Why Play Max Coins?

            Generally speaking, I advise players to play max-coins when playing video poker.  For most versions, this means 5 coins.  The penny Player puts up 5 cents, the nickel player 25 cents, the quarter player puts up $1.25 and the dollar player has to put up $5 per hand.  This is done for one simple purpose.  On most video poker machines, the top payout - the Royal Flush - changes from 250 for 1 to 800 for 1 when that 5th coins is put in.  If you are playing a Progressive, the only way to win that jackpot is to play 5 coins.

            A payout of 800 for 1 on the Royal is worth approximately 2% of the total payback of the machine.  A payout of only 250 reduces this down to about 0.65%.  So, the Player is giving up more than 1.25% of payback if he plays below max-coin.  In similar fashion, if the machine is offering a Progressive, which should push the Royal payout to above 800, then the Player would be surrendering even more payback by playing below the max-coin level.

            The notion of playing max-coin does NOT mean you should wager 5 times the amount you feel comfortable wagering.  Instead it means you should consider lowering your denomination to the next lower level and then play 5 coins.  So, rather than playing 1 quarter, you should play 5 nickels.  This, of course, assumes that all things are otherwise equal.  It is certainly possible that when you go to a nickel machine (or change to the nickel option on a multi-denominational machine) that the paybacks may change as well and you may find that the payback on the nickel machine is well below that of the quarter.   This makes things a bit more complicated.  If the quarter machines pays 99.5% at max-coin, then it will be closer to 98% if you play 1 quarter.  If the nickel machines pays 98.5% at max-coin, then you'll still be better off playing max-coin nickels.

            There are a few times when you may want to play less than max-coin.  The first is when you are first leaning how to play.  As you are more apt to make mistakes at this point, you might be better off simply playing 1 nickel at a time.  Yes, you will be playing at a lower payback, but at this point, your goal is to become a better player while playing on a real machine.  Ideally, you'd spend most of your 'learning' time playing on your computer (or phone or tablet) at home for free ,but I realize that playing for free may be a lot less exciting than even playing for a single nickel.

            Another reason that you may not want to play max-coin is your bankroll.  If your bankroll is not large enough to support playing max-coin then you might be better off playing single-coin.   Once your bankroll is gone, you're done and you need to make sure you have enough money available to ride out the cold streaks.  Of course, one solution to this issue is again to simply drop down in denomination.  So, this advice really only applies if machines of a lower denomination are not available.  Since the advent of the multi-denominational machine, finding machines that play the denomination you want to play has become much easier, however.   So, this second reason may have limited practical applications.  But, if you find yourself in a situation where your bankroll will support 5 nickel play, but you only have quarter machines available, you may want to consider playing a single quarter as opposed to five quarters.

            One critical point to consider.  Just because you switch a machine from quarter play to nickel play, do NOT assume that the paytable is the same even if you are switching to the same variety of video poker.  There are no requirements that state that a machine must use the same paytable when you move from one denomination to another.   In similar fashion, don't assume that a bank of similar (or identical) looking machines all have the same paytable.  Casinos frequently and presumably purposefully mix the machines up, making sure to sprinkle higher paying machines in with lower paying ones.  I dare say that you may find no rhyme or reason to the pattern of machines on the casino floor.

          

Frustration

            I consider myself to be a very competitive person.  Anybody who has ever played against me in a board game or on a sports field is pretty aware of this.   I play fair and hard.  I'll never cheat and don't throw tantrums.  But I really hate to lose.  So, you can only imagine what I feel like when I'm having 'one of those nights' while playing video poker.   Gambling isn't exactly the type of thing one does if they hate to lose.  Even if you're playing video poker or blackjack, games that are near 100%, you're still going to lose more than 50% of the time over short sessions.  Not a bad record if you're the Marlins, but I prefer to win, well, closer to 100% of the time.

            When I'm on the sports field, I have a significant amount of control in the outcome.  If I'm playing tennis, well, it is just about all on me.  If I'm playing softball, I can do my best to get on base when I'm at bat and make all the plays that come to me.  I can't help my right fielder catch the ball, however.  In this regard, gambling is more of a team sport than a single Player sport.  I'm an expert at just about any game in the casino that I will sit down to play.  So, I can make sure that I'll play each hand the way I should to maximize my overall payback.

