Page 26 - January 2012 • Southern California Gaming Guide

Bob Dancer: Video Poker
HLow Do You Determine the Best Play?
et’s say you’re playing 9/6 Jacks or Better, where full houses return 9 for 1, and ushes return 6 for 1. You are dealt Q♥ Q♣ T♣ 9♣ 8♣. You suspect, correctly, that the best choices are
between holding QQ and the suited QT98. How can you know which play is better?
One way is to use a strategy card. Every strategy card worth having tells you that holding the clubs (a 4-card straight ush with a gap) is better than holding the queens (a high pair). It’s really not a close play at all. But how did the makers of the strategy cards decide which play was better?
e most common way used to rank hands is called “expected value,” or ev, for short. It is sometimes calculated on a per-coin basis. I prefer to calculate it in dollars and cents, assuming you are a dollar player, and I call it the dollar expected value, or $ev. Both methods are equivalent.
Let’s look at the suited QT98 rst. When you draw one card, there are 47 di erent possible draws. One of them, the J♣, gives you the straight ush worth $250. Eight cards, all clubs other than the J♣, give you a ush worth $30. ree cards, any jack other than the J♣, give you a straight worth $20, and two cards, the other two queens, provide you with a pair worth $5. e other 33 cards you could draw give you nothing. We calculate the ev of this as follows:
$ev =(1 x $250+8 x $30+3 x $20+$2 x $5+33 x $0)/47 = $11.91
Although there were several possibilities to consider, when we draw only one card we can gure out the 47 di erent combinations by hand. When we draw two cards, there are 1,081 di erent combinations. ree-card draws give us 16,215 combinations. Four-card draws give us 178,365 combinations and 5-card draws give us 1,533,539.
Every hand gives us 32 di erent ways to play. ere is one way each to either keep all ve cards or throw them all away, ve ways each to draw either one card or four cards,
and ten ways each to draw either two or three cards. No one can work out all 32 di erent ways easily. Fortunately computer programs provide this information virtually instantly.
When we draw three cards to a pair of queens, as we said, there are 16,215 possibilities: 11,559 of them leave us with the high pair worth $5; 2,592 of them leave us with two pair worth $10; 1,854 of the possibilities leave us with
3-of-a-kind worth $15; 165 of the possibilities leave us with a full house worth $45; and the remaining 45 times leave us with 4-of-a-kind worth $125. Multiplying all of this gives us a $ev worth $7.68.
Since $11.91 is greater than $7.68, all strategy cards say to go for the straight ush. In all of my playing and writing, I base my decisions on $ev, and suggest that you do the same.
But it’s not the only way to go.
Expected value is based on the long run. If you start from this position zillions of times and you want the play that will add up to the most over this impossible-to-accurately- de ne long run, ev is the way to go. I’m happy to always bet based on long-run considerations, and I accept that there will be many losing days along the way. I often write,
“Today’s score doesn’t matter,” because I’m willing to take several losing sessions in a row because I know that sooner or later the good hands will come.
But some players are more interested in winning the next hand. ey don’t want to consider zillions of times. ey want to consider now. If that’s the way they feel,
holding the queens is a better play. Because then, they’d be guaranteed to at least get their money back. If they held the clubs in the hand in question, they’d lose money 70% of the time. To me that’s not particularly important, because winning $250 once every 47 times makes up for a lot of $5 losses.
Other people are willing to go with ev, as long as it is easy to memorize the play. In Double Double Bonus, for example, many players just hold the A from either A♥ K♣ J♦ 5♠ 3♥ or A♥ Q♣ J♦ 5♠ 3♥ even though those players studying ev know that QJ is the better play in the second hand.
It isn’t that players are intentionally making a wrong play, it’s just that they have memorized the simpli ed Double Double Bonus rule that“If there are three unsuited high cards including an A, just hold the A” rather than the better rule that “If there are three unsuited high cards including an A and a K, just hold the A. If the high cards are speci cally AQJ, hold QJ.” e second rule (which is determined based on ev) is more accurate, but more complicated.
Is memorizing a better rule worth the e ort? It is to me, but you’ll have to decide for yourself.
Listen to Bob’s radio show Gambling With An Edge, on Thursday evenings 7 to 8 p.m. Pacific Time on radio station 1230 AM in Las Vegas online at klav1230am.com. Dancer’s products may be ordered at bobdancer.com or at 1-800-244-2224 Monday through Friday from 9 a.m. to 5 p.m. Pacific Time.
PAGE 26
SOUTHERN CALIFORNIA GAMING GUIDE
JANUARY 2012