Strategize


            Every casino game that is more than pure luck has some strategy associated with it.  This goes beyond the basic strategy that simply says you're better off not playing at all.  For many games, the strategy can be summed up with a simple sentence or two.  For Three Card Poker, it is Play Q-6-4 or better.  Four Card Poker has a two sentence strategy that tells you when to fold and when to Raise.  Let It Ride's strategy takes a few sentences telling you when to pull down the 1 and 2 wagers.

            As strategy gets more complex, it is helpful to try and put it into as easy as a format as possible to help a mere mortal to utilize it.  It is relatively easy to program a computer to play a game perfectly.   Very few humans can take every game to this level.  Also, expending that much energy on memorizing a very complex strategy can pretty much sap the fun right out of the game.  Blackjack utilizes a relatively simple matrix that crosses the Player's hand with the Dealer's upcard. 

            Creating a strategy for video poker is quite a challenge.  As said earlier, telling a computer which one of the 32 ways to play a hand is relatively easy.  But, there are 2,598,960 unique 5-card deals from a standard deck.  Coming up with a way to group these together in a way that a Player can use is a whole different story.  I believe it was my father, Lenny Frome, who was the first person who accomplished this.  He grouped hands together in a way that Players could easily understand and hopefully memorize. 

            A video poker strategy table consists of only two columns.  The first contains the hand rank as it was categorized by my father.  The second contains the expected value of the hand.  Ironically, this second column isn't even needed to play video poker properly.  It is there just for reference.  So, that means the video poker strategy table consists of a single column - usually with about 30-40 rows/entries in it.  To play video poker the correct way, you have to memorize the order of these entries.  This is not nearly as daunting as it seems.  About 10-15 of these entries are more than a little obvious.  So, you're left with about 25 hand types that you need to learn.

            Let's start at the top of the strategy table which contain the most obvious hands:

·       Royal Flush
·       Straight Flush
·       Four of a Kind
·       4- Card Royal
·       Full House
·       Flush
·       Three of a Kind
·       Straight

            We'd be having a great night at video poker if these were the only hands we were dealt.  These are all big winners, all with expected values of 4.00 or better.  In fact, only one of these hands is not a sure winner - the 4-Card Royal.  This is also the only hand that might overlap with any of the others, creating the only strategy decision in the bunch.  What do you do if you are dealt a Straight (or a Flush) that is also a 4-card Royal?  Well, now you know the answer.  You have to throw away the sure winner to go for the big winner.  The good news is that if you have a 4-Card Royal, you have a very good chance of still winding up a winner.  There are 47 possible draws, 1 of which will result in the Royal.  Another will give you a Straight Flush.  6 or 7 more (depending on whether you threw away a Straight or Flush) will result in a Flush.  5 or 6 will result in a Straight and a host more will give you at least a High Pair which will seem like small consolation.

            While this decision might be agonizing, mathematically, it is very clearly the proper play.  The expected value of the 4-Card Royal is 18.66.  The expected value of the Flush is 6 and the Straight is 4.  Of course, don't expect to see this hand every hour.  A 4-Card Royal will show up once in about 2700 hands and only about a third of these will be a Straight or a Flush.   One other key point to note.  Do NOT throw away a Straight Flush to go for the Royal.  That Straight Flush has an expected value of 50 which far exceeds the 18+ of the 4-Card Royal.


            Next week, I'll move down the strategy table to the hands that require a bit more thought.

Table your Hunches


            Last week, I described how all casino game strategy is based on expected values.   You hit or stick in blackjack not because you hope the next card is of a certain value, but because there are certain probabilities as to what the next card will be and how it will affect your hand and your chances of winning or losing.   If you're dealt two face cards, you don't give much thought to strategy.  Hopefully, you're not one of those Players who even thinks about splitting 10's! 

            But, if you are dealt a 16 and the Dealer has a 7, you start giving thought to the strategy.  With a 16, you have 5 cards that will help you and 8 that will bust you.  The odds don't look to good and this is why a lot of people stick on this hand, albeit incorrectly.  You can stay put, but with a 16, the only way you can win is if the Dealer busts, which will happen only 26% of the time.  So, your choices are a 61% chance of busting right away or sticking and having a 74% chance of losing that way.  Of course, by hitting you also have an opportunity improve your hand.  All of the 5 possibilities improve your hand.  If you pick up an Ace, you'll be most likely to push.  Pick up a 5 and you'll win more than 92% of the time.  Don't get me wrong, it is not a strong hand and the decision to hit is not an overwhelming one, but it is still the right move.  In the simplest form, if you face this situation enough times - which you will if you play for a few hundred hours, you'll find that you do better by hitting than by sticking.

            In blackjack, you don't have to memorize all of the math behind the game.  You don't have to figure out how many cards will bust you or bust the Dealer.  To learn to play blackjack, many Players use a simple strategy table.  It is a simple little chart that shows every possible Player hand and each possible dealer upcard.  It then shows what to do - hit, stick, double, split, surrender, etc..  Guys like me have already done all the number crunching for you.

            Video poker is no different than blackjack except the decision making process is far more complex.  In blackjack, the result is essentially binary - you win or you lose (okay, you can tie also, so it is not really binary).  In video poker, you can have 1 of many results - ranging from a Royal Flush down to a High Pair or you can lose.  Since each of the different winning hands pays a different amount, the specific result must be taken into account.  If someone invented a game of video poker in which all hands above a certain rank paid a fixed amount, then we'd be able to lump all the hands into win or lose.  But, we need to know the probability of each final outcome with a different payout in order to appropriately determine the value of getting that hand.  Surely, it is more valuable to wind up with a Straight Flush than just a Straight.

            Video poker is also more complex than blackjack in that there is more than just a handful of different possibilities for each hand.  The Player can hold all 5 cards or discard all 5 cards or anything in between for 32 different possible plays.  Yes, most of these possibilities will be quickly discarded, but they still must be considered from a mathematical perspective.  They are only discarded because the human mind can quickly recognize possible draws that would clearly not be the best strategy. 

            Despite the extra complexity of video poker, the similarities are still stronger than the differences.  In the end the decision still comes down to the expected value.  Like in blackjack, you don't have sit there trying to figure out how many cards you need to complete a Straight or the like.  Again, guys like me have already done the job.  We have looked at every possible deal, every possible draw for every possible deal and summed up all of the final hands.  Using this distribution, each possible draw is assigned an expected value.  Whichever draw has the highest expected value is deemed the right play.  The last step in the process is too try and categorize the way each hand is played into a format that a human can use to play the hands.  We call this a strategy table.

            Unlike blackjack where the strategy is a matrix that crosses Player hands with Dealer hands and tells you what to do, a video poker strategy chart lists all the possible playable hands in order in a simple table.  The table usually contains the expected value of each hand too, but this is just for information.  To use the strategy table, you basically work from the top and find the first hand that your dealt hand can make and that is the way to play the hand.  So, if you are dealt a hand that is a 4-Card Straight and a Low Pair, you start at the top of the table and work downward.  If a 4-Card Straight appears first, you play that.  If a Low Pair appears first, you play the hand that way.  If you can't find any hand that matches the hand you were dealt, then you fall to the bottom of the table and find a RAZGU which means throw all five cards.


