Distinguished Royals

            I've spent the past few weeks walking through the strategy table for full-pay jacks or better video poker.  This week, we are in the heart of the table, which is to say we are in the middle of the really bad hands.  But, bad hands are the harder hands to play correctly and are just as important as the good hands in achieving the theoretical strategy of any particular game.  We finished up last week with the 4-Card Straights.  From here the hands only get uglier.  The next several entries are:

·       3-Card Double Inside Straight Flush with 2 High Cards

·       3-Card Inside Straight Flush with 1 High Card

·       3-Card Straight Flush with 0 High Cards

·       2-Card Royal Flush - "V3"

            If you're relatively new to strategy tables, this part of the table has problem just given you a doozy of a headache!  The good news is that it is not nearly as confusing as it might appear.  Many of the hands listed above cannot co-exist - meaning that you can't have more than one in a particular hand.  Thus, remembering the exact order may not be as important as it might appear to be.  For example, you can't have a 3-Card Double Inside Straight Flush with 2 High Cards in the same hand as a 3-Card Straight with 0 High Cards.  You'd either have to have at least 4 cards of one suit or have 2 sets of 3-Cards of different suits - rather difficult with 5 cards. 

            There are still important things we can learn from this section of the table.  We separate the hands the way we do because in some games the impact of the subtle differences and the order of the hands will be different and thus become pertinent.  The first thing you might notice is the relationship of the top three hands.  We get a sense of the importance of a High Card.  A 3-Card Double Inside Straight Flush with 2 High Cards has a higher expected value than a 3-Card Inside Straight Flush with only 1 High Card.  Essentially, the value of the extra High Card is greater than the value of the additional Straight Flushes (and Straights) that may occur as a result of having an Open vs. Inside vs. Double Inside Straight Flush.  What this should also tell us is that you shouldn't hold your breath for those Straight Flushes.  They will occur, but not often.  At the same time, I have written at length over the years about how the Straight Flush is the forgotten hand of video poker.  Playing 3-Card Straight Flushes correctly is very important to drawing them in proper abundance.  While their pays are far short of the Royal, they still pay double what Quads pays so their value should not be dismissed.

            Next up is the 2-Card Royal Flush - "V3".  2-Card Royals are given 4 different designation from "V0" to "V3".   We need to do this because the expected values of many of the hands in this part of the table differ by only 0.01 or 0.02.  As not all 2-Card Royals have identical expected values, we need to distinguish between them.  V3 means that the 2-Card Royal contains neither a 10 nor an Ace.  An Ace in a 2-Card Royal essentially makes it a Double Inside Royal.  All 2-Card Royals have the same number of ways to make a Royal - one.  But, with the Ace, we eliminate all ways to make a Straight Flush.  While a '10' doesn't have this problem, it does have the problem that it is not a High Card.  So, Aces are worth less than Jacks, Queens and Kings and 10's are worth less than Aces.  Thus, a 2-Card Royal with neither an Ace nor a '10' is the one with the highest expected value.  A V2 2-Card Royal means that the 2-Card Royal has an Ace, but no 10.  A V1 2-Card Royal is one that has no Ace, but does have a 10.  Lastly, a V0 2-Card Royal consists of a 10 AND an Ace.

            For the moment, I'll jump to below the strategy table - to the V0 2-Card Royal.  We are 'below' the strategy table because this hand does not exist on the strategy table for full-pay jacks or better.  This means that we DO NOT PLAY an A-10 2-Card Royal.  Barring the other three cards forming an otherwise playable hand, we would simply hold the single Ace.  More on that in a couple of weeks.