            Unfortunately, luck still plays a significant portion of casino gambling (kind of like my right fielder catching the flyball?).  I can't control which hands I'm dealt.  In the long run, I know I will get my fair share of each type of hand.  In a given night, the difference between winning and losing is about getting your fair share of key hands.  You're not going to make money off of 4-Card Straights, so you don't usually keep track of how many you got. 

            When we look at the final paying hands of video poker, it should be no surprise that most of the payback comes from the bottom 3 hands.  Jacks or better gives us about 21-22% of our payback.  Two Pair gives us 26%, and Three of a Kind gives us another 20-21%.  This is almost 70% of a total of 99.5% payback.  Straights give us over 4%, Flushes over 6% and and Full Houses around 10%.  That brings us to 90%.   Four of a Kinds give us about 6%, Straight Flushes a mere 0.5% and Royal Flushes the remaining 2%. 

            The more common a hand is, the more likely no matter how weird your session is going that at the end of it, you're going to have very close to the number of those hand that you are supposed to.   So, if you play 3000 hands and the average shows that you should have about 650 High Pairs, you're not going to find out that you only had 500 of them.  Maybe you have 630 on a bad night and 670 on a good night, but you'll get very close to the 21-22% payback you are supposed to.

            On the other end of the spectrum is the Royal Flush.  If you play 3000 hands, you're well below the roughly 40,000 hands it takes to play to catch a Royal.  If you play a session and miss the Royal, you're inherently playing at 97.5%.  If you hit one then, well, you're assuredly playing well over 100%.   As a result, there really isn't a lot to discuss where the Royal is concerned.  It is literally hit or miss.  Straight Flushes simply don't add enough to the mix and are also so rare that you can't really look to them for a good or bad night.

            The critical hand is the Four of a Kinds.  Earlier I said that they make up 6% of the payback.  That is on a jacks or better game.  Move to Bonus or Double Bonus or Double Double Bonus and these number goes way up.   You win or lose in these games based on two key factors.  Do you get your fair share of Quads and which Quads do you get (when playing the bonus games)?   If you play 3000 hands, you can 'expect' to hit about 7 Four of a Kinds.  It would not be uncommon to play this many hands and get only 2 or 3.  If you have one of these nights, you're not likely to walk out a winner.  Quite frankly, you may not walk out with any of your bankroll left.  Fortunately, it is just as common to get 10 or 11 of them.  In these cases, you are very likely to walk out a winner.  If you're playing Double Double, you'll also want to hit some of the bonus Quads and/or the 'double' bonus quad with one of the kickers. 

            Playing the right strategy is, of course, a critical component of getting your fair share of Four of a Kinds.  But, the right strategy does only so much to make the 5th card in Quad 3's also be a 2, 4 or Ace.  Sometimes it just takes luck to have that good night.  Sometimes my right fielder actually catches the ball.  All I can do is hope.

Still Wild About Deuces Wild

            A few weeks ago, I wrote about full-pay deuces wild video poker and it's 100.6% payback.  It has gotten harder to find 100+% payback machines, but this one can still be found in many of the casinos that cater to the locals (i.e. OFF the strip!)  People are still amazed to find that such machines exist at all.  As I've written many times, the casinos don't mind leaving a few of these around in lower denominations.  This way they can say that they have positive payback machines, but they don't really have to worry about the professionals swarming on them.

            Even if you are an Expert Player who can play at 800 hands per hour, you're dropping $1000 in the machine every hour.  At 0.6% advantage, you can expect to win $6 per hour.  It certainly beats losing, but no one is getting rich at $6 per hour.  If you're willing to sit in a casino for 40 hours per week just as you would any other job, you might be able to clear $12,000 per year.  Of course, you won't be collecting a regular paycheck.  Some weeks you're going to lose and others you're going to hit the big payout.  But, at the end of the year, should be fairly close to that $12,000.  This will be your reward for playing roughly 1.6 million hands of video poker and putting into the machine a mere $2 million!

            I'm not going to recommend you quit your day job and try this.  In fact, I won't even recommend you give up looking for work, if you currently are, and become an professional video poker Player.  For almost everyone reading this column, you are a recreational player and video poker is a form of entertainment.  Some nights you win, some nights you lose.  Depending how long you play for per session, you'll lose roughly 2 out of every 3 times you play.  But, if you pick the right machines and learn the right strategy, your night out might cost you $20 and you can get some entertainment and a few drinks.