            Next week, we'll begin breaking down a strategy table for full-pay jacks or better.  You'll be on your way to becoming an Expert Player.

The Advantage of Expert Play


            This morning, I had a discussion with a friend of mine about a game he is developing.  I explained that playing 'perfect' strategy would be nearly impossible due to some subtle complexities of the way the game is played.  As a result of this, the game would not likely play anywhere near its 'theoretical' payback.  Many games have this 'problem'.  Blackjack pays 99.5%, but very few players play anywhere near this.  Ultimate Texas Hold'em has a payback well into the 99% range too, but stats from the casinos make it clear that very few Players, if any, can manage this high of a payback.

            My friend stated that he thought that he would be able to play the game close to the theoretical because he is an accomplished Poker Player.   I asked him if he was an accomplished video poker Player and he said that he wasn't.  I told him that any table game against a Dealer was really nothing more than playing video poker and had no resemblance to poker even if the game resembles poker.   Poker is about reading Players, understanding their betting patterns and their tells.  Video Poker is about one thing - math.   There is no one to bluff.  All that matters is what is the probability of all final hands given what I choose to discard.   Let's take a look at a simple example:

5♠        5♦        6♣       7♥        8♦

            In theory, there are 32 ways to play this hand, but I think we can quickly rule out 29 of them.  I don't think anyone is seriously going to consider holding only the off-suit 6-8 or holding all 5 cards (which would result in an immediate loss).    There are really on 3 possibilities, 2 of which are identical.  The Player can either hold the Pair of 5's or the 4-Card Straight (hence, the 2 identical possibilities as it doesn't matter which 5 the Player keeps.)

            If the Player keeps the 4-Card Straight, 8 cards will result in a Straight and the rest will result in a loss.  So, if we add up the total payout, we'd have 8 Straights at 4 units each for a total of 32 units.  There are 47 possible draws.  We divide the 32 by 47 to get 0.68.  This is called the Expected Value (or EV) of this hand using this possible discard strategy.

            Calculating the Expected Value of holding the Pair is a bit more complex, but easy enough to calculate using a computer.  There are 16,215 possible draws if the Player holds 2 cards.  We look at these possible draws and look at the final hands.  The Player can wind up with a Four of a Kind, Full House, Three of a Kind or Two Pair.  We add up the total payout of all of these winning hands and divide by 16,215.  The result is an EV of 0.82. 

            This Expected Value is greater than that of the 4-Card Straight, so the proper play is to hold the Low Pair.  When Playing video poker (and virtually every other casino game), the proper play is to follow the one with the highest EV.  You don't go with a 'hunch' that a 5 is coming up or that you just feel a 4 or a 9 is going to fill out that Straight.  There is a distinct probability of each of these events occurring and we use those probabilities to our advantage.  This is what allows a Player go achieve the theoretical playback of a game. 

            It is an 'advantage' because most Players don't play this way.  Because of this, the casinos can off the games with a relatively high payback, knowing that they can rely on human error to pad their profits.  For the Players who play according to the math, they have the advantage of being able to play to the theoretical payback over the long run.


            Mastering video poker takes some significant effort.  The strategy is a complex one and learning whether to hold the Low Pair or the 4-Card Straight is merely one example of where a strategy where you play by what you think is right may in fact be quite wrong.  The good news is that thanks to guys like me, the toughest party of learning the strategy (creating it) has already be done for you.  The next step is learning that strategy and putting it to practical use.  We'll save more of that for next week.

Video Poker Primer


            It was just over 10 years ago that I started writing for Gaming Today.  I have to be honest, that really blows me away.  That means I've written roughly 500 columns when I take into account off weeks and the fact that for the first 6 or 9 months, my column was bi-weekly.  I remember when I wrote my first few columns, I would wax poetic about how my father (Lenny Frome) had written nearly 1000 columns for a variety of different publications.  I remember when I hit column number 100, I remarked how far behind I was.  Now, my total count is probably about 600-700 columns and I can almost see myself someday surpassing my dad's total.  That said, I definitely don't plan on taking steroids or PEDs to get me there.

            Part of what is so amazing about having written 500+ articles is that I have somehow managed to come up with that many things to write about.  I'm not really sure that there are 500 unique subjects to write about.  I have to remember that if I borrow a subject from 2005 that there is a strong likelihood that if someone reads it today, they didn't read that article from 8 years ago.  So, in that spirit, I'm going to start back at the beginning today and discuss some basics about video poker.

            Video poker is truly a unique game in the casino.   Far too often it is lumped together with Slots, but there is little in common except for the technology.  I don't think of a video blackjack machine as a slot machine and the same is true for video poker.   As the world starts turning more to online gambling, the separation will no longer be about the technology.  Instead it should be about the essence of the game.  Video Poker is a game that is based more on skill than almost any other game in the casino.  This doesn't mean that luck doesn't play a part, especially in the short run.  But, if I were to challenge a random Player to a slot competition, there would be no way to gain an advantage.  If I were to challenge a random Player to a video poker competition, I'd like to believe that I would have a distinct advantage.  The longer the competition runs, the more strategy and skill will rule the day and the less that luck will impact the results.

            How is video poker a game of skill?  Because the Player must make a decision that will clearly impact his results.  This decision is frequently NOT of the 'no-brainer' variety.  Technically, in the game of Casino War, the Player must make a decision to - whether or not to go to War when the Player and Dealer tie.  But, the proper decision is the same all the time - to go to War.  So, while technically, there is 'strategy', I doubt very many people get this one wrong.  In Three Card Poker, there is one strategy decision - to Play or Fold.  The decision is also relatively simple.  If the Player has Q-6-4 or better, he should Play.  As simple as this sounds, many Players don't follow this rule (and I don't mean that they go with Q-6 or Q or better), and as a result, they give up a larger portion of their bankroll to the casino than they need to.

            Video Poker strategy is far more complex than this.  First of all, the decision is not one of Fold or Play, but rather which cards to Discard.  There are 32 ways that a Player can make each of these decisions, ranging from keeping them all to discarding them all.  Granted many of these possibilities will fall into the brainless category.  If you are dealt Three of a Kind and two off-suit kickers, which cards to discard is pretty obvious.  If you are dealt a Straight, then you don't have to discard at all.  Oh wait, what if it is also a 4-card Straight Flush or a 4-Card Royal, then what is the proper play?

            If you are dealt the following:

4♦        4♠        5♠        6♠        7♣

the decisions get a bit more complex.  You might keep the Pair of 4's, or the 4-Card Straight or maybe the 3-Card Straight Flush.  This is 3 of the 32 ways the hand can be played.  The other 29 are quickly discarded, so there isn't a need to go through 32 possible decisions for each hand.  Obviously, you're not going to keep the off-suit 4-7 in this case.