            The proper play of 2-Card Royals is critical to learning how to master video poker strategy.  Unlike the prior 3 hands, 2-Card Royals overlap with EVERYTHING.  You'll have 2-Card Royals with High Pairs, Low Pairs, 4-Card Straights, 4-Card Flushes, 3-Card Straight Flushes, 3-Card Inside Straight Flushes, etc...   If you blindly go after every 2-Card Royal, you'll hit more than your fair share of Royals, but you'll lower the payback of your play.  If you ignore 2-Card Royals, you'll miss you fair share of Royals AND lower the payback of your play.  The only answer is to play them when you are supposed to.  Based on the portion of the strategy table shown, you can easily have a 3-Card Double Inside Straight Flush with 2-High Cards AND a 2-Card Royal - V3.  For example, you could have 8-J-Q suited.  From the strategy table, we learn that we keep the 8 in this case.  You might also have a 3-card Straight Flush completely apart from a 2-card Royal.  For example, 3H, 4H, 5H, JD, QD.  In this case, we discard the 2-Card Royal in favor of the 3-Card Straight Flush with 0 High Cards.

            I've now covered about 2/3 of the strategy table for jacks or better video poker.  Next week, we continue through the rest of the messy hands. 

Stroll Through the Strategy Table

            This week we continue our walk through a video poker strategy table.  Specifically, the strategy table for full-pay jacks or better video poker.  Last week we left off at the 4-Card Flush which was the last of the hands with an expected value of greater than 1.0.  These are the hands that result in net wins in the long run.  The rest of the strategy table have expected values below 1.0.  This means that in the long run we will not get back our entire wager.  But, that doesn't make them any less important.  When playing video poker, playing every hand correctly is critical if you want to achieve the theoretical payback.

            It could be argued that playing the hands below 1.0 correctly is more important than playing the ones above this line correctly.  First, the hands below make up the lion's share of hands.  Second, the hands below are by far more complex than the ones above.  You don't have to worry about confusing a Two-Pair with a 4-Card Straight Flush as this is an impossibility.  But a 4-Card Straight vs. a 3-Card Straight Flush might leave you shaking your head. 

            Without further ado, here are the next batch of hands on our strategy table:

·       4-Card Straight with 3 High Cards

·       Low Pair

·       4-Card Straight with 2 High Cards

·       4-Card Straight with 1 High Card

·       3-Card Inside Straight Flush with 2 High Cards

·       3-Card Straight Flush with 1 High Card

·       4-Card Straight with 0 High Cards

            The first thing you'll probably notice is that with the exception of the Low Pair, the number of High Cards is specified.  When the inventor of video poker decided to pay on Jacks or better, he added an incredible layer of complexity to the strategy.  Simply put, in any hand without a Pair or better, any card that is a Jack or higher is worth considerably more than any other card.  The reason should be fairly obvious.  We have the opportunity to win with High Pairs.  For each High Card in the hand, we have three additional cards that we can draw that will turn our hand into a winner.  These three cards add just over 0.06 to the expected value of the hand. 

            Sometimes, this 0.06 means nothing and sometimes it means everything.  We just need to look at the first three hands to see the impact.  If you have a 4-Card Straight with 3 High Cards and a Low Pair, you keep the partial Straight.  If you have a 4-Card Straight with 2 High Cards and a Low Pair, you keep the Lower Pair.  These hands are not very common, but they illustrate the impact of the High Card.   So, if you have 10-10-J-Q-K (assuming no 3-Card Royal), then you keep the Straight.  If you have 9-10-10-J-Q then you keep the Low Pair.  Having a 9 instead of a King lowers the expected value so that it falls just below that of the Low Pair.

            If we keep moving down the chart, we find that the next entry is the 4-Card Straight with 1 High Card.  As this is adjacent to the 2 High Card version, there really is no impact in this case.  We could lump these two hands together if we want to remove 1 hand from the strategy table.  We keep them separate because there are versions of video poker where it is relevant and we want to make sure the Player doesn't get 'lazy'. 

            In between a 4-Card Straight with 1 High Card and a 4-Card Straight with 0 High Cards we find 2 other hands.  They are both variants of a 3-Card Straight Flush.  The first is an Inside Straight Flush with 2 High Cards and the second is a 3-Card Straight Flush with 1 High Card.  This can start looking more confusing than it really is.  Most of these hands CANNOT occur in a single hand.  It is not possible to have both a 3-Card Straight Flush with 1 High Card and a 3-Card Inside Straight Flush with 2 High Cards.   But, you can have a 4-Card Straight with 1 High Card with a 3-Card Straight Flush with 1 High Card.  (8C 9D 10D JD 4H).  We learn from the strategy table that the right play is the 4-Card Straight.

