Video Poker Temptations: Calculating Expected Value Over Instinctive Holds

Video poker players regularly receive hands that present a conflict between immediate payouts and the lure of much larger prizes. A column published in Casino Player Magazine by Jerry “Stickman” Stich examines several such situations, using expected value calculations to show when players should resist the obvious choice.

Stich opens with a Jacks or Better example in which a five-card straight guarantees a 20-coin payout on a five-coin bet. The same hand holds a four-card straight flush offering a potential 250-coin top prize. Most players would discard the straight to chase the straight flush, yet the expected value of that draw totals 17.23 coins—below the certain 20 from the made straight. The correct hold is therefore the paying straight.

Further illustrations make the point that payout size alone misleads. A high pair of queens carries an expected value of 7.68. Drawing instead to a gapped four-card straight flush (8-9-10-Q) produces an expected value of 11.91, making the break of the pair the superior long-term play. In a separate dealt hand, a five-card flush paying 30 coins must be discarded when a four-card royal flush shows an expected value of 97.76. One royal hit more than compensates for preceding losses, Stich observes.

The pattern does not always favor the draw. A three-card straight flush holds an expected value of only 3.03, while a low pair in the same hand reaches 4.12. Here the pair is the better retention.

When to Break Paying Hands

These examples demonstrate that intuition based on payout ladders frequently leads to lower returns. The sole reliable method is to consult a basic strategy table that ranks every hold by expected value. Players need not compute the individual figures; they simply follow the ranking from highest to lowest.

Stich states that in non-wild-card games only two holds ever displace a high pair: a four-card royal flush and a four-card straight flush, whether gapped or not. The only time a paying flush or straight should be broken is for a four-card royal flush; against a four-card straight flush the high pair remains preferable.

Applying the Math at the Tables

The column from Casino Player Magazine underscores that consistent use of expected-value ordering improves results without requiring complex mathematics during play. Patience and adherence to the ranked strategy ultimately outperform the temptation of chasing single large hits.

Reporting: Casino Player Magazine

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