            Unlike table poker (which involves even a higher level of skill), the strategy in video poker is based strictly on math.  You don't play hunches and you're not trying to beat another Player.  You don't have to worry that you might pull your Straight and he might come up with a Flush.  All that matters is the likelihood (aka probability) of each final hand and how much that hand pays.  But, I'll leave that for next week.  For now, I'll be happy if I've convinced you just a little bit that video poker is not slots.

            

Think Loss Rate


            How much of a difference is there in terms of payback from one casino game to another?  Most table games have a payback between 97 and 99.5%.  Video Poker can range from about 95% to 101%.  Slot machines probably range from about 85% up to 95%.  Sidebets, quite frankly are all over the place, ranging from just over the legal limit of 75% and going up to the low-mid 90%.  While there is a lot of overlap, one of the largest determining factors is strategy.  More complex strategy means a combination of more human error and/or Players not even trying to follow it.  Simple strategy is much easier to learn and follow.  Three Card Poker has one simple strategy rule.  Follow it and you should approach the theoretical payback of about 98%.  Don't follow it and you can only do worse.

            Video Poker has paybacks considerably higher.  Not all of the versions, but you can still find plenty of them well above 98%.  Video Poker's strategy, however, is far more complex than Three Card Poker's strategy.  The average Video Poker machine has more than 30 different strategy items that need to be memorized and in the appropriate order so that you know how to play the hand.  So, first you need to review the hand and determine the realistic ways the hand can be played and then you have to know which of these ways has the highest expected value, which tells us which way the hand should be played.

            In most games, many of the hands are pretty obvious even if you knew little.  If you're dealt a 6-7-8 in Three Card Poker, I don't think you need to have read a book to know what to do.  What if you are dealt K-3-2?  What about Q-8-2?  What about Q-3-2?   For each hand, the Player is really asking himself if he is better off Playing or Folding.  Those are the only two options in Three Card Poker.  The answer is pretty obvious for the Straight and a good deal less obvious for the other three hands.  The strategy is determined by the math behind the question of whether the Player is better off Folding or Playing.  By Folding, the Player forfeits his original wager (one unit).  By Playing, he wagers an additional unit.  If Playing can return at least that additional unit (on average), then the hand is worth Playing.   The Player does not have to perform some complex calculation on each hand.  The decision is to Play or Fold and the math works out very neatly.  For every hand stronger or equal to Q-6-4 the Player is better off Playing.  For Q-6-3 or less, he is better of Folding.  You've just become an expert at Three Card Poker strategy.

            Video Poker is not nearly this simple.  First of all, there is no folding and no additional wagers.  You make an original wager and your only goal is to maximize the amount of money you get back on average for each hand.  If you're dealt a Straight off the deal, there isn't much to think about - unless of course it is also a 4-Card Straight Flush or a 4-Card Royal - then what?  What if you're dealt Three of a Kind and 3-Card Royal?  How about a Pair and a 4-Card Flush?  Does it matter if it is a High Pair or a Low Pair?  (Yes, it does!)  

            In Video Poker, the hands are categorized into about 30-40 different hand ranks and partial hand ranks.   Each of these is assigned an expected value.  This expected value is calculated by looking at ALL the possible draws for that hand and tabulating the total units won for each final winning hand.  We then divide this total by the number of possible draws so that we can compare apples to apples.  So, to look at a simple example.  Suppose you are dealt the following hand:

4♥        5♥        6♥        7♥        8♦

            The decision here should NOT be driven by your favorite Clint Eastwood line ("are you feeling lucky, punk?").  It should be driven by the math.   The straight has an expected value ("EV") of 4.00.  There is no draw in this case and the EV is simply the payout of the hand.  If you decide to discard the 8, there are 47 possible draws.  2 will result in a Straight Flush, 5 will result in a Straight (remember that you would have discarded a card that could also have made it a Straight) and 7 that will result in a Flush.  All other cards result in a losing hand.  So, do you throw away the sure 4 units to go for the Straight Flush?  When we add up the payouts of the winning hands, we get 162 units (2 x 50, 5 x 4, 7 x 6).  We divide this by 47 (the number of possible draws) and get 3.45.  As this is less than the EV of the Straight, we keep the Straight.  In the long run, this will be the better move.


            While most Player would play this correctly (I guess?), the simple reality is that except for those that learn the right strategy, there will be a significant number of Players who will NOT play this correctly.  Throw in the roughly 25% of hands that require a real decision and the casinos can count on Player error to help pad their winnings.  This is why they can offer the 99.5% paybacks on so many full-pay jacks or better Video Poker.   Someone like myself might sit down and get the 99.5%, but the vast majority of Players will play well below this level.   They are likely to play in the 97-98% range if they have some idea of what is going on and perhaps as little as 95% if they just 'wing it'.   The difference between 99.5% and 96% may not seem like a lot, but I always suggest you turn that around to the loss rate - 0.5% vs 4%.  Now there is a 700% increase from one to the other.  The impact to your bankroll could be staggering.

Nutritional Labels for Casino Games?


            Today's column topic comes from my Freshman college roomate.  He posted a question to one of my old columns on my blog (gambatria.blogspot.com).  He wanted to know if I thought if the casinos would ever have to disclose all the key statistics about each game - a sort of 'nutritional label' for each game.  My response was that I didn't think so for 3 reasons.  The latter 2 were more political than mathematical.  This column is about that first reason.  With the exception of slot machines, all that information about each game is already fully known.

            While admittedly, if the average person were to walk up to a game that he has never seen before, he isn't going to know what the payback or win frequency is.   I'm an expert and I couldn't necessarily tell you these key stats about a game I've never seen before.  I might be able to take a good guess about it, depending on whether we are talking about a complete game or a sidebet.  There isn't a lot of variation in table game paybacks.  There are probably very few that are below 97% and, of course, none above 100%.  Sidebets can have a much larger range, as some are as low as 75% and others go up to the mid 90's or even a smidge higher.   If I were to walk up to a video poker machine that has a foreign paytable, but is based on one of the better known games, I can probably peg the payback to within .25% by doing some quick math in my head.

            There is little doubt that putting the key statistics on each machine would make this information far more readily available than the way it is currently done.  But, I wouldn't equate this to a can of soup without a nutritional label.   The list of possible ingredients and the exact quantities in the soup is nearly endless.  Throw in the fact that there are hundreds of thousands of food products (or more?) and it is completely impossible to make a choice based on nutritional content without these labels.  When you walk into a particular casino, you have perhaps a dozen or so choices of which table game to play.  Yes, each casino may have its variation of rules.  One may offer a 6-deck shoe for blackjack and the other may have a single-deck game.  One may hit on soft 17 and the other may stop on all 17s.  But, if you spend time reading a book or two on gambling, you'll quickly learn and likely remember the paybacks of most of these rule variations.