           

            One last point that I should mention.  All the 4-Card Straights to this point have been Open Straight Flushes - meaning that they can be completed on both ends.   This means that as we have completed about 60% of the strategy table, we have accounted for all Pairs and for all 4-Card Straights (Open ended) and 4-Card Flushes.  The remaining 40% of the strategy tables contains very 'not pretty' hands.  It is a mish-mosh of 3-Card Straight Flushes, Inside Straight Flushes and even Double Inside Straight Flushes, along with 2-Card Royals and hands with just High Cards.  To make matters worse, these 40% of the entries account for nearly 50% of the hands.  

            Next week, we'll continue our stroll through the strategy table.

Get the Inside Scoop

            Last week I began reviewing the strategy table for full-pay jacks or better video poker.  I got about 20% of the way through the table by volume, but not very far in terms of useful information.  The top 8 hands were mostly of the no-brainer category as they were the pat hands with the exception of the 4-Card Royal.  This week, I'll keep moving down the table and provide some insight into the nuances of video poker strategy.  Please remember that this particular strategy is applicable ONLY to full-pay jacks or better.

            After a Straight, we find the following entries on our table:

·       4-Card Straight Flush

·       Two Pair

·       4-Card Inside Straight Flush

·       High Pair

·       3-Card Royal Flush

·       4-Card Flush

            The first thing you might notice about the above entries is that we have two entries for a 4-Card Straight Flush and a 4-Card Inside Straight Flush.  There is a big difference between the expected values for Straights that are open and those that are Inside (or Double Inside).  The common definition of Inside Straight is when the opening is in the middle and not on the ends (i.e. 5-6-7-9).  However, this leaves off some Inside Straights.  It is more accurate to define a 4-Card  Inside Straight as one that can only be filled ONE WAY.  So, an A-2-3-4 can only be filled with a 5 and thus is an Inside Straight.   With this definition you can see that an Inside Straight can be completed with only 4 cards while a regular Straight can be completed with 8 cards.  Straight Flushes are no different - except they have the possibility of being turned into Flushes as well. 

            In this particular case, there is really no benefit to splitting out the 4-Card Straight Flushes.  The one hand that lies between them can't possibly be a 4-Card Straight Flush (Inside or not).  We show them separately because in some version of video poker, the hands that appear in between may be able to overlap with them and we will find that in some cases we will want to keep a 4-Card Straight Flush ONLY if it is not an Inside Straight Flush.  Also, as we will see as we move down the table, this distinction becomes very important as we take a closer look at 4-Card Straights.

            The 4th entry on the table is a critical one - High Pair.  It is the 4th most common hand.  Thus, playing it correctly is very important.  Looking at the entries above it and below it what we learn is that a High Pair is played OVER any 4-Card Straights and 4-Card Flushes.  We will, however, play all 4-Card Straight Flushes over a High Pair.  But, we will NOT play a 3-Card Royal over the High Pair.  So, if you have a suited J-Q-K along with another Queen, you stick with the sure winner - the Pair of Queens.

            Below High Pair, we have a 3-Card Royal Flush and a 4-Card Flush.  There is much to learn here as well.  The most obvious is that if you have a 3-Card Royal and a 4-Card Flush, we hold the 3-Card Royal.  This can be a tough choice because the likelihood of hitting the Royal is still relatively small.  But, by holding a 3-Card Royal we give ourselves more chances for a Straight.  We might still hit a Flush and we have the longshot at the Royal.  Also, with a 3-Card Royal, we leave ourselves 2-3 cards that can be matched up for a High Pair.  The expected values are not really all that close with a 1.41 for the 3-Card Royal and 1.22 for the 4-Card Flush.  The decision is relatively clear. 

            From these entries we also learn that if the Player has a 3-Card Royal that is also a 4-Card Straight Flush (8-10-J-Q), we hold the 4-Card Straight Flush.  With the 4-Card Straight Flush, we still have many chances for Straights and Flushes so we don't throw away the extra card even if it gives us a chance to get the Royal.