            With a 100.6% payback, you would definitely be picking the right machine with Deuces Wild.  So, the only other thing for you to do is to learn the right strategy.   At first glance, the strategy table for Deuces Wild might look daunting due to its size, but when you look closely, you'll see it is broken down by the number of Deuces.  If you make sure to learn it this way, you'll find it much easier to learn AND you'll be doing yourself a huge favor in terms of learning to play properly.  Deuces is not a hard game to learn.  It is just so vastly different from any other game, that people make lots of mistakes.

            One of the most important things to learn is when to hold just the Deuces when drawing.  it is so tempting to want to hold the best possible portion of a hand, but sometimes you simply box yourself into a corner by doing so.  For example, if you are dealt the following:

2          2          6D       7C       QD

            You may be very tempted to hold the 4-Card Straight figuring that there are so many possible cards to complete the Straight (a 3, 4, 5, 8, 9 or 10).  If you pick up a 6 or a 7, you'll have Quads.  This is clearly superior to going for the 4-card Flush, which would require one of the remaining 11 (or 10 if the 2 was a Diamond) diamonds to make a Flush or a 6 or Q to complete the Quads.

            The problem with either of these is that they completely eliminate the possibility of any of the bigger payouts while in essence targeting some of the lower paying hands.   Further, we the two Deuces, we can do no worse than wind up with Trips, so it is not like we are giving up a sure winner.  Proper strategy says that unless you have a Royal, Five of a Kind, Straight Flush, Four of a Kind or a 4-Card Royal, you hold ONLY the two Deuces.

            When we take a closer look at the strategy, we find that we ONLY go for a 4-Card Straight or 4-Card Flush IF we have NO Deuces.   Be very prepared when dealt Deuces in Deuces Wild to frequently play them 'bare' (hold only the Deuces).  Of the 2,598,960 possible 5-card initial deals, 48 will consist of 4 Deuces (obviously, you're done when this happens).  Three Deuces will occur 4,512.  About 90% of these will be played as just the three Deuces.  Two Deuces will happen 103,776 and nearly 75% of these will be played as just the two Deuces.  A single Deuce will be dealt 778,310 times.  About 45% of these will be played as the single Deuce.  This is the 3rd most common hand in Deuces, following a Pair and a Razgu. 

            If you want to learn to play Deuces Wild, we have three different products that can help you.  You can find the strategy tables for full-pay Deuces Wild in our book Expert Video Poker for Las Vegas ($5).  We have the strategy table for full-pay Deuces Wild plus a variety of variations of full-pay Deuces Wild in Winning Strategies for Video Poker ($5).  Lastly, we have our Deuces Wild Tipsheet ($2.95) which contains the strategy tables for 3 different Deuces paytables and has the most detailed information on the full-pay variety of any of our 3 sources.  You can order any or all of these directly from us.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133

Jackpot Power

            As we get deep into the political season, we're all going to be frequently reminded how it is possible to make numbers say just about anything we want them to.  Quite frankly, it is not just the arena of politics this happens in.  It can be done with all types of math - casino math, included.

            By now, many of you well know that a full-pay jacks or better machine pays about 99.5%, which is a very solid number for a casino game.  Many of you may even be aware that the Royal Flush contributes 2% of this amount.  But what does this really mean?  It means that if the machine was defective and NEVER dealt a Royal Flush, but dealt all the rest of the hands in the frequencies we would expect, the payback of the game would be closer to 97.5%.   This is about the same payback we would get from a short-pay (8/5) jacks or better machine so should we expect roughly the same experience?

            ABSOLUTELY NOT!  One of the measures I like to use is what I call a 'session simulator'.  This process simulates a session of play for a particular game.  For video poker, I use 3 hours of play at 700 hands per hour.  For this particular demonstration, I ran 1000 of these sessions under 2 conditions.  The first was a full-pay jacks or better machined that NEVER paid a Royal Flush.  To be clear, the only way this could ever really happen would be if the machine was broken or rigged.  As I don't believe the latter happens in any reputable casino, nor would a broken machine likely stay on the floor for this many hands - this is merely for illustration purposes and to prove a point.

