy booklet on the best way to play for Tournament Play.  But, it’s not because of all this that I know what I’m talking about.  It is because I can prove mathematically that Q-6-4 is the best strategy that I know what I’m talking about.

            How does one go about proving this?  In the case of Three Card Poker, it is very simple.  There are 22,100 unique 3-card hands you can receive from a 52-card deck.  For each of these, there are 18,424 possible Dealer hands.  Using a computer program, I run every one of these hands (just over 400 MILLION hands) and determine for each of the 22,100 Player hands whether the Player is better of Playing or Folding.  If the Player wins back at least the 18,424 units he would wager playing against each of the Dealer’s 18,424 possible hands, then he should Play.  If not, he will lose less by Folding than he would by making an additional wager.  When you analyze the results of this program, you find that the decision point is at Q-6-4.

            At Q-6-4, the Player will wager 18,424 additional units, but win back 18,546.  His net loss will be 18,302 which is still a bit better than Folding and losing 18,424.  At Q-6-3, he will win back only 18,377 creating a net loss of 18,471 which is a bit more than he would if he just Folded.

            So, the poster, seemingly attempting to mock my answer, suggests three other possible strategies – QJ, Q10 and even King High.  How do these stack up?  Well, QJ will get you a payback of 97.61%.  Q10 will get you a payback of 97.28%.  If you want simplicity and go with King High then the payback falls to 96.84%.  The payback for Q-6-4 is 97.98%.  So, there is a clear difference, but it may not seem so big to some of you.  So, let’s flip this around to look at the house advantage (100%-payback).  For Q-6-4, we give up 2.02% to the house.  For QJ it become 2.39% or nearly a 20% increase.  For Q10 it goes up to 2.72% for a 35% increase.  Last but not least, for King High, the house advantage goes to 3.16% or a 55% increase. 

            There are times when you may want to simplify the strategy to reduce errors with a tradeoff of some payback.  However, I really don’t think remembering Q-6-4 should push anyone’s brain to the limit.  It’s your money, you can lose 20-55% more by picking a different strategy or you can become an expert and remember Q-6-4.  Not because I wrote the book and not because I ‘must know what I’m talking about’, but because it IS the BEST strategy.