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Best of Alan Krigman

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When Do You Break a 'Made Hand' in Video Poker?

19 January 1998

Video poker buffs face a common dilemma. Whether to break up a "made hand," a guaranteed winner, trying for a larger return. An example might be 5-H, 8-H, 10-H, J-H, J-S in a jacks-or-better nothing-wild game. Should you hold the jacks - at least 1-for-1 and maybe improving to two pairs, triplets, a full house, or four of a kind? Or should you hold the hearts - hoping for a 6-for-1 flush or at least another jack to salvage the original 1-for-1.

Caution might counsel holding made hands. Adventure might advise going for broke. Sagacity might suggest a more scientific system.

Every initial video poker hand has an "expected value." This a theoretical average payout, based on the probabilities and returns associated with different final results.

For instance, say the payout menu for draw poker with nothing wild shows 25-for-1 on four of a kind, 9-for-1 on a full house, 3-for-1 on triplets, 2-for-1 on two pairs, and 1-for-1 on a high pair. The expected value of an initial four of a kind would be 25 and full house would be 9 - the same as the final values. The expected value of initial triplets would be 4.3 - the guaranteed 3-for-1 plus allowances for draws to a full house or four of a kind. Likewise, the expected value of initial two pairs is 2.6 - 2-for-1 plus a possible full house. And the expected value of an initial high pair is 1.5 - 1-for-1 plus possible draws to two pairs, triplets, a full house, or four of a kind.

Back to the example in the introductory question. The expected value of the high pair is 1.5. The expected value of the four card flush is only 1.2. So the holding pair promises more profit.

What if the starting hand were 8-H, 9-H, 10-H, J-H, J-S? Now, dumping the jack of spades leaves a four-card outside straight flush. This has an expected value of 3.6 - which exceeds that of the high pair. So it's potentially more profitable to go for the gold. And, if the starting hand happened to be 10-H, J-H, J-S, Q?H, K-H, the expected value of the four-card royal would be 18.7 - a strong favorite over the made pair.

Happily, you don't have to memorize long lists of expected values or - I shudder to mention such a thing - do the arithmetic. Learning a few simple rules is enough to cover most situations.

With nothing wild and a typical payout menu, the math favors sacrificing made hands in only three cases. Break a high pair against any four-card straight flush. Break a straight or a flush against a four-card royal.

Additional made hands are underdogs in games with deuces or a single joker wild. With no extraordinary bonuses, give up a straight, flush, or triplets with one wild card in favor of any four-card straight flush; break a straight or flush with no wild cards in favor of a four-card royal.

Bonus payouts may muddy the waters. Take Double Bonus Plus nothing-wild jacks-or-better machines. Here, four of a kind pays 160-for-1 on aces, 80-for-1 on deuces through fours, and 50-for-1 on everything else. Triplets pay 2-for-1. But triple aces has an expected value of 9.0 while that of a full house is 8.0; if your initial hand is a full house containing three aces, discard the pair and hope for the fourth ace. Otherwise, regular rules apply.

Improving expected value by breaking made hands is straightforward for most versions of video poker. Machines with unique payout menus appeal to some solid citizens, but may require special strategies to reap what seem like the benefits. Good players will investigate the nuances of such games, rather than frantically feed a new cash cow, assuming their friendly neighborhood casino has suddenly become a great philanthropic trust.

As Sumner A Ingmark, the venerable poet of video poker, voiced plainly:


On poker machines, the players' cut'll,
Improve or decline with judgments subtle.

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.