            I've stopped at this particular point in the Strategy Table because the 14 hands I've listed (over the past 2 weeks) are the only ones with an expected value greater than 1.0.  That means these hands are net winners in the long run.  Some will be winners 100% of the time.  Some will not.  But in the long run, we can expect to get more back than we wagered.  These hands make up about 40% of the table and about 25% of the total hands dealt.  Beginning next week, we'll review the hands with an expected value below 1.0.  Even though these are losers in the long run, it doesn't make them less important.  In fact, they may be more important because they account for a larger percentage of hands dealt.

           

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.

            

Buy More Tickets

(*Note: this column was written on the 3rd day of the recently completed government shutdown)

            As we finish Day 3 of the government shutdown, it is hard to find a news story that is about anything else.  I was pleasantly surprised (initially) when my eye caught a story on Yahoo's main news page that dealt with lotteries.  Apparently, they were revealing the secret of how to win the Powerball Lotto.  Who doesn't want to win Powerball?  I read the article, which was all of about two paragraphs. 

            It began by talking about last month's sole winner, who won $400 million.  He 'beat the odds' by hitting the lottery which is a 1 in 175 million chance (I'll take their word for this).  Per the article, the odds of getting struck by lightning is a mere 1 in 10,000 (again, I'll take their word for this).  Finally, the article gets to the important question "How can you increase your chances of winning the lottery?"  Then they apparently provide the way.  A statistician in Louisiana has discovered that certain numbers come up more often than others!

            The most frequent powerball number is 20.  The most common white ball numbers are 42, 16, 35, 26 and 19.  There you have it.  The winning numbers!  So, to increase your changes all you need to do is play these 5 numbers with the number 20 and you can start spending your millions!   I didn't actually look up the historical winning numbers, but I'm going to take a strong guess that this particular combination has NEVER come up before, but undoubtedly they are on their way.

            Now, nothing in this article gives the actual frequencies of these numbers.  Nothing shows that they show up an abnormally high amount of times.  Let's assume that Powerball has been drawing twice a week for 20 years.  That is 2000 total draws.  That is 10000 numbers drawn (white balls) and 2000 red balls drawn.  There are 59 white numbers and 35 red balls.  On average each white number should be drawn 169.4915 times.  So, for all we know the 5 numbers he cited showed up 170 or 171 times while the rest of the numbers showed up 169 times.  Clearly a massive statistical edge!   On the red balls, the average is 57.14.  So, 20 may have shown up a couple more times that all the others.  Again, a clear statistical advantage!

            I've always been strong at math.  I realize not everyone is.  I don't expect everyone to be.  But, bad math packaged as an article on the front page of Yahoo news really drives me absolutely nuts.  To add insult to injury, the article went on to suggest you should buy your ticket in Pennsylvania because that's where the largest number of winning Powerball tickets have been sold.  It doesn't even take into account the possibility that more tickets have been SOLD in that state than many others! 

            I've often said (semi-jokingly) that the world's largest casino is the stock market.  But, there is one critical way that the stock market greatly differs from gambling.  With stocks, past performance CAN BE used to determine the likelihood of future performance.  While there are no guarantees, there are likelihoods.  A stock that has paid a dividend for the past 100 years is not likely to stop paying it next year (barring any specific news being known).  Stocks have their ups and downs, but you are NOT really dealing with random events.

            The same cannot be said for what happens in a casino (or a lottery).  The last 3 numbers on the roulette wheel could've been red and the likelihood of the next number being red will still be 18/37 (or 38).  The last 10 numbers could've been red and the probability will STILL be 18/37 (or 38).  The last 5 hands of video poker could've contained the 2 of diamonds in the initial deal and the probability of it showing in the next hand's deal will still be in 5 in 52.   Nothing changes when we are talking about the lottery.  It does not matter if one number has appeared more often than others.  Next week's numbers are completely random and each number has the same probability of being drawn as the next. 

            Okay, I'll admit it.  Maybe I'm just jealous that after a decade of writing for Gaming Today, Yahoo has not covered a single one of my columns, but some guy writes a complete nonsensical piece of useless information and that makes their front page.  The sad part will be how many thousands of people will read that article and actually run out to play those numbers.  There is only ONE way to increase the likelihood of winning the lottery - buy more tickets. 