            In this scenario, the Player still managed to walk away a winner about 28% of the sessions.  This compares to about 29% when a regular full-pay jacks or better is played.   Why is there such little impact to this?  Under normal circumstances, the Royal would hit only about every 20 cycles or so.  Some of these cycles would already be winners, so the Royal Flush doesn't change this.  It only changes the magnitude of the win.  In the cases where the session was about to be a loser, the Royal most likely flipped ONLY these into winners.  However, when we look at the long run, the overall payback of ALL the sessions put together was where we expected it to be - at about 97.5%

            When we put the 8-5 jacks or better machine (with the Royal occurring as it should), we find that the Player wins only 14% of his sessions.  His winning sessions are cut by half!  The overall payback of all the sessions is also what we would expect it to be at 97.5%.

            So, why do two different machines paying about the same amount create such different short-term results?  This goes to a concept of volatility.  There is a mathematical formula for volatility, but I'm afraid if I start explaining it at that level, you're all going to turn the page.  That is why I like to use the session simulator as a means of explaining what volatility does and is.  When a large amount of the payback is concentrated into a very infrequently occurring hand, there is a larger degree of volatility.  In the case of the full-pay jacks or better game without the Royals, I removed a large degree of the volatility.  This is why a game with a considerably lower payback that the original version can still have a not very different short-term result.

            So, what does this all mean for you?  There are two points I'd like you take away from this week's column.  The first is to realize how important the Royal Flush is to your long-term results in video poker.  If you are on a cold streak of Royals, your short-term results may not look all that different from 'normal', but you may find that your larger bankroll is suffering.  If you play for 3 hours at a time, you may find that you're still leaving the casino a winner 3 out of 10 times, but for some reason your wallet still seems a lot lighter than it should.  The good news is that in the long run, those Royals will show up as often as they should (assuming you are playing Expert Strategy).  Ironically, when the Royals are running hot, you'll still walk away a winner about 3 out of 10 sessions.  But, a few more of those sessions will be big winners.

            The second point I want everyone to think about is if a 'mere' 800 unit payout occurring roughly every 40,000 hands can make this type of impact to a game, imagine what happens on a slot machine that can pay hundreds of thousands or millions of dollars for a 'hand' even more infrequent.  The average payback on a slot machine is ONLY 92-93%.  If we consider that many of them will have a massive top pay that might occur only every few hundred thousand hands (or million hands), what % of the overall payback does this account for? 

            With these occurrences being so infrequent (and COMPLETELY unknown as to how frequent), the payback of the machine without the jackpot could easily be 80-90%.  I'd put this through my session simulator but as it is not possible to know the frequency of all the payouts, there is no way to do it.  Just for fun, I built an 82.5% video poker paytable and put it through the process and it showed that the Player will walk away a winner only 5% of the time.  As we've already shown, it would then be possible to create an infrequent, very high paying jackpot which will push the overall payback up, while barely changing the short-term results. 

            The end result is one that we know all too well for slots.  Very few people walk away a winner even in the short run, which pays for the handful of people who win the big jackpots.  I'll take video poker any day!

Video Poker Progressives

            A couple of weeks ago, I described in detail how the math behind Progressives work.  In that column, I mentioned how video poker progressives works just a little different.  There are still two paybacks to be concerned with - the long term theoretical that the casino is concerned with and the specific payback at any point in time that should be the attention of the Player.  The majority of the calculation is still the same in that we multiply the payout of a winning hands by the frequency of the winning hands  and sum up these values.

            What is different about video poker is that the frequencies of the different winning hands can vary as the amount on the meter changes.  For those of you who are video poker Players, this should be no surprise.  For years, I've been telling you that a single unit change in the payout of a hand not only changes the payback but can change the strategy.  Each time you change the strategy you potentially increase the frequency of some hands at the expense of others.

            As a very simple example of this, imagine how the strategy changes as we go from a standard full-pay jacks or better machine to a Double Double Bonus machine.   Because the payout for Four Aces is so high, we actually find that the Player should discard Two Pair in favor of a single Pair of Aces.  This will obviously reduce greatly the frequency of Two Pairs and Full Houses and increase the frequency of Three of a Kinds and Four of a Kinds. 

            So, it should be no surprise that as the jackpot for a Royal increases above 800 that the strategy will begin to shift.  Hands with the potential to be a Royal will have their expected values increase.  This will lead to more Straights, Flushes and of course Royals and the expense of Pairs, Trips and Quads.  Of course, we will also throw away a variety of partial Straights or Flushes to go for the Royal, so this will work against the Straights and Flushes and might increase the number of High Pairs. 