            For many games, there is almost no variations available - especially for the base game.  Want to play Three Card Poker?  It has a 97.98% payback for Ante/Play.  While there are some variations of Pair Plus, the overwhelming number of them have the same paytable, paying 92.72%.   These numbers are not known because Shuffle Entertainment published them, they are known because any mathematician/programmer can calculate these numbers using a variety of techniques.  In the case of Ante/Play, there are a total of 6 cards dealt to the Player and the Dealer (3 each).  There are 22,100 possible Player hands and 18,424 possible Dealer hands for each of the Player hands.  Thanks to the speed of today's computers, a program can run through ALL of these hands (numbering well into the Trillions), determine the right strategy for each Player hand and tell us absolutely everything we would ever want to know about the game - the payback, the win fequency, the probability of winning given any Player hand, how often the Player folds, how often the Dealer doesn't qualify, etc... 

            Unlike food, casino games are, well, gambling.  Part of gambling is rewarding those people who are more prepared and more knowledgeable about gambling.   The strategy for Three Card Poker doesn't take a PhD to learn.  It takes about 20 seconds (or less).  Play a Q-6-4 or better.    You could read this just about anywhere on the internet.  If you want to know the details about the strategy (how and why), you can read a booklet on the game (I suggest my very own Expert Strategy for Three Card Poker, but that's just me!)  Armed with this strategy you are very likely to do better than someone who has no idea what to do over the short run and almost assuredly so over the long run. 

            For years, people have asked me if I'm banned from casinos because of my in-depth knowledge of table games or if I'm 'hated' by the casinos for arming people with the strategies for how to play the games.  I'd like to think that I've had at least some influence on how people play.  But, I don't think the casinos care one bit.  Even with the best strategies, all casino games (except a few video poker variants) have house advantages.  The casinos are totally fine with a few people playing near the theoretical payback as results are all relative.  A few people who are winning in the short run or who are doing better than the rest can keep the rest of the Players in the game.  After all, if the other guy can win, why can't I?  Of course, this is far more true IF you know the right strategy. 

            I've often surmised that if I were to stand near a Three Card Poker table, handing out my booklet for free that only 20-25% of the Players would actually use the strategy.  Half of these people would probably give it up within the hour when the results don't match the theory - ignoring the time factor that is required for this to happen.  What this really translates to is that I don't think it would matter one bit if the casinos were to put a little sign on each table that had the payback and win frequency of the game.  Most Players would probably ignore them.  After all, how many people really read those nutritional labels on food anyhow?  And that's about what actually goes INTO your body!

            

Advantage: Dealer


            I don't think this will shock any of you.  Every table game has a house advantage.  Numerous mechanisms are used to build this house advantage.  By now, most Players are probably used to most of these methods, that they barely notice them.  If the game of Three Card Poker were played such that the Player made a wager, got three cards and then simply went head-to-head against the Dealer's 3 cards, the game would be a 100% payback.  Any game in which the Player and Dealer get the same number of cards and no decisions after the initial wager is made is simply one big push.

            In the game of blackjack, the Player must act first.  If he busts, he loses.  It won't matter if the Dealer busts also.  This is an advantage for the house.  The Player's ability to double down, split and decide when to hit/stick are advantages for the Player.  I've often be quite amazed that the game of blackjack was developed centuries ago without the use of computers (obviously) and somehow managed to deliver a payback right where you would want it! 

            In the game of Three Card Poker, the Player and Dealer receive the same number of cards, so that's an even game.  The Player, however, gets to decide when to Play/Fold so this is an advantage to him.  He can take his really weak hands and walk away from them without making another wager.  He can wait for his stronger hands and Play.  In the background to this process is the fact that because the Dealer always gets 3 cards, the Player knows what the 'average' hand for the Dealer is.  In fact, he can know the frequency of every possible hand.  This is what allows him to create the proper strategy for Playing vs. Folding.  If the game ended here, the Player would have a significant advantage.  To offset this and get back to a house advantage, the Dealer must qualify with a Queen High Hand.  As a result of this, the Dealer essentially surrenders 30% of his weakest hands and cuts the payout to the Player in half.  For a small portion of these hands, a bad Player might actually benefit - by Playing a hand below Q-6-4 and going against the right strategy.  Despite these occasional wins, the casinos will more than gladly make up for this with all the Jack High hands that the Player will lose.

            Ultimate Texas Hold'em adds a twist to the idea of Dealer qualifying.  In UTH, if the Dealer doesn't qualify, the Ante wager pushes, but the Play wager stays in Play.  If we were to use this rule in Three Card Poker, it wouldn't make a difference to the overall payback because a Player should fold every hand that would result in loss where the Dealer does not qualify.  However, in UTH, Players sometimes make a 4x wager or a 2x wager with something less than a Pair.  If the hand doesn't develop (usually you're shooting for a Straight or a Flush), the Player may be left with a very poor hand.  If we used the TCP qualifying rule, the Play wager might push and the Ante wager would pay even money.  In UTH qualifying, the Ante pushes and the Play wager is in play.  The Player could be left with a Queen High hand.  If the Dealer has an Ace High hand, the Ante will push and the Play wager will lose.  This subtle difference in how qualifying is handled gives the casino just a smidge more edge.  In the case of UTH, this is the difference between the game having no house edge and having just the right amount of house edge.

            Moving on, we find ourselves at Four Card Poker.  Four Card Poker has no Dealer qualifying.  Every hand is in play.  All wagers are in play (assuming the Player doesn't fold).   So, where does the house advantage come from?  The Dealer gets an extra card.  Despite the name of the game, the Player gets five cards to make his best 4-card hand.  The Dealer gets six cards to make his best 4-card hand.  This little 'advantage' is enough to get rid of qualifying and to allow the Player to make a 3x Play wager if he so chooses.  If the Dealer were to get the same number of cards as the Player, then each would win the same percent of hands.  Even to allow an optional 1x Player wager would require the adding of some sort of qualifying.  To allow a 3x Play wager, the qualifying might not even be enough.  Instead the Dealer gets an extra card, meaning that he will win a larger percentage of the hands. 

            I'm sure that if I were to look at all the games on the casino floor, I'd see a variety of other different methods for creating a house advantage.  While each has a math component and provide different amounts of house advantage, the real impact of the methods is more psychological than mathematical.  How do you feel about the Dealer having a stronger hand, on average, by being dealt more cards?  If you beat the Dealer, you might win more than you would if you play him in a game where you are each dealt the same number of cards.  There is no real correct answer.  There is simply a variety of proven methods for doing this - and probably even more that haven't been thought of yet.


House Money Breaks the Mold



            As most of you know, I wear two hats in the gaming analysis world.  There are some that might see my two roles as being opposed to each other.  Quite frankly, at first, so did I.  Over the years, however, I realize that they are more complementary than anything else.  On one hand, I analyze games already created and write about them, with the goal being to educate the Player to become the best possible Player he can be.  On the other, I help invent games.  Some may think I do this using my knowledge of how Players act to create games designed to trip them up.  This simply is not the case.  Even when working with inventors, I do my best to steer the game in a direction that offers the highest paybacks possible.