Imitation is the Sincerest Form of Flattery

            A couple of weeks ago, I two days walking the halls of the Sands Expo at the Global Gaming Expo.  If I had to pick one word to describe the event, it would definitely be "SLOTS".  Like last year, I think they dominated the show.  For those who have been reading me for years, you know my thoughts on Slots from a Player's perspective.  But, I do give the slot manufacturer's a lot of credit for creativity.  This year, they kept it up, not only in the games that are being developed, but in terms of the marketing.  There were zombies everywhere.  I'm not sure if there was only one manufacturer who had a zombie themed game or if there was more than one.  But there were a lot of zombies in some really good make-up all over the halls.

            As much as I write about video poker in my column, my real love is table games and that's what I'm at the show to really see.   This year, brought a particular trend to its apex (or perhaps more appropriate, its nadir).  Besides the three big table game companies (SHFL, Galaxy and DEQ), there were virtually no new table games.  I did see a couple of other new games, but they were almost afterthoughts from gaming companies involved in other aspects.  I saw exactly ZERO small independent game inventors showing any new games.  I recognize that the cost of a booth at the G2E is not cheap and could easily wipe out the budget of a small inventor, but I always found it fun to talk to someone new about their game.  I didn't get a chance this year.

            I did get introduced to a few inventors who did not have booths at the game who wanted to talk to me about their ideas.  I find that most ideas seem to fall into two categories.  The first is the rather 'far-fetched' category.  These are ideas that aren't necessarily bad, but I have to wonder about their odds of commercial success.  One inventor remarked to me about how all the casino games are poker-based.  He found this to be problematic.  I find this to be indicative of what is likely to be successful commercially.  It is NOT that games that are not poker based haven't been invented and tried, it is that none have ever had the staying power in the casino.  Some might be fun and social for a few hours, but they don't seem to have the ability to create repeat customers the way poker-based games do.

            The second common category of games are the copycats.  People look at a game like Three Card Poker, which is undeniably the most successful proprietary table game (both financially and in terms of number of tables) and try to emulate it in some way.  Now, many table games have some form of patent protection on them (many do not!).  But I am not talking about copying to the point of patent violation.  I'm simply saying that people look at Three Card Poker as some magic formula and try to replicate it.   You know this is happening when they begin describing their game with "It is just like Three Card Poker but......."

            For the past several years, the casinos have been going through a Texas Hold'em craze.  While I think it has peaked overall, it has still left a lasting impression.  Games that might have been developed as 7-card Stud games are being developed with 5 community cards in Texas Hold'em style.  After the dust settled, there are currently 2 very successful Texas Hold'em table games.  The first is Texas Hold'em Bonus Poker - developed by Mikohn/PGIC and purchased by SHFL Entertainment a few years ago, and Ultimate Texas Hold'em - developed directly by SHFL.  I did the original math on UTH for SHFL.  It was by far the most challenging game I had ever worked on to that point and perhaps since.  It was also one of the most rewarding because of the success it has become.  It is generally acknowledged as the 2nd most successful game of all-time with several hundred tables in the market place and is the only game on the horizon that has any chance to knock Three Card Poker out of the number 1 spot.

            Like Three Card Poker, one of the surest signs of the success of UTH is how many times I have heard the phrase in the past few years from an inventor, "It is just like Ultimate, but....."  There is an old saying that imitation is the sincerest form of flattery.  I guess if everyone is trying to create a game just like UTH, then UTH must be a pretty darn good game.   Is it possible to improve upon Three Card Poker or UTH?  I suppose it is possible.  But, 15-20 years after the invention of Three Card Poker, it is not a minor improvement to Three Card Poker that might take it out of the top spot.  It is a game that while still poker-based, introduce many new concepts.  It is a game that has more uniqueness to it than similarity to Three Card Poker.  I think if someone wants to knock UTH out of the number 2 spot, it won't happen because someone tweaks UTH, it will be happen because someone comes up with a new and better idea. 

            To all the inventors out there, don't think of new ways to flatter the existing games by imitating them.  Come up with new games with new ideas if you want to make your mark.