            Thus, pinpointing the exact frequencies can be a bit tricky.  Fortunately, the far easier of the paybacks to determine is the payback at any point in time.  This is because at any point in time, we can know the exact amount of the Progressive jackpot and use this number to determine the exact strategy and in turn the exact frequency of each hand.

            The most common video poker Progressive is an 8-5 machine, meaning it pays about 97.3% when the jackpot is reset to 800 (per unit wagered).  At this level, the frequency of the Royal is about 1 in 40,200 hands.  If the jackpot were to climb to 1600 (per unit wagered) then the payback of the game will go up to about 99.5% and the frequency of the Royal goes up to 1 in 32,700 hands.

            Of course it is rather unlikely that you're going to see a Progressive for a Royal get this high.  With only 1% of the amount wagered (at most) going to the meter, the average amount that will be added to the Progressive Jackpot is somewhere between $327 and $402 (1% of the previously mentioned frequencies).  Of course, something that can occur 1 in 40,000 hands or so can easily occur every 10,000 hand or 80,000 hands.  So, it is not impossible to see the progressive meter go to 1600.  It would have to go to about 1800 for the game to become positive (payback over 100%).  This is not impossible, but not very likely.

            As the payback goes up, the strategy changes and the frequency of the Royal increases, making it harder and harder for the jackpot to keep increasing as the likelihood that it gets hit goes up.  Because of this, it is a bit harder to calculate easily the long term theoretical payback.  It is reasonable, however to approximate it using the same process used for regular progressives.

            In this case, I would take the frequency of each hand using the reset value of the jackpot and multiply each by the payout of the hand and sum these up.  Lastly we would add the percent of each wager going to the jackpot to the total.  This means that the long term theoretical payback of a Royal paying 8-5 with an 800 unit reset amount is about 98.3%.

            I have to admit, if I were designing a paytable for a video poker progressive, I would probably make the likelihood of the game going over 100% a bit more common.  I think it would be a lot of fun to the frenzy that would/should occur each time the payback at any point in time goes over 100%.

            

Royal Alterations

            Last week’s column discussed how by altering your strategy, you can make Royals appear more often.  Let’s face it, by altering your strategy, you can make any hand you want to appear more often.  Just because Royal Flushes are the highest paying hand does NOT mean that by getting more of them you will automatically win.  If your goal is the bragging rights as the King or Queen of Royal Flushes, it might be worth it to you.  In reality, however, you’ll also be ‘flushing’ your bankroll by doing this.

            That isn’t to say that there isn’t a right time to alter your strategy in order to make a Royal appear sooner.  The obvious case of this is when you are playing a Progressive, where the meter is considerably above the normal 800 for 1 payout.  The intriguing part about playing Progressives is that the strategy keeps changing as the meter increases.  Even under normal circumstances it would be unusual for the meter to get to double the normal payout, but nowadays with some professionals monitoring progressive payouts, the likelihood is even less.  As soon as the meter gets to the point where the game is positive, a team of Players can hit a bank of machines and just keep playing until the jackpot is hit. 

            The Expert Player realizes that as the jackpot goes up, the strategy changes and the frequency of a Royal Flush can increase, which can push the payback up even more.  Using Expert Strategy for a full-pay jacks or better machine will result in a Royal (on average) every 40,400 hands.   If the Royal is paying 1600 for 1, we alter our strategy to make a Royal appear (on average) every 32,700 hands.  This increase in frequency allows us to extract an additional 0.9% of payback out of the Royal Flush hand.  Of course, this change in strategy costs us about 0.7% of payback on all the other hands.  The net increase is 0.2%, however.  So, you can play the Progressive using the altered strategy at 99.5% or you can use standard (8-5) strategy and play it at 99.3%.  It doesn’t seem like much of a choice to me.

            So, what are some of the changes we use when playing a Progressive paying 1600 for 1 on a Royal?  One of the biggest is that the 3-Card Royal now outranks a High Pair.  Yep, this one is going to hurt.  You going to throw away a sure winner (High Pair) and go for the Royal Flush.  Your odds of hitting that Royal is a bit more than 1000 to 1.  But, it’s paying 1600 for 1!  Throw in the fact that you still have many chances to hit a Straight Flush, a Flush, a Straight, Trips, Two Pair and a High Pair and quite frankly, the math isn’t even close.  The 3-Card Royal has an expected value of more than 2, while the High Pair is down at 1.5.