            Let me be clear.  Games are created with a house edge.  If you consider that to be 'rigged', then there isn't much more to discuss.  No casino is going to purposefully put a game on the floor that has a Player edge.  The one and only exception, to the best of my knowledge, is video poker, where there still remains some full-pay machines that pay over 100%.  However, as most of these are at too low of a denomination to really do harm to the casino, they are content to let the very few profit at the expense of the overwhelming majority. 

            In the last several years, I have the pleasure of helping to develop Mississippi Stud and Ultimate Texas Hold'em.  These two games boast paybacks in the mid to high 98% range and up.  Part of the reason they are able to do this is because they require intricate strategy in order to achieve these theoretical paybacks.  This is also one of the reasons why video poker can offer such high paybacks.  To achieve these paybacks require that a Player play using a robust strategy that most Players do not bother to learn.  Slot machines in contrast offer absolutely no strategy.  As a result, the casinos cannot rely on human error for any part of their profits and they must offer lower paybacks.

            The same is true of sidebets for table games.  For the most part, it has pained me when I see the paybacks on sidebets.  It is not uncommon for them to be the mid 80% to low 90% range.  Some, go even lower into the high 70's.  Some sidebets, especially Progressives, offer huge payouts for the Player and so Players are willing to trade this low payback for the remote chance of the life-changing payout.  Like slot machines, casinos must offer these lower paybacks because the sidebets offer no strategy and they cannot rely on any human error to drive profits.  The problem with attempting to offer sidebets with strategy is that the strategy almost assuredly works against the basic strategy of the underlying game.  This is a 'no-no' because the combined payback will now be lower than the two separate paybacks AND it can require the Player to learn some new hybrid strategy that may be more trouble than it is worth.

            Less than a year ago, one sidebet broke this model completely.  I've written about it before, and I have to admit that it is the only sidebet that actually gets me excited.  On the one hand, it is definitely a sidebet.  On the other, it is almost an entirely new game within a game.  Yet, if a Player chooses not to play it, it does not impact the base game.  Quite frankly, even if he does choose to play it, it doesn't affect the base game.  But, it does require learning a strategy for the sidebet.  The game is called House Money , and it is a sidebet to blackjack.

            The game is really quite simple.  If you make the House Money sidebet, you will get paid if the first two cards you are dealt for blackjack are a Suited AK, a 2-Card Straight Flush, a Pair or a Straight.  This works out to be about 21.5% of the time.  The most common payouts are 9,4,3,1 respectively (although there are multiple paytables).   Now, the fun begins.  After you are paid for your sidebet, you have the option to take all of your winnings from your sidebet (which includes the original sidebet wager) and you can add it to your base blackjack wager.  This is AFTER you have seen your two cards and AFTER you have seen the Dealer's upcard.   So, if you're dealt a 10-J suited, you will win 4 to 1 for your sidebet.  Assuming you wagered $5, you will now have the right to take the entire $25 (the $20 you won plus the $5 sidebet wager) and add it to your base blackjack wager. 

            In the case of the 10-J you would ALWAYS want to do this.  The Dealer will check for blackjack prior to you making this additional wager, so you are not risking your winnings if the Dealer has blackjack.  Imagine have a $5 wager on the base game and $5 on the sidebet when dealt this hand.  Dealer turns a 7 up and then flips over a 10.  Your $5 sidebet becomes $25, which turns your base wager into a $30 wager.   When you win this, you just won $50 for being dealt a suited 10-J and winning the blackjack hand.

            One strange fact about House Money is that the payback of the sidebet actually goes UP with more decks.  This is because some of the winning hand are more frequent with more decks.  With 6 or 8 decks, House Money pays 97+% and it makes absolutely NO IMPACT to the base game of blackjack.   That said, it is imperative that you choose to let your winnings ride (i.e. cap your wager) at the right times AND that you play proper blackjack strategy.  If you are dealt a 5-6 against a 7 and choose not to cap your wager OR cap your wager but then 'chicken out' and not Double Down (which requires doubling the ENTIRE wager), then you will not achieve the 97+% payback.



            Below is a matrix that shows the proper strategy for House Money for 6 and 8 deck shoes when the Dealer hits a soft 17.  There are some minor modifications if you are playing with less shoes or if the Dealer sticks on all 17s.  As for basic blackjack strategy, you can find that almost anywhere on the internet or in a book on blackjack.


Hand
Dealer Upcard
2
3
4
5
6
7
8
9
10
A
A-2
Y
Y
Y
Y
Y
Y
Y
N
N
N
2-3
N
N
N
N
Y
N
N
N
N
N
3-4
N
N
N
N
Y
N
N
N
N
N
4-5
Y
Y
Y
Y
Y
Y
Y
N
N
N
5-6
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
6-7
N
N
N
N
N
N
N
N
N
N
7-8
N
N
N
N
N
N
N
N
N
N
8-9
N
N
N
N
N
N
N
N
N
N
9-10
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
10-J/J-Q/Q-K
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
K-A
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
2-2
N
N
Y
Y
Y
Y
N
N
N
N
3-3
N
N
Y
Y
Y
N
N
N
N
N
4-4
N
Y
Y
Y
Y
Y
N
N
N
N
5-5
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
6-6
N
N
Y
Y
Y
N
N
N
N
N
7-7
N
N
Y
Y
Y
N
N
N
N
N
8-8
Y
Y
Y
Y
Y
Y
N
N
N
N
9-9
Y
Y
Y
Y
Y
Y
Y
N
N
N
10-10/JJ/QQ/KK
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
A-A
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y - Cap the wager                   N - Take the winnings

            House Money can now be found in Las Vegas at the following casinos - The Cannery, Fiesta Las Vegas, Green Valley Ranch, Jerry's Nugget, Monte Carlo, Palace Station, The Palazzo, Santa Fe Las Vegas, Sunset Station, Texas Station and The Venetian.
            

VP Machines Playing Themselves



            This past week, I received an e-mail from a reader who told me about some video poker machines at the Soboba Indian Casino in Banning, California that sort of played themselves.  After being dealt the initial five cards, the machine would mark the cards that should be held (presumably according to some form of 'perfect' strategy).   If you wanted to hold a different set of cards, you had to 'uncheck' the hold buttons on those cards and hold the ones you wanted.  My reader wanted to know if this is the direction that video poker is heading.

            A little over a year ago, I received an e-mail from a company called Incredible Technologies that asked my opinion on a video poker game that they were offering at Red Rock Station.  It allowed the player to 'earn' strategy tips through winning hands.  This is not quite the same as the first situation as this only provides the Player with tips that he still has to listen to as opposed to going out of his way to ignore the strategy.   Is this the direction that video poker is heading?

            I tend to doubt it, and quite frankly a significant part of me certainly hopes not.   Just to be clear, my reasons for hoping this is not the new wave of video poker machines is NOT any fear of being made less relevant to video poker strategy or fear of losing some revenue.   While most of my columns for Gaming Today deal with video poker, most of my income is derived from table games.  In the 10+ years that I've been analyzing games, I think I've left my mark in that arena and don't have to worry about being the video poker guru that my father was.

