Getting Ugly

            For the past few weeks, I've been slowly walking through the strategy table for full-pay jacks or better video poker.  I'm about 2/3 of the way though and what's left is well, just not pretty.  The expected values of the rest of the table are below 0.60.  This means you can expect, on average, a return of only 60% of your wager.  But, as I've explained the past few weeks, learning to play the ugly hands is at least as important as learning how to play the good hands.  It is also probably more difficult to learn these hands as there are a lot of subtle nuances and a great deal of overlap.  For example, one of the hands from last week was the 2-Card Royal with no Aces or 10's.  This week's top hand is a 4-Card Inside Straight with 4 High Cards, which is really a 4 High Card hand.  There is only one way this occurs -  J Q K A.  But, if we compare this to the 2-Card Royal we realize that if TWO of the J/Q/K are suited, we actually go that route instead of the 4-Card Inside Straight.  

            Let's take a look at the next few entries and see what we can learn from them:

·       4-Card Inside Straight with 4 High Cards

·       2-Card Royal with an Ace, but no 10

·       3-Card Double Inside Straight Flush with 1 High Card

·       4-Card Inside Straight with 3 High Cards

·       3-Card Inside Straight Flush with 0 High Cards

·       3 High Cards

            Okay, so we've already covered a critical point of these hands above.  Adding to the complexity however is the 2nd rule down when compared with the 1st.  IF the 2 suited cards are an Ace and either the Jack, Queen or King, THEN we keep the 4-Card Straight! 

           

            Next up is the 3-Card Double Inside Straight Flush with 1 High Card.  So, a suited 8-9-Q would cover this.  This can't overlap with our 2-Card Royals, but can overlap with a 4-Card Inside Straight (8-9-Q suited with a Jack off-suit).  This would make it a 4-Card Inside Straight with 2 High Cards.   You'll note that the 4-Card Inside Straight with 3 High Cards is below the 3-Card Double Inside Straight with 1 High Card, so surely the 2 High Card version is even lower.  In reality, we won't find it on this strategy table at all as a 4-Card Inside Straight with 2 or less High Cards is NOT a playable hand in full-pay jacks or better.  In this case we would keep the 3-Card Straight Flush over the 4-Card Straight.

            The next hand is the 3-Card Inside Straight Flush with 0 High Cards (i.e. 5-7-8 suited).  If we have a 6 off-suit this would be a 4-Card Straight with 0 High Cards which is much higher in the table and thus would be played as the 4-Card Straight.  If we have a 4 off-suit, then it is a 4-Card Inside Straight with 0 High Cards.  If the 2 High Card version is not playable then for sure neither is the 0 High Card Version.  We would play the 3-Card Straight Flush.

            The 3 High Card hand is a critical hand to learn about.  It is frequently misplayed.  There are four possible High Cards - Jack, Queen, King and Ace.  However, 3 High Cards is a bit of a misnomer.  In order for the hand to be 3 High Cards, it MUST be J-Q-K.  If we have J-Q-A we would discard the Ace unless the Ace matches in suit to one of the other two then it would play as a 2-Card Royal.  In similar fashion, we would ONLY play J-Q-K if the three are of different suits.  Otherwise we would again have a 2-Card Royal (V3) and would play the hand that way.  The 2-Card Royals are frequently overlooked when there is a 3rd High Card, but this is simply not the right way to play the hand. 

            There are only 5 more hands on our strategy table and I will cover them next week.   These five hands all have expected value below 0.50.  Unfortunately, they account for about 1/3 of all hands dealt - so they are critical to learn.

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.

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.

          

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.

The Nature of the Game

            My elder son has finished up his year in college and came home the other day.  As we do our best to keep him entertained while in Vegas, we went to the Laugh Factory at the Tropicana the other night.  Invariably, when comedians are in Las Vegas, they will tell jokes about the dry heat and about losing money while gambling.  I think I've been very honest about the odds of long-term winning while gambling.  With the rare exception of some tough to find video poker games and/or the ability to count in blackjack, you're simply not going to win in the long term.  But, this doesn't mean that you have to 'lose your shirt' either. 

            A few weeks ago, I showed how playing blackjack for an hour, a $5 Player should expect to lose only a little over $1/hour.  This, of course, assumes playing properly.  If you are too timid to double down on soft hands, or don't like splitting 2's looking into a 7, then, well, all bets are off as to what your payback will really be.  The comedian was hopefully joking when he talked about struggling to add up his cards while playing blackjack.  If you're really struggling with this, maybe you should try Casino War or Three Card Poker.