            Another significant change in our strategy is that the A-10 Royal is now playable.  Normally, when playing jacks or better, we do NOT hold a 2-Card Royal consisting of A-10.  We only have 1 way to fill it for Straights and/or the Royal Flush (with the JQK), which greatly reduces its expected value.  However, with the Royal Flush’s payout pumped up to 1600, we’re still better off holding the 2-Card Royal vs. holding just the Ace.  Keep in mind, however, that this hand is just barely playable.  This means that many other combinations of cards might be held instead (such as a 3-Card Straight Flush), so don’t forget to look at your WHOLE hand before getting overly excited about a suited A-10.

            Besides learning some of the changes to the strategy for a Progressive, another key point is learned.  Every change to the paytable can impact the strategy.  Now, if you sit down and play a full-pay bonus poker game using jacks or better strategy, I’m not saying you’ll get wiped out in 10 minutes.  But, what is the point of learning strategy if you’re just going to wing it when you change which type of game you’re playing.  0.1% or 0.2% might not seem like a lot to give up – but in reality, this may increase your loss rate by 20-50%!

            One of the best ways to learn how to play all the different games out there is to learn the strategy tables from a book like Winning Strategies for Video Poker and then practice what you’ve learned on your PC using Masque’s Video Poker Strategy Pro.  For a limited time, we’re offering a package of both the book and the software for only $14.95.  For an additional $5 ($19.95 in total) we’ll also include Video Poker: America’s National Game of Chance which is 200 pages of Lenny Frome’s best articles, quizzes and stories.  If you’d like to order, please send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603. 

Royal Appearance

            Last week’s column was prompted by a reader who raised some concerns that Players who use their frequent player cards are somehow cheated by casinos.  The ‘proof’ of this is that some locals (i.e. frequent Players) don’t seem to get as many Royals as the tourists.  Previously, I had cited at least two reason for this. 

            The first is selective memory.  We tend to remember things we want to remember.  When we go through an extended cold streak, every other scream of “Royal” is burned into our brains.  I’m guessing that in the week you hit your last Royal, someone else did too that week, but it didn’t bother you one bit.  If you’ve gone a year without one, everytime someone gets one, it hits you like a ton of bricks.

            Secondly, even if you’re trying to be relatively objective about it, you also have to remember that ‘you’ are greatly outnumbered by ‘them’.  Even if there are a couple of you playing together, there are dozens if not hundreds of other people playing around you.  It is no surprise that they WILL actually get more Royals than your group will.

            There is, of course, another possibility – other people ARE actually get more Royals than you are!  So, am I buying into the whole ‘rigged’ video poker machine theory?  ABSOLUTELY NOT! 

            But, the number of Royals you get over an extended period of time is greatly influenced by the strategy you use.  So, there are two possibilities.  YOU may be using the wrong strategy which is reducing the probability of a Royal OR the other guy is using the wrong strategy which might INCREASE the probability of a Royal.

            Let’s look at these two scenarios.  The proper strategy for any particular video poker machine is one that maximizes the overall payback, not one that maximizes the probability of hitting a Royal.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        5♠

            Do you hold the Low-Pair?  The 4-Card Flush?  The 3-Card Royal?

            The correct answer is the 3-Card Royal.  If you’re playing one of the other two, not only are you hurting yourself from a payback perspective, you’re lowering your chances of hitting a Royal.  By the way, the decision is not even close.  The expected value (EV) of the 3-Card Royal is 1.41.  The 4-Card Flush has an EV of 1.22 and the Low Pair a meager 0.82.

            So, if you’re not playing this hand correctly, don’t be surprised if some others around you are hitting more Royals.  Of course, they may have their own issues.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        Q♠

            The correct answer is hold the High Pair with an expected value of 1.54.  Now, you may be doing this, but that ‘tourist’ behind you may not.  What is the impact of holding the 3-Card Royal.  Well, he’ll lower his overall expected payback, BUT he will increase his probability of hitting a Royal.

            The examples I used here are not the most common occurrences, so these will not make a big difference to the frequency of a Royal happening.  Far more common are the hands that include a 2-Card Royal that also include 3-Card and 4-Card Flushes and Straights.  I have little doubt that there are many novice Players who get Royal fever and just play every 2-Card Royal instead of 4-Card Straights and Flushes or 3-Card Straight Flushes.  Doing so, will make them hit more Royals than you will, but they won’t be any richer for it. 

