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Best of Alan Krigman

Gaming Guru

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Should You Bother to Learn the Optimum Strategy for Video Poker?

1 February 2005

Many casino visitors think that, in games requiring decisions during the action, what the gurus call "optimum strategy" doesn't matter much. They're right in that someone can win with guesswork and lose with the laws of probability; further, while arithmetic occasionally yields conclusions contrary to those that sensible solid citizens would reach using their little grey cells, the two often coincide or differ only slightly. However, they're wrong in that their prospects would improve if they have the numbers on their sides. A few hands of deuces wild video poker can serve to illustrate both effects. For this purpose, assume a game that pays according to the accompanying table for a five-coin bet.

Payoff schedule on a typical deuces wild
video poker machine, for five coins bet
   
hand
return
natural royal
4,000
four deuces
1,000
wild royal
125
five of a kind
75
straight flush
45
four of a kind
25
full house
15
flush
10
straight
10
three of a kind
5

Pretend you're dealt A-H J-H 7-D 6-D 5-H. Intuition might suggest holding the ace and jack of hearts, hoping for a natural royal with backups from three of a kind through anything except five of a kind or four deuces. The statistically expected return on this hand, considering all possible outcomes and their chances, is 1.44 coins. Dumping the lot has an expected return of 1.62 coins.

Make believe, instead, that you start with K-S J-C 10-C 7-H 4-D. Would the previous example tell you to discard them all? The math says otherwise. Doing so has an expected return of 1.60 coins but holding the jack and 10 of clubs is worth 1.86. The situations diverge owing mainly to the additional ways to make a straight flush, flush, or straight in this instance than in the first.

What if you begin with 2-S A-H K-S J-H 8-C? Keeping the deuce along with the ace, king, and jack may seem a good choice since there are lots of ways you could get a straight or triplets. This option has an expected return of 3.30 coins. But holding only the deuce, ace, and jack is considerably better, having an expected return of 5.14 coins. And a truly proficient player would pitch everything but the deuce for an expected return of 5.18 coins.

How about receiving 2-D 2-H A-D 10-D 3-D? Standing pat guarantees 10 coins back for the flush. But you know you'll receive at least five, with triplets, by retaining only the deuces. This, indeed, is a better alternative, with an expected return of 16.30 coins. Better, but not best. When the beads come to rest on the abacus, they reveal that keeping everything other than the three maximizes the expected return at 21.91 coins.

Some distinctions are clearly more important than others. It's obviously worth knowing how to boost expected return from 10.00 or even 16.30 to 21.91 coins. Likewise from 3.30 to 5.18 coins. On the other hand, the offset between expected returns of 5.14 and 5.18 won't make either you or the casino bosses rich. Still, although gambling can be entertaining and exciting if you just toss your money into the air and see where it lands, it's far more interesting and satisfying when you know what you're doing.

How can you learn an optimum decision strategy? There are primers aplenty on the topic. Browse in any bookstore within shouting range of a casino, or shop on the Internet, and take your pick.

Another method, which can be more fun, is to play video poker on a computer with software showing the expected value corresponding to various choices and even telling what's best. Buy a program. Or play on-line, free, for any of several different video poker configurations, at http://wizardofodds.com. (You can also print out rules for various versions of video poker at the same authoritative website.) It shouldn't take long practicing like this for you to reach a point where the most propitious choices, or at least those that are close to optimum, come to you on auto-pilot. It's a path to proficiency for which the pedantic poet, Sumner A Ingmark, plainly expressed a preference when he penned:

Seek leisure activity not just recreational,
But with a proclivity to be educational.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.