            In that same column where I talked about the average you can expect to lose while playing blackjack, I also spoke of the average you can expect to lose while playing full-pay jacks or better video poker.  As the two games have similar paybacks, the only real difference is the average amount you wager in an hour of each game.  Much to many Player's surprise, a max-coin quarter video poker actually wagers more in an hour than a $5 blackjack Player.  That said, however, the game of video poker is far more volatile and while the average loss rate by only be a couple of bucks an hour (depending on speed of play), actual results will wind up all over the place.  Blackjack is a much less volatile game and we will find that our actual results will really tend to be very close to the theoretical amount.

            To help illustrate this point, I ran 100,000 multi-hour sessions of blackjack, each consisting of 100 hands.  I then tabulated the amount won or lost, rounding to the nearest dollar.   First of all, the Player had a winning session nearly 46% of the time.  He lost 49% of the time, with the remainder being breaking even.  Around 32% of the time, the Player will wind up within $20 of his starting point, with only a slight slant towards the losing side.    He will wind up within $40 of his original bankroll more than 55% of the time.   He will wind up losing $100 or more only 5% of the time.  To be clear, this is NOT the same as saying that if he starts with $100, he will go 'bust' only 5% of the time.  The simulation I ran does NOT take into account a Player who may have at some point been down more than $100 and then came back to lose less than $100.  This will not be a huge number, but it will add to the total.

            I'm not downplaying the impact of losing $100.  This is not a small amount and could be considered to be a high cost for 2+ hours of entertainment.  At the same time, we are only talking about a 1 in 20 chance.  At the same time, the Player has a 4.4% chance of WINNING $100 or more.   That's why it is called gambling.

            But, the overall point is that the notion that everytime you gamble you're going to lose your shirt is simply not accurate.  If we assume that 'paying' up to $25 is a fair price for the 2-3 hours of entertainment value, then we find that the Player will meet this goal 62% of the time.  In fact of this 62%, he will actually wind up winning money nearly 75% of the time. 

            As stated earlier, this all assumes playing properly.  This tends to be what trips up Players far more often that the basic nature of the game.  Blackjack has a payback of about 99.5% when played properly.  Played improperly, the payback could drop dramatically,  If you drop it to 98%, which is still a respectable payback for most table games, this may not seem like a lot.  However, turned around, it means the casino advantage increases fourfold.  If I were to simulate such a strategy, we would find that the numbers are not so generous to the Player, and the likelihood of losing one's shirt will go up considerably.

            Thus, while the nature of the game it still one where the Player will lose in the long run, the Player can still greatly control (within reason), just how much will be lost by learning to play using the right strategy.

Win Frequency Overrated

            Why does a good blackjack Player stick on bustable hands aginst a Dealer 6?  The quick answer is that with a 6 upcard, the Dealer is likely to bust.  Of course, this is not completely accurate.  The Dealer's bust rate with a 6 is 'only' 42%, which means 58% of the time, he won't bust.  So, first he is not 'likely' to bust.  He is just more likely to bust with a 6 than with any other card.  58% of the time, he will wind up with a 17 through 21 and will beat your hand.  So, why stick?  Well, we need to take into account how often the Player will bust if he takes a hit.  If the Player busts, it doesn't matter what the Dealer does.  This is all a wordy way of saying that the Player is more likely to win if he sticks than if he hits.  Or, in other words, his expected value is higher if sticks than if he hits.  Depending on his specific hand, it might be a relatively small difference between these expected values or it might be a big difference.  But, the difference doesn't matter.  The correct play is the one that has the highest expected value.  This is the key thing to learn for EVERY casino game.

            Blackjack is essentially a binary game.  You either win or lose your base wager.  With the exception of blackjacks itself and Doubles and Splits, the wager is a single unit and the outcome is either even money or the Player loses.  Thus, the critical factor becomes win frequency because for the most part, one win is worth as much as any other win.  In video poker, the outcomes are a bit more varied and thus the analysis is actually a good deal more complex.  If we define 'winning' as any hand that is Jacks or Better, that leaves us with a win frequency of 45% (roughly), but not all wins are created equal.  There are essentially 9 different levels of winning, ranging from Royal Flush down to a High Pair.  The payouts range from 800 for 1 down to a push (which is all you get paid when you have a High Pair). 

            This explains why when playing video poker the win frequency is not very relevant.  Take the following hand as an example:

8♣       9♣       10♣     Q♣      Q♥

            There are two ways to play this hand.  A Player can keep the pair of Queens and have a sure winner.  He'll still have a chance to improve to Two Pair, Trips, Full House or Quads.  But, his win frequency will be 100%.  His other choice is to go for the 4-Card Inside Straight Flush.  If he chooses to go this route, his win frequency will be around 30%.  Of the 47 draws, 8 will result in a Flush, 3 in a Straight, 2 in a High Pair and 1 as a Straight Flush.  The other 34 will result in a loss.  If you're motivated by win percentage, then the right play is to stick with the pair of Queens.  If you're motivated to use the proper strategy, you use expected value to guide you.  When the math is all done, we find that the 4-Card Inside Straight Flush has an expected value of 2.39.  The Pair of Queens has an expected value of 1.54.  It's not really much of a choice.  The 4-Card Inside Straight Flush is by far the superior play.