            Under normal circumstances, for a jacks or better machine, a Royal should appear about once every 40,000 hands or so.  By altering one’s strategy it is very easy to reduce this to once every 30,000 hands or so, which is considerably more frequent.  But, it will come at a cost of lowering the payback by a significant amount too.  So, the next time you’re upset that someone else got a Royal, start worrying about how you’re playing and not what’s happening around the corner.  They may pay dearly for their Royal appearance.

           

To Card or Not to Card

            This past week I received an e-mail from a reader who wanted to know whether the casinos could essentially reward “non-frequent” players with better hands in video poker.  As we all know, the craze of the past decade or so is to have a frequent shopper card for each store.  My keyring is lined with them.  I’ve got one from grocery stores, drugstores, bookstores and countelss others.  Casinos are no different.  When you play, you put your frequent player card into the machine and it keeps track of how much you wager and in turn rewards you with points for comps, etc…

           

            So the question being asked is – can/do the casinos make the machines pay more for people who do NOT put a card in the machine.  The reader who sent this e-mail was echoing sentiments he has heard from other local and/or frequent Players.  He also stated that it ‘seems’ like more Royal Flushes go to non-regular Players.

           

            I could probably write several pages about this topic, looking at it from a variety of different angles.  I’ll try to hit the highlights of some of these today.  As I have stated many times in this column, it is the law in most casino jurisdictions (Las Vegas certainly included) that any video game that uses what appears to be an ordinary object (i.e. a deck of cards) MUST be completely random.  This means that at any point in time, the probability of any card not already dealt showing up is the same as any other card not already dealt showing up.  Given this, it is absolutely NOT possible to favor one set of Players over another.

            This is NOT to say that you can’t make a computer do this.   As an IT professional with over 20 years of experience, I know that it would be very easy to favor Players based on such criteria.  Even if it were legal to do so, I’m not so sure that I would necessarily favor the infrequent Player over the frequent Player at casino games.  As we all well know, many tourists will joyfully lose money at a posh casino as long as they can enjoy the marble columns while they are doing it.  Locals, on the other hand, tend to look for better paytables and care less about the physical surroundings.

            It is in this very topic that the three key components of Expert Strategy collide – knowing which games to play, knowing the right strategy and knowing what to expect.  My reader did not present any true evidence that one group of people are getting Royals at a higher rate than another.  He only stated that it ‘seemed’ that way.  Nothing makes the casinos happier than a Player doing something less than optimal because it feels right.  There is only ONE way for things to swing when a Player does this.  In the long run, the casinos will win more and the Player will win less.

            While the casinos have certainly cut back over the past few years on points, comps and cashback, there is still one simple math fact.  If we go with the notion that the casinos DO NOT play favorites based on whether or not the card is in the machine, then removing your card from the machine only serves one purposes.  You get an overall lower payback by not getting your comps and cashback.

            The decision to pull one’s card from the machine would appear to be based on the notion that it ‘seems’ as if others are getting more Royals and thus it MUST be because the house is favoring someone else.  All of us who have played for hours have gone through dry periods in which we’re sure that everytime we discard a King, it is replaced by a King – especially when drawing on a 4-Card Straight or 4-Card Flush.  Or we seem to be dealt an overabundance of a certain Low Pair which never seem to turn into trips.  A significant portion of this is simply our minds playing tricks on us.

            There is only one of you.  Even if you’re playing with a spouse or a friend or two, there is still only two or three of you.  Then there is the rest of the casino, which you ‘assume’ are not regulars – especially if you don’t remember seeing them all the time.  Even if they truly are NOT regulars and they are NOT playing with a card in the machine, there are still far more of them than there of you.  When you hit a Royal, you probably don’t notice all the people around you who haven’t hit them.  When you go through a rough patch, all of a sudden you notice every time someone else hits one. 

            Of course, there IS the possibility that other Players are getting Royals more frequently than you are – but it doesn’t mean the casinos are out to get you.  Nor does it mean that the other guy is doing himself any favors.  But, I’ll save that for next week!  In the meantime, leave your frequent Player card in the machine.  Don’t make a cold streak even worse by leaving your comps and cashback on the table.

That's Why They Call It Gambling

            I’m in Las Vegas this week, penning this column from my hotel room.  The other night, I was playing video poker at Sam’s Town, next to a guy who was playing single-line Multi-Strike video poker.  I’m familiar with how the game works, but I have to admit, my knowledge of the strategy changes for this intriguing game is extremely limited.  I know that you have to alter your strategy to increase win frequency at the expense of payback when you are on the lower 3 lines without having received a ‘Free Ride’.