            No, my reasons for hoping that this is not a new trend is that I think it is bad for Players.  Well, bad for good Players.  I supposed it might be good for bad Players.  The problem with this is that it tends to move video poker machines a few steps closer to slot machines.  There will still be significant differences.  The biggest being that we will still be able to know the payback of a video poker machine by looking at the paytable.  However, if all Players begin to play very close to the theoretical payback because the casinos hand the Player the strategy, then there will be NO way that they will be able to continue to offer 99%+ paybacks.  Casinos can offer games with high paybacks because they know that such a small number of Players utilize these strategies.  They can rely on human error to drive profits while still (truthfully) claiming paybacks near 100%.  It is the best of both worlds for them. 

            That brings me to the reasons why I doubt this is going to be a new hot trend that will overwhelm the video poker market.  Why would the casinos want to mess with what already is such a great situation.  They get to advertise machines with paybacks at near or over 100%.  Yet, they know that the games are almost never played anywhere near this amount.  Just like blackjack with a 99.5% payback but holds 9-15%, video poker machines do about the same.   Given the speed that video poker can be played, the profits that can be gotten from even quarter machines can easily outpace blackjack. 

            Most casinos are well aware that people such as me exist.  We write articles trying to get people to play the proper strategy.  We sell books and software to make Players, well, better Players.  At the same time, casinos know that despite this wealth of knowledge that is out there, most Players either don't bother with it at all or make some half-hearted attempt to use it or use it and then abandon it when they don't break the bank.  I've often surmised that I could hand out free copies of Expert Strategy for Three Card Poker at the entrance of a casino and STILL 75% of the Players who would sit down at a Three Card Poker table would not bother to follow the strategy in the least.   So, on the whole, casinos are not very afraid of Players bearing strategy because they are such a minority.

            However, handing the Player the strategy and then daring them to pick a different one may be far more than casinos are willing to do where strategy is concerned.  It is one thing to question when a Player wants to stand on a soft 16 in blackjack.  It is something all together different when a big flashing light comes on to say STICK when a Player has a 16 vs. a Dealer 2, and then only way the Dealer can hit is if he is willing to turn off the stick sign and go out of his way to hit.  In the case of video poker, if a Player really wants to not use the house strategy, then he is likely to find a different machine altogether.  After all, who wants to have to turn off the machine's decisions before entering his own on every hand?  So, there is a good chance that the actual payback of the video poker machine is going to quickly approach whatever the theoretical payback is.  Since the casinos will never allow games to be offered at 99% in this case, there only choice would be to greatly reduce the payback of video poker, which in turn will scare off all the good Players while at the same time, probably increasing the payback of many of the bad Players, as their errors will no longer be a factor.

            So, the only way I can see casinos adopting this concept is if they have some crazy reason to scare off some of their most loyal Players and want to reduce profits.  Nope, I don't see this as a big trend.  At best, perhaps some casinos will use them as a great marketing ploy, but that is it.

            

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.
             

Strategy is Underrated



          I can't stress enough the importance of using the right strategy when playing in the casino.  Over the years, I've heard all sorts of excuses for why people abandon strategy, ranging from it doesn't matter in the short run to some anecdotal story about how someone they know threw strategy to the wind and it paid off massively.  Yeah, that's nice.  If you're a sports fan, you know the importance of having a good coach or manager.  There are reasons why Pat Riley, Joe Torre and Bill Parcells are in such high demand.  Yes, it is because they win.  And they win because the utilize the right strategies for their respective sports.  This doesn't mean that once in a while their strategies won't fall apart.  Nor does it mean that there won't be times that they'll execute their strategy perfectly, yet still the other team will win due to a bad bounce.  I doubt any of these coaches would abandon their strategy over a bad bounce or a single loss.

            The same is true when you walk into the casino.  The coach/manager of your 'team' is you.  You decide which game to play.  This is the first key step in your strategy.  In fact, this leaves you with more power than any of the aforementioned coaches.  I'm sure many of them wish that they could pick their opponent on any given day, but they don't get to.  You on the other hand can decided whether to play slots, video poker or a table game.  If you decide on video poker (always a good choice), you decide which variation and to some degree, which paytable.  You can choose the short-pay paytable or make sure you find the full-pay paytable for the game of your choice.   Joe Torre isn't going to hit the field with only 8 fielders, why should you play jacks or better video poker that pays only 8 for a Full House instead of the full 9?

            Once you decide on your game and paytable, the real nitty gritty part of the strategy begins.  There are 52-cards in the deck.  There are 2,598,960 ways you can be dealt 5 cards from a 52-card deck.  There are 32 ways to play each of these deals, ranging from discarding none of the cards to discarding them all.  You have to make a decision on each of these hands which ones you will keep and which ones you will discard.  Fortunately, in about 75% of the cases, it is fairly obvious which ones you want to keep.  The other 25% is the challenge.  Back to our baseball analogy.  Most of the time, there isn't a lot for the manager to do.  He doesn't really have to tell his leadoff batter to 'get on base' every time he comes up.  I think it is fairly obvious that's what he will be trying to do.

            Unlike the baseball manager who has to outguess the opposing manager and players, the video poker Player doesn't need to outguess anyone or anything.  Video Poker is a game of pure math.  For each of those 32 possible ways to discard, there is a finite number of ways the hand can be completed.  Using computers, we can determine the final hand rank of every one of those hands and determine, on average, how many units the Player can expect to have return to him.  It is true that we don't know exactly which cards will come up this time, but we do know that over time, the actual results will approximate our expected results.  Based on this, we learn that the best play for the Player is to play the hand whichever way results in the highest expected return of units.  We call this 'expected value' or EV for short.

            This concept is used for EVERY single decision made in the casino in every game with any strategy.  The decision to hit or stick in blackjack is decided by which of these two decisions results in the higher expected value.  We Fold on Q-6-3 in Three Card Poker and Play on Q-6-4 because in the case of the Q-6-4, Playing has a higher Expected Value than Folding.  The opposite is true for Q-6-3.

            You are in complete control of how to play these hands.  In the case of video poker, the decisions you make are ones that can result in the machine you are playing having a 100.5% payback or a 96% payback.  One payback means you will win in the long run and the other means you will lose (and lose a lot more) in the long run.

            Does playing the right strategy mean you will win every session?  Absolutely not.  It just means your chances of winning increases greatly.   In today's world, the manager that utilizes matchup charts that show how hitters have done against certain pitchers is likely to be far more successful than one who just feels that now is the right time for a certain pinch hitter - he's due to get a hit.    Utilizing the right strategy is important in a variety of situations.  I can't stress enough that the casino is most definitely one of these situations.