            Decisions for casino games are made based on the criteria of expected value.  This is not a concept unique to any particular game.  The same methodology that developed blackjack strategy is essentially the same one used for video poker or Three Card Poker or Ultimate Texas Hold'em.  Some of the toughest decisions are of the type I just described where the Player might have to give up a sure winner to go for a hand that in the long run will pay more, but will have a significantly lower win frequency.  The example I gave here is probably not all that hard to follow.  Since the sure win is only a single unit, it won't feel like you are giving up much.  

            But, you may have to make a similar decision if you are dealt a Flush that is also a 4-Card Royal.  If you're playing max-coin quarters, you'll be giving up a sure $7.50 to go for that big payout of $1000.   IF you're a dollar player, you'll be risking $30 to win $4000.  Definitely worth it, but it might just be a little harder to walk away from that sure $30.

The Definition of Payback

            I never get through a holiday without a serious discussion of what I do for a living with someone I've never met before.  Family (and friend) functions tend to bring together people for a large meal leaving them with loads of time to discuss all sorts of things.  As I have one of the more unique jobs around, my vocation tends to take up a larger than proportionate amount of the time we spend together.  This past holiday season was no different.

            First I listened to one person tell me how he has a system for roulette.  Admittedly, he didn't get a chance to explain it to me in much details when I had to tell him that it doesn't work.  No system does.  He told me how each time he came to Vegas, he would use this system and invariably walk away with a few hundred dollars.  Of course, his sample size was about 6-12 sessions, which isn't exactly statistically significant.  Based on what he told me, I commend my new found friend for his discipline which can be an important part of any successful gambling story.  Know when to get out when you are ahead.  But, that said, if you really have a system that nets you $400 in an hour or two, it is forever repeatable, which means you do it every night and then you send out a team of people to repeat your system.  No 'real' system could work only if you use it once every few weeks.

            Next up in the discussion came my favorite topic (ha!) - slot machines.  The system here was to attempt to outguess when the machine was going to pay off by altering the amount wagered for each 'pull'.  It was hard to keep a straight face when we got to this point.  I've heard of people varying their bet when playing blackjack in an attempt to guess the next cards.  If you do this well, it is card counting.  If you simply try to outsmart the shoe, you're just guessing.  If you try it with a slot machine, you are definitely guessing. 

            We've all seen the disclaimer that says 'past performance is not an indication of future returns'.  Nothing could be more true with slot machines.  What happened in the last spin has absolutely no bearing on what happens in the next one.  A slot machine is programmed to have a winning spin some percent of the time.  Every time you spin the wheels, the chance of winning is this exact percent.  With some combinatorial math we can also say that the probability of having X winning hands in Y spins will be some percent (assuming we know the probability of winning in any given spin).  But that is only true for the next Y spins.  We absolutely, positively CANNOT use any of the past spins in our calculation.  If the past 100 spins were losers, the probability of winning on the next spin is still whatever it is.  If the past 100 spins were winners, the probability of winning on the next spin is the same percent. 

            When I suggested to my new friend that he might want to avoid slot machines due to their 92+% payback, which makes them some of the worst payers in the casino.  Of course, when you look at the machine you have no way of knowing if it is programmed at 98% of 85%, which is as much as part of the problem as the average of 92+%.  My friend wanted to know how this payback was calculated especially when taking into account the way he plays - altering his wager from spin to spin.

            I explained that the payback used for any game is the highest payback that can be obtained by a Player assuming he plays using the best possible strategy he can.  For a game like video poker this means he uses perfect strategy to play each hand and that he plays max-coin in order to get the benefit of the 800 for 1 payout for Royal Flushes.  For slot machines, there is no strategy, so that does not impact the payback.  With slots, the impact of max-coin can frequently be even greater than with video poker.  Not only do you buy additional lines with additional wagers, you sometimes also buy additional combinations of winning hands.   As a result, playing less than max-coin can be even more punishing to your bankroll.  The payback of a slot machine thus assumes a max-coin play on each spin.

            Payback (for any game) is the amount that a Player can expect to have returned out of the TOTAL amount wagered.    The amount you buy-in for is completely irrelevant to this definition.  If you sit down at a blackjack table for $20 and play 100 hands of a $5 table, you'll wind up wagering about $565 (when you account for splits and double downs).  With a 99.5% payback, you can expect to lose about $2.80.  This works out to be 14% of your buy-in, but if you had bought in for $100 it would've been 2.8%.  Just further proof that the buy-in is not relevant to the payback discussion. 