What is the Allure of Progressives

            There is a theory in physics that goes for every action there is an equal and opposite reaction.  In gambling, there is a similar theory.  For every table game there will eventually be a sidebet.  And, for every sidebet there will be a Progressive version of the sidebet.  The math behind Progressives is probably the least understood math of any type of gambling.  It really isn't that hard once it is explained properly, but I've worked with a lot of inventors on a lot of Progressives, and it is fairly obvious to me that few people, even in the industry, understand how a Progressive works mathematically.

            Generally speaking there are 3 components of a sidebet - the fixed pays, the seed and the contribution rate.  Normally when we calculate the payback of a sidebet, we simply multiply the fixed pays by the frequency of each winning hand and sum up these values.  For a Progressive, we have to alter one step slightly and add one.  For the jackpot event, we use the seed amount as the equivalent of the fixed pay for that event.  Each time it is hit, the casino is on the hook to put that money back on the meter, so it is similar to a fixed pay in that regard.  We then need to add the contribution rate - which is the amount of each dollar wagered that goes on the meter - to the total payback calculated.    I'll save more details for another day, as this is not the point of today's column.  What is the point is to discuss how a Progressive differs from other wagers.

            While the top pay for most sidebets are pretty large, the amount they contribute to the overall payback is usually pretty small.  If you pay 1000 for a 1 in a million even, the contribution rate is a meager 0.1%.   In video poker the Royal Flush contributes only 2% to the payback of the game.  If we were to look at most table game sidebets, we'd probably find that most top pays contribute about 1-2% (or less) to the overall payback.  But, when we switch to a Progressive, we find that the top pay frequently contributes 15-20% to the payback when we take into account both the seed and contribution rate.  What does this mean for the Player?

            As I said, the Royal Flush accounts for 2% of the payback of video poker.  What this usually means is that until you hit one, you're only playing at about 97.5% which can be a bit rough.  When you hit one - and if you are a regular player, you WILL hit one, you bring the theoretical payback back to 99.5%.  Hit the Royal more frequently than 'normal' and you're likely up money as you will be above 100%.  With Progressives, it doesn't quite work the same way.  That top hand is either more rare or you'll be playing a game that deals much more slowly than video poker, meaning that there are no guarantees that you will EVER hit it.  So, even if the sidebet were paying 99.5% like video poker, ONE PLAYER is going to wind up winning 15-20% of that payback and everyone else will be playing at 77.5% - 82.5%. 

            When you consider the fact that many sidebets have paybacks far lower than 99.5%, you realize that the picture for those that don't hit the jackpot is even more bleak.  So, why do people play Progressives?  There are two main reasons.  One is a bit emotional and the other a bit more practical.

            First, Players have always been willing to accept low paybacks for a chance to win a life-changing amount of money.  The Lotto has made a lot of money for a lot of states.  Most states payout only 70% on their lotteries.  This is lower than the legal minimum of any casino game here in Nevada.  But, for the chance, however slim, of winning millions of dollars, Players are willing to throw a few dollars in for the hope of getting struck by lightning. 

            The second reason deals with the way Progressives work and makes far more mathematical sense.  To the casinos, the payback of a game is the long-term payback, which is calculated as I described earlier.  You'll note that what I described completely ignores the specific value on the meter at any point in time.   This money is merely an accumulation of the contribution rate over time.  It really doesn't matter to them (mathematically), if a jackpot that is supposed to hit about once a year, doesn't get hit for 3 years.  However, to the Player, the payback of ANY wager is dependent upon the specific payouts for each winning hand at the point in which you make the wager.  It doesn't really matter if the contribution rate is 10% of 20%.  If a Jackpot which is supposed to average $250,000, goes all the way up to $600,000 then the payback at that point in time is WELL above the theoretical payback. 

            It is possible that at a particular point in time that the payback of a wager could be over 100%.  At this point, it makes sense to play the game mathematically.  The problem is, however, that it will be one person that will benefit from this occurrence and it may not be you.  Then again, it might!

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.