Player Friendly



            This past week, I met someone who was visiting Las Vegas from California.  I told him about my work with video poker and he asked me what is the best game to play.  My natural reaction to that is to just laugh.  How am I supposed to answer that?  Besides the fact that 'best' is a very subjective term.  Admittedly most people want me to answer which games are the best mathematically.  But, as this guy was stating on the strip, the odds (pardon the pun) that the best game is anywhere near is rather slim.  In fact, I'm a bit scared to tell him to play a particular type of machine in fear that he'll find it, but not at anything near full-pay.

            As the conversation continued, he told me that he likes to play Double Double Bonus Poker.  I was certainly not surprised to hear this.  It is a very popular game and he cited the biggest reason that it is - the extra chance to get a huge jackpot with the Four Aces and a kicker.  He also told me about the time that he was playing a ten-play Double Double Bonus machine and was dealt Four Aces plus the kicker on the initial deal.  Multiply that by 10 and it is a NICE payday even if you are playing a relatively small denomination or not max-coin.

            When you get dealt a hand like that, you might just be hooked for life.  It reminds me of the day I was playing golf with a friend.  Neither of us are all that good.  I still had a great time, but he wasn't happy with how poorly he played.  Well, until we got to about the 17th green and he rolled in about 30 foot putt.  Then he wanted to know when we could play next. 

            I suggested to the man that he try to find some Double Bonus machines, which at full-pay have a 100.1% payback.  Double Double Bonus has a payback of only 98.8%, also at full-pay.  I then told him that the best paying machines were variants of Deuces Wild, but only if he played proper strategy.  I really didn't know if he had a clue as to proper strategy for even Bonus games, yet alone Deuces Wild.  I figured that he would still be better off sticking to what he was familiar with than trying to play a game like Deuces without the benefit having attempted to learn the strategy.  While there are differences between Double and Double Double, at least he is still in the same general universe with those two.

            Of course, the real problem with answering his question is that he was going to be playing on the strip, which isn't exactly know nowadays for having too many full-pay machines.   Much to my surprise, I checked my source for video poker inventory - www.vpfree2.com - and found that the casino he was staying in (I won't name it), DOES have a some full-pay machines, but all at denomination of $1 or more.  It took me a second to fully comprehend this.  Usually casinos only put out full-pay machines for low denominations.  If you want to play at nickels they'll allow some winners.  Then it hit me,  NONE of their full-pay machines were over 100%.  If you want to play Double Double at full-pay, they'll be happy to let you at $5 per hand ($1 max-coin).  With a payback of 98.9%, the casino can expect to clear more than $30 an hour!  Of course, they may have some quarter machines to play, but those will be short-pay and you may find the same loss rate as a result. 

            I'm not naive.  I fully realize that most video poker machines have paybacks below 100% and that means that you will lose over the long run.  I have stated many times that gambling is just a form of entertainment for almost everyone.   But given the nature of gambling is that the cost is variable and that sometimes you can win money, your goal should be to minimize the losses and give yourself the best chance to win.

            To do this, you need to find games that have paybacks as close to 100% (or over) being played at a denomination that you feel comfortable with.  If you are okay with playing a $1 machine, that's great, but make sure you have enough bankroll for it.  Don't expect to walk over with $100 and play all night.   If you start with $100 don't be surprised if it is gone in a hurry and once your bankroll is gone, there is no coming back from it. 

            If you don't feel comfortable playing $1 machines or you don't have enough bankroll to do it, make sure that when you step down in denomination that the paytable doesn't take a big step down too.  Or, as I told this gentleman, if he really wants to find good video poker options, he might have to venture to one of the 'locals' casinos where the paytables are known to be a bit more Player friendly.

How do you say "Soft Hand" in Spanish?


            A couple of weeks ago, I discussed the strategy regarding Soft Hands in blackjack.  Soft Hands are those that contain an Ace which is counted as an 11.  Many of these hands should be played as a double down because of both the ability to significantly improve the hand (to a 17-21) AND due to the high probability that the Dealer will bust - as we mostly double down against Dealer Upcards of 2 through 6.

            As is the case with video poker, however, we must remember that the strategy changes with every paytable change or rule change.  We find slight changes to our strategy if we go from the Dealer hitting Soft 17 to the Dealer Sticking on all 17's.  However, if we go to the Blackjack variants of Blackjack Switch or Spanish 21, everything changes.

            In Spanish 21, the 10's have been removed from the decks, so that we are playing with a shoe of 48-card decks.  As may of us know, 10's and Face cards are our friends when playing blackjack.  They enable us to make good solid hands like 20's.  They help us Double Down on 10's and 11's and get strong hands.  Most importantly, they bust any Dealer hand above an 11.  When you hear about card counters, they are keeping track of the percent of 10's/Faces in the deck.  When there are more than 'normal', the game tips more into the Player's favor.  So, taking 4 of them out of each deck is NOT to the Player's advantage.

            Spanish 21 offsets this by giving the Player a host of other advantages.  The Player can double down on any number of cards.  So, if you start with a 5-3 and hit a 3 for 11, you can still double down.  Player 21's beat Dealer 21's.  Player Blackjacks beat Dealer Blackjacks.  There are also several 'bonus' 21 hands thrown in for free.  Get three 7's and win a small bonus.  The house advantage for Spanish 21 is about 0.8% which makes it a little greater than regular blackjack, but ONLY if you learn the proper strategy.

            Some of the biggest changes occur in the Soft Hands.  Not much changes in terms of how your hand will turn out.  The biggest impact is to the Soft 17's and 18's which have less of a chance to draw a 10, but a slightly greater chance to draw the little card you need to improve the hand.  The problem is that the Dealer will Bust less often.  The Bust rate for a Dealer 6 goes from 44.6% in regular blackjack to 40.6% in Spanish 21.  The changes to the Bust rate is enough to get us to make radical changes to our Soft Hand strategy. 

            To begin with, we NEVER Double down on a Soft 13 through 15 in Spanish 21.  We simply hit these hands.  We Double Down on a Soft 16 only against a 6.  However, if we have 4 cards or more, we hit these hands (remember that you can Double on 3 cards in Spanish 21).  Since there are special payouts for 5, 6 or 7+ card 21's, the lure of these payouts is stronger than the ability to Double Down. 

            Soft 17's are Doubled Down against a Dealer 4, 5 or 6.  BUT, only if the Player has 2 cards against the 4, 3 (or less) cards against the 5 and 4 (or less) cards against the 6.  If he has more cards than the minimum, he hits the hand in search of the 5+ card 21.

            Soft 18's bring us the most opportunities to Double Down.  We stick against a 7, but will Double Down even against an 8 as long as we have 3 cards or less.  We also Double Down against a 6 (5 cards or less), a 5 (4 cards or less) or a 2 through 4 (3 cards or less).

            Essentially we throw out everything we know about Soft Hands in Blackjack if we are planning on learning how to play Spanish 21.

            Next week, I'll discuss Soft Hands in Blackjack Switch and the impact of the Push on Dealer 22 rule on our strategy.  For those that want to get a jump on learning, I'm offering a 2 for 1 deal.  Order Expert Strategy for Blackjack Switch for $6.95 and get Expert Strategy for Spanish 21 for free.  Both books include a multi-color pocket-sized strategy card.  Send check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

            

The SWITCH is ON!