            If you play 1000 hands of video poker (quarter machine, max-coin), you'll wager $1250.  If you're playing full pay jacks or better with a 99.5% payback, you can expect to get back $1243.75.  No matter how much you put into the machine, you should expect to have lost $6.25.  If you play less than max-coin, your expected loss will be higher.

            Slot machines are no different.  If you spin the wheels 1000 times on a nickel machine with 27 lines, you'll wager $1800.  You won't know the exact payback of that machine, but if we use a generous 95% payback, you can expect to get back $1710 of that $1800 wager and sustain a $90 loss.   If you choose to vary your bet from spin to spin, your payback might be even lower, raising your expected loss.

            In all these cases, the paybacks are expected 'long-term' paybacks.  Long-term can mean different things to different games.  In a 2-3 hour session of playing, your results can and will greatly vary from the examples shown here.

When 2 is better than 3

            When my father developed the first strategies for video poker, a few surprises definitely showed up.  Playing 4-Card Flushes over Low Pairs was not such a surprise, but playing the Low Pair over 4-Card Straights was.   One of the other significant surprises was how to play the numerous hands that contain High Cards.   If you had 3 High Cards of the same suit, it wasn't much of a surprise to hold all three.  Even if one of those 'High' cards was only a 10.  A 3-Card Royal is a pretty strong hand, even if it takes a bit of a long shot to actually hit the Royal.

            Without the mathematical analysis of video poker to guide the Player, most found themselves holding on to all cards Jack or Higher.  This would probably be the right play if you were sitting at a Poker table.  When playing Poker, there is little benefit to drawing a Royal over a Straight or a Flush.  All are very likely to leave you as a winner and the amount you win will not change based on your final hand value.  In the meantime, you'll increase your chance (or will you?) of grabbing a High Pair which will may be enough to win the hand.

            But video poker is not table poker and a Royal has a good deal more value than a Straight or a Flush - 200 to 130+ times as much.  This makes taking the risk of getting the Royal far more worthwhile in video poker than table Poker.  As a result, the decision of what to do when you're dealt a J♥, Q♦, A♥ not as clear as one might think.  Let's take a look at the detailed analysis.

            If the Player holds the 3 High Cards, there are 1081 possible resulting draws.  32.2% of the time the Player will wind up with a High Pair.  If the Player holds only the 2 suited High Cards, he will wind up with a High Pair 30.3% of the time.  So, the probability is a little less, but we're not talking a huge difference.  The Player may only have 2 High Cards instead of 3, but he will draw 3 cards instead of 2 helping to even things out a bit.

            Moving on, with the 3 High Cards, the Player will draw a Two Pair about 2.5% of the time.  With the 2 High Cards he will pull a Two Pair about 4.4% of the time.  The score has been quickly settled with the High Pair frequencies.  For as often as the Player will wind up with fewer Pairs he will wind up with more Two Pairs.  Given Two Pairs pay twice as much, this puts the 2 suited High Cards in the lead.            The pattern continues with Trips, with the Player drawing about twice as many by holding onto only the 2 suited High Cards.  

            Things turn around when we look at Straights.  It should be no surprise that the probability of drawing a Straight goes way up when you hold 3 High Cards as compared to 2 High Cards.   The exact probabilities will be impacted by the specific cards, but in this particular case the probability with 3 High Cards is about 1.5% vs 0.3% for 2 High Cards. 

            For the 3 High Card hands, the hands stop there.  There is ZERO chance of drawing a Flush, Full House, Quads, a Straight Flush or the Royal.  For the 2 High Card hand, we still have a 1% chance of drawing a Flush and slim, yet possible chances to get a Full House, Quads or the elusive Royal.  In this particular case, there is no chance for a Straight Flush, but if I had chosen a suited J-K for my example, this would exist as well.

            If we were to ignore all the hands Flush and above, the two hands would have nearly identical expected values, with the 3 High Card hand slightly higher, However, there is no reason to ignore these hands.  In fact, we specifically play the 2 High Card hand for the specific reason that we have the opportunity to draw all these relatively high paying hands simply by discarding the 1 off-suit card, all while barely impacting the overall expected value of the lower hands. 

            As a result, the decision is not really a hard one to make, even if it was an originally surprising part of the strategy.  Our 2-Card Royal with an Ace has an expected value of about 0.58.  Our 3 High Card expected value is a mere 0.46%. 

            This type of hand is a fairly common one and repeatedly playing it the wrong way will take a bite out of your bankroll.  This is why the 'seat of your pants' approach or using table Poker strategy can be quite ruinous to your results.  Sometimes, 2 can be better than 3.

Strategy is Underrated

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

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

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

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

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

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

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