          

Better is Better than Best

            A long time ago, I remember reading an article about product marketing in which it stated that you'll never (rarely?) see a company say that there product is better than a similar product.  Why?  Because if you say something is better you have to prove that it is better.  If you, on the other hand, say your product is the 'best' product then it is possible for the other product to be 'best' too.  Best, in marketing parlance, simply means as good as, whereas, better means superior.  So much for those Run, Spot, Run books which talk about good, better and best.  In marketing it is more like good, best and better.

            As bad as it is in the English language, I think it gets even worse when it comes to math.  You can make numbers say just about anything you want them to.  In the past couple of years, much has been made about the 1% (or is it 2%) of the country that is the wealthiest members of our society.   Then there are those that focus on the remaining 99% (or is it 98%).  I don't get political in this column, so please understand I am making no political commentaries here - only mathematical ones.  A friend of mine posted up on Facebook the other day some statistics about what happens if you look at the top 1% of the world instead of just the U.S.A.  All of a sudden a very significant portion of the country is in the top 1%.   Which statistic is more relevant?  I know people who are millionaires who think they are doing 'ok' and I know people who make very modest salaries who are as happy as can be.   The relevance is more likely in the message that someone is trying to send rather than anything absolute. 

            In the case I just discussed, I'll assume that all data presented was reasonably accurate.  A such, no lies were told.  No misinformation was disseminated.   Data was simply presented in a way to try and get some particular message across.  A few months ago, I wrote a column in which I asked if the U.S. has had a Democrat or Republican President more.  In the past 5 years, it has been a Democrat.  But in the last 8 out of 13 years, we had a Republican.  But, in 13 of past 21 years, a Democrat.  In 20 of Past 33 years, a Republican.  I can keep going backwards through the 20th century.  Someone attempting to make a political point is likely to use whichever statistic backs his point the best, even though it may have only minor relevance to the point.

            When it comes to gambling, the numbers can be manipulated just as much, if not more so.  If I had to take a guess, I'd say that the average video poker machine in Las Vegas probably has a payback of 97%.   Now, if I'm a casino whose average video poker payback is only 96%, I might put together some advertising that simply says 'come to Vegas where the video pokers pay an average of 97%!' .  The implication is that the casino pays this as well, but that's not what they said.  On the other hand, a locals casino that likely has a significantly higher average payback is much more likely to say 'come to the XXX casino, where OUR video poker machines payback 98.5%'.  Of course, we don't really know how they calculate these averages.   With slot machines they simply can present how they paid in the prior month because there is no human error involved.  With video poker machines do they simply take a straight average of all their video poker paytables?  Do they weight $1 machines more than nickel machines?  Maybe there is a uniform method for doing this or maybe they have enough wiggle room to give you whatever number they feel will send the right message. 

            Of course the 'average' payback has very limited value to an Expert Player.  In the simplest example, let's assume we have 2 casinos with 2 video poker machines each.  One casino boasts a 98% average and the other a 97% average.  So, should you head over to the one with the higher average?  What if their 2 machines each have a 98% payback.  But the other casino has one paying 94.5% and the other paying 99.5%.   The only machine out of the bunch worth playing is this last one, even though the casino's average is lower than the others.

            One of the local casinos here boasts of having the most machines paying over 100%.  I'll assume that they are telling the truth with this, but that doesn't mean that their machines don't pay 100.01% and that all of the machines below 100% pay 96%.  Now, to the experienced Player you will still happily seek out the 100.01% machine, but this doesn't mean that you can just show up and sit down at any machine and know that you are playing 100.01%.  At the same time, you would be better off finding a 101% machine at another casino that may have only 3 machines of this type and whose average machine pays 96%!

            So, what's my point?  Don't be sucked in by numbers that can be made to say anything they want.  The payback of a machine is an absolute number, calculated with mathematical certainty.  It doesn't mean that every time you play (even if it is for a few hours), that you will experience this payback.  It does mean that over time, your experience should begin to approximate this theoretical payback, assuming you are using the right strategy.  When you look at the paytable on a machine, that tells you the payback of the machine.  This is all that matters.  Marketing numbers that the casinos produce are just that - numbers they produce.  After all, why trust the group that has actually made better, better than best?

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.

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.