            My recent trip to Las Vegas was more personal than business, so I didn’t spend a lot of time scouting out new games.  One game that kept popping up without looking for it much was Blackjack Switch.  I found at least one table (and fairly crowded) in about every casino I went to.  I didn’t have a lot of time to see how people were playing it either.  I find it very hard to believe that most people know the right strategy for switching, although many hands are obvious.  I’m also guessing that many people were using whatever strategy they use for regular blackjack to guide them when to hit or stick and this could be rather problematic to their bankroll too.

            To refresh everyone’s memory, Blackjack Switch requires the Player to play two hands of blackjack.  After the initial 2 cards are dealt to everyone and the Dealer’s upcard is exposed, the Player has the option to request that the 2nd card of each of his two hands be switched with one another.  So, if dealt a 10-6 and a 5-10, he can change this to be a 10-10 and a 5-6, which is quite a bit better.  The big tradeoff is that if the Dealer busts with a 22 it is considered a push to any Player’s non-bust hand except for a Natural Blackjack.  It is this rule that makes all the changes to our basic blackjack strategy.

            It is nearly impossible to describe the Switch strategy in a column like this.  With 10 possible upcards and a couple dozen different combinations of individual hands, there are literally thousands of possible combinations.  Instead, I have created a table of expected values for each combination and you need to add up the two values for your pre-switch hands and the two values for your potential post-switch hands – and whichever provides the higher expected value is the right strategy.  Again, many of the hands are obvious, so you won’t need to do this for those.

            Easier to describe is the new hit/stick strategy.  For starters, throw out most of what you think you know of blackjack strategy.  The Dealer busts with 22 a LOT of the time.  These hands becoming pushes means relying on the Dealer to bust to provide you with a win is greatly reduced.  As a result of this, we find that we Double Down and Split far less often – or more correctly, in far fewer circumstances.  We NEVER Double Down into a 10/Face or an Ace (not even with an 11).  The ONLY Double Down with Soft hands are a Soft 17 or 18 looking into a 5 or 6.  Splitting is reduced quite a bit as well.  The rule of ‘always’ splitting 8’s is gone.  Don’t split them into 10/Face or an Ace. 

            The interesting thing is that although there are far fewer conditions in which we Double Down, we don’t necessarily Double Down much less frequently.  As a result of Switching, we create the Double Down situations far more often.  We also wind up with many more strong no-hit hands – which is hardly a bad thing.

            The rules for hard hands only undergo a few changes.  Don’t yell at a Player for hitting a 12 into a 4 as that is the right move.  Hitting a 13 into a 2 is also correct.  However, 14 and above remains as per normal blackjack – only hit if the Dealer has a 7 through Ace as his upcard. 

            Blackjack Switch provides the opportunity for a Player to earn the same payback as regular blackjack – about 99.5% - while spicing up the game a bit.  The hit/stick strategy is actually probably a bit easier than regular blackjack, BUT it MUST be learned anew.  If you choose to use regular blackjack strategy on Blackjack switch, you will double the house advantage.  More critical is learning when to switch.  If you NEVER switched, you’d be giving the casino a nearly 10% advantage.  Of course, even if you just guessed at the switch strategy, you’d probably do better than that – but still far off from Expert Strategy.  Just making a handful of mistakes repeatedly could easily  double, triple or quadruple (or worse) the house advantage.

            A few months ago, I released Expert Strategy for Blackjack Switch.  It is a 14-page booklet that explains the rules of the game and how the strategies (both Switch and hit/stick) were developed.  It will also give you some idea of what to expect when you play it.  It comes with a full-color business-sized strategy card for you to take with you to the casino, which includes BOTH strategies on it.  It normally sells for $6.95, but for Gaming Today readers I will make it available for $5.95.  If you’d like to order ONLY the strategy card, it is $2.95 and if you’d like additional cards (when you buy the book), they are only $1.50 each.

            Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.  There are now about 150 Blackjack Switch tables out there.  Don’t be left behind – the Switch is ON!

The Case For War



            No, not the War in Iraq or Afghanistan or even Libya.  To be honest, I can’t believe I’m writing about this game.  I can’t believe people now gamble on a game I used to play with my grandmother when I was 4.  What next, Casino Candyland?

            But, if people are going to play it, I have a responsibility to write about it and inform the players about what they are playing, what to expect and what strategy to use.  Much to my surprise, when I was done with the analysis, I found that the payback for Casino War really wasn’t that bad given the type of game it is.  So, if you’re looking for a simple game, requiring very little strategy and no knowledge of Poker, maybe this game is for you.

            For those who are not familiar with the game, it doesn’t get any easier than this.  The Player makes a wager.  The Player gets one card.  The Dealer gets one card.  High Card wins.  If the Player wins, he gets even money on his wager.  In case of a tie, the Player can either surrender half of his original wager or make an additional wager equal to the first one.  If he makes this wager, the Player and the Dealer each get an additional card.  Again, High Card wins.  If the Player wins at this point, he will win even money on his 2nd wager and push on the original wager.  If the Dealer wins, the Player loses all wagers.  If they Tie again, the Player WINS even money on both wagers.  There is also a sidebet that pays 10 units if the Player and Dealer Tie.

            Casino War is usually played with a shoe of 6 or 8 decks.  From the Player’s perspective, there really isn’t much difference between the two.  The overall payback of the game is little higher with 6 decks, but not enough to get worked up over.  The sidebet pays about 1% more with the 8 deck shoe because ties are more common, but as we’ll soon see, this is immaterial.

            The entire house advantage comes from Ties.  Without them, Casino War would be a 100% game with no advantage to the Player or the House.  As such, we can calculate the house advantage by calculating the frequency of Ties.  Once a Tie occurs, the Player and the Dealer will still each win with the same frequency, but when the Player wins, he will win even money on one bet and push on the other.  In essence, he will be wagering 2 units to win one.  The casino gives a small advantage back to the Player by paying even money on both wagers if they Tie again after the initial tie.

            When all the math is done, we find that the overall payback of Casino War is a rather respectable 97.8%.  Obviously, this is not what we can expect to achieve from Blackjack, Spanish 21 or even Four Card Poker, but it is in the same range as Three Card Poker.  Given that there is almost no strategy involved, this is not too bad.  The only strategy question that does exist for Casino War is whether the Player should ever surrender half of his original wager after the first tie.  Although the player has a significant negative expectation once the first tie has occurred, he is still better off wagering instead of Folding.  This is essentially because of the possibility of the Double Tie which will allow the Player to win even money on both wagers.

            Personally, I prefer games with tougher strategy that provide more of a challenge, but I believe that no matter what game you’re going to play, you should go in with your eyes open, play with the best strategy and know what to expect.            

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!”


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 (www.facebook.com/pages/Blackjack-Switch/167559943295302)

            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 www.gambatria.com 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