            For those unfamiliar with the game, allow me to try and explain the game.  There are four ‘levels’ in Multi-Strike.  To move up to the next level, you have to get a winning hand on the prior level.  Each of the levels pay progressively more than the previous one.  Thus hands on Level 1 pay 1 times the paytable.  Level 2 hands pay 2 times the paytable.  Level 3 hands pay 4 times the paytable and Level 4 hands pay 8 times the paytable.  To play the game you have to wager at least 1 unit on EACH level.  Thus to play ‘max-coin’ you have to wager 20 units – 5 coins times 4 levels.  This means you are paying for a level that you may never reach for each hand.  On each level, you play a brand new hand of video poker. 

            Roughly speaking, a Player playing proper ‘normal’ video poker strategy will win 45% of his hands.  This can be raised a bit if you tweak the strategy to focus a bit more on winning as opposed to how much you win.  However, at 46-47%, you would get slaughtered playing Multi-Strike because the odds of winning the 3 hands at Levels 1 through 3 would not be enough to be worth putting up the extra coin each time.  Thus, the game also incorporates what is called a ‘Free Ride’.  This is randomly generated by the machine to give the Player an automatic trip to the next level.  The Player continues to play the level that gives him the Free Ride, but even if he loses the hand, he still proceeds to the next highest level.  The impact of this feature is to bring the win frequency very close to 50%.

            I’ve never analyzed Multi-Strike, so I can’t provide you with a payback of the game.  Also, there are numerous versions of the game to correspond to regular games (i.e. Jacks or Better, Bonus, Double Double, etc…).  Additionally, the game does not clearly provide the frequency of the Free Ride feature at each level which is required to calculation an accurate payback.  I have seen published numbers from IGT (maker of the game), but there is no way to know for sure if there aren’t different variations and which games are programmed for what frequency.

            Then again, the point of this particular column was not necessarily an analysis of Multi-Strike.  The Player I mentioned earlier came across an interesting hand.  He was dealt an Ace High Straight that was also a 4-Card Royal on Level 3.  The Straight paid 4 units times 4 (for Level 3) for a total of 16 units (I didn’t notice what denomination the guy was playing).  He now faced the choice of sticking with that win and guaranteeing a shot at Level 4, OR going for the Royal Flush which would pay 1000 units (250 times 4).  By going for the Royal, he would also risk not winning at all and thus, not being given an opportunity to play the Level 4 hand.

            First, I’d like to look at this as if it didn’t happen in Multi-Strike.  So, the question is, when dealt a Straight that is also a 4-Card Royal, what is the right play?  Keep in mind, in this particular case, the Player was NOT playing max-coin, so the payout for the Royal was ‘only’ 250.   To fully analyze this situation, we need to look at every possible outcome of going for the Royal.  However, even at a quick glance, we get our answer.  The Player is essentially risking 16 units to win 1000, which is more than a 60-fold increase.  With 47 cards remaining in the deck, he has a 1 in 47 chance of hitting the Royal, which means his potential winnings are greater than the risk.  This tells us that he should go for the Royal.  When we realize that he will also have an additional chance to get a Straight Flush, 7 more ways to get a Flush, 5 more ways to get a Straight and 9 ways to get a High Pair, the decision to go for the Royal becomes an easy one.   The expected value of going for the Royal is about 8.19, while holding the Straight was only 4.

            Of course, in the specific case I’ve spelled out, the decision was a bit tougher.  By going for the Royal, he still has 23 out of 47 chances to wind up a winner and get to Play Level 4.  But, by holding the Straight, he has a 100% chance of playing Level 4.  We cannot dismiss this from the equation.  The expected value for Level 4 is about 7.84 (assuming a 98% payback multiplied by 8).  However, this assumes that we definitely get to play it.  In the case of going for the Royal, we need to multiply this by 23 and divide by 47 to account for the probability of getting to Level 4.  This is only 3.84. 

            So, we need to add these amounts to the respective EVs stated earlier.  While the decision gets quite a bit closer, going for the Royal still edges out the Straight by about 0.19.  I have to admit that I didn’t exactly do this calculation in my head when the guy looked my way (not knowing who I was) and I said “I’d go for it.”  Good thing for me and for the guy playing that he hit the Royal!  Yes, folks – that’s why they call it gambling!