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.

Rare Gems - Straight Flushes

            One of the ironies about video poker paytables is that they don't always reward hands more for being more rare.  If I were to ask you which occurs more often in video poker - a Flush, a Straight or a Full House, I'm guessing most of you would say a Straight, followed by a Flush and lastly a Full House.  It is really a trick question.  Without knowing what the paytable is, there is no way to answer the question accurately.  The only thing we know is that, in general, a Full House outranks a Flush, which outranks a Straight. 

            On a full-pay video poker machine, assuming you use Expert Strategy, you will actually hit more Full Houses than either of the other two.  A Straight will occur just slightly more often than a Flush.  Upon close inspection, we realize that this is by far a product of the payouts for each hand than it is a product of the hands themselves.   If we take a look at the game of All American Video Poker - which would appear to now be obsolete - we will see a very different pattern develop.  In All American, a Straight, Flush and Full House all pay 8.  With no reason to go for one or the others, the pure probabilities of hitting each hand begin to show up.  As a result, the frequency of Straights and Flushes increase dramatically, to the point where they occur nearly twice as often as a Full House.

            A similar phenomenon occurs with a Straight Flush.  Generally speaking, it occurs just about 4 times as frequently as a Royal Flush, while paying only 1/16th of the amount.  Or we can look at it the other way and say that it is more than 20 times as rare as a Four of a Kind while only paying twice as much.  When we throw in the Bonus Video Pokers, it only looks worse.  This far more rare hand might actually pay LESS than many of the Quads we can hit, which are far more common.

            Of course, I'm wondering how many of you have hit nearly as many Royal Flushes as you've hit Straight Flushes.  I doubt you remember your Straight Flushes as vividly.  Winning $62.50 on a max-coin quarter machine isn't quite as memorable as a cool $1000, but that isn't my point.  If you use Expert Strategy on a jacks or better machine, you should hit a Royal every 40,400 hands or so and a Straight Flush every 9200 hands.  The key phrase is "if you use Expert Strategy."  Since most Players, at best, use pieces of strategy, I'm guessing that the Straight Flush shows up far less often because the partial Straight Flush is frequently overlooked when the Play.

            If dealt the following, what's the right play?

J♠        8♦        Q♦       3♥        9♦

            Do you play the 4-Card Inside Straight with 2 High Cards, the 3-Card Double Inside Straight with 1 High Card or the 2 High Cards?  As always, there is just one way to determine the right play.  We go to the Expected Values of each.

            Calculating the Expected Value for the 4-Card Inside Straight is fairly easy.  We can draw the Straight with 4 cards and we can draw a High Pair with 6 more.  This will return 22 units to us.  Divide by 47 and we get a result of just below 0.47.  For the other two, I ran them through a program I have that calculates the exact Expected Value given the specific discards.   The Two High Cards have an Expected Value of just below 0.50 and the 3-Card Double Inside Straight Flush has an Expected Value of just below 0.53.  This is the proper play. 

            While the odds of hitting the Straight Flush are 1 in 1081, this is still far greater than hitting it with either of the other two hands (it is zero in these cases).  Ironically, it is not the tremendous payout of the Straight Flush that causes us to play the hand this way.  By holding a 3-Card Straight Flush, we give ourselves numerous chances to hit just Straights and Flushes - a combined 1 in 20 (roughly).  Throw in opportunities for Three of a Kind and Two Pairs and this hand simply beats the others.

            Now, no one expects you to calculate the Expected Value of even the 4-Card Inside Straight on the fly or to carry a small computer to run my program that calculates the exact Expected Value for each hand.  It is much easier to simply use a strategy table that lists out each playable hand.   If we look up the three hands in a strategy table, we find a 3-Card Double Inside Straight Flush has an Expected Value of 0.54, the Two High Cards have an Expected Value of 0.49 and the 4-Card Inside Straight with 2 High Cards doesn't even make it onto our strategy table because the Two High Cards always outranks it.  These values are the average of all hands of that type so they don't always equal the exact Expected Value taken into account the exact discards.

            In the end, the frequency of a hand occurring is a product of the paytable and following the right strategy.  If you want to get your share of Straight Flushes, you can't do a lot about the former, but the latter is fully in your control.