Friday, June 29, 2012

Player Friendly

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

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

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

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

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

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

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

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

Wednesday, June 13, 2012

The Penalty Box

            In last week's column, I analyzed a particular hand that could be played multiple ways.  The hand was as follows:

J♠        8♦        Q♦       3♥        9♦

            From a quick glance, one might think to play the hand as a 4-Card Inside Straight with 2 High Cards, a 3-Card Double Inside Straight Flush with 1 High Card or simply as Two High Cards.  As always, the decision comes down to which of the hands has the highest Expected Value (EV).   In last week's column, instead of simply relying on the EV in a strategy table, I used a program that I created that allows me to put in the EXACT 5 cards and tell it which ones I'm holding and which ones I'm discarding.  It then gives me the exact EV of the hand in question.  Why do I do this instead of just using the value in the strategy table?

            The values in the strategy tables are averages of all hands of that particular type.  The accuracy is thus dependent on a few factors, ranging to the nature of the specific hand to the specificity of that hand.  For example, we list the Expected Value of a 4-Card Flush as 1.22.  In reality, there is not a single 4-Card Flush that has that EV.  While there is always the same number of possible ways to draw the Flush (9), the number of High Cards in the hand will impact the exact expected value because it changes the number of ways we can pick up a High Pair.  If we have 0 High Cards, the EV is 1.15.  With 1 High Card it is 1.21 and with 2 High Cards it is 1.28.   We could just as easily list these three hand separately on the strategy table, but it wouldn't change the strategy we would employ at all.  There are no other hands that have an EV between 1.15 and 1.28.  So, in this case we lump all the 4-Card Flushes together and show the average EV for all 85,512 possible 4-Card Flushes.

            In a similar fashion, we have a single entry on our Strategy table called the 4-Card Royal which has an expected value of 18.66.  but not all 4-Card Royals are created equal.  We might have 10-J-Q-K which allows for pulling the suited 9 and picking up a Straight Flush.  Or we can pick up an unsuited 9 for a Straight.  However, we also only have 9 ways to pick up a High Pair.  Thus the EV of this hand is rather different from that of J-Q-K-A which has no way to pick up a Straight Flush and also has only one way to pick up a Straight (both ends are NOT open).  But, we get 3 additional cards that will give us the High Pair.  

            But, there is another item that can affect the specific Expected Value.  What happens if we are dealt a Flush 3-J-Q-K-A.  The Flush has an EV of 6.00 while the 4-Card Royal has an EV of 18.66.  But, when we discard the 3, we lose one opportunity to draw the Flush.  This will certainly NOT drop the EV of the 4-Card Royal to below that of a Flush, but we should recognize the impact of the specific card we discard.  When we discard a card that could help improve the final hand, it is called a 'penalty card'.  In this particular case, there is no impact to our strategy as a result of discarding the 3, so we are safe to lump all 4-Card Royals together.

            However, as we go down further on our strategy table, we begin to break apart the hands into smaller groupings.  We don't have all the 4-Card Straights listed together the way we do the 4-Card Flushes.  Because a Straight only pays 4 and there are only 8 ways to complete them, the EV of Straights drops to the point where it is very close to many 3-Card Straight Flushes, 2-Card Royals and even High Card hands.  Many of these hands also tend to overlap a lot, as in the example at the beginning of this article.  The hand is 2 High Cards, a 3-Card Straight Flush and a 4-Card Inside Straight all at the same time.  Slight changes in the hand make up could make it other hands all at the same time.

            When a hand overlaps as this one does, there is usually at least some penalty card situations.  In this case, if we choose to play the hand as 2 High Cards, discarding the 8 and 9 create the penalty card situation.  We wouldn't want to draw an 8, 9 and 3, but we wouldn't mind drawing an 8, 9 and 10.  While this may not be the most common outcome, it is one that would complete the Straight and give us one of the highest possible payouts for the 2 High Cards.  So, discarding them may reduce the ACTUAL Expected Value slightly from the one we may find under 2 High Cards in the strategy table.

            Likewise, when we hold the 8, 9 and Q, we are discarding the Jack which is a penalty card.  It can be used to complete a Straight or we might pick up another Jack to make a High Pair.  So, I calculate the exact Expected Value in last week's column to make sure the result was 100% accurate.

            As I've said many times in my column, you don't need to memorize the Expected Value of any hand because the value itself is meaningless.  What matters is the relative value.  You need to know which hand has the higher EV.   Once in a while, a penalty card situation will cause a hand as it is shown on the strategy table to have an ACTUAL Expected Value that actually drops it to below that of another playable hand from that same 5-card draw.  This in essence creates an exception condition to how the hand should be played when using a strategy table.  The hand should STILL be played according to which has the higher Expected Value, but because we are using the 'average' shown on a strategy table, we don't actually do this.

            When my father, Lenny Frome, developed Expert Strategy, he was well aware of this situation.  He felt that the impact on the payback of these exceptions was too small to be concerned with relative to the idea of listing out what could be several to dozens more lines on the strategy table.  Learning Expert Strategy can be enough of a challenge.  He didn't want to complicate it further by trying to list out hands that might look something like this:

·         4-Card Straight with 2 High Cards, EXCEPT if there is a 3-Card Straight Flush, but ONLY if the 2 High Cards are part of the 3-Card Straight Flush

            I tend to agree with my father and learning these extra rules are only for diehards and even then, the risk of error might be more than the extra 0.001% it might yield in payback.

Thursday, June 7, 2012

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.