The Nature of Paybacks

30 July 2020

By John Grochowski

Given optimal strategy in video poker, you’ll see full houses just about as often as flushes and flushes just about as often as straights.

Paybacks differ widely. The goal of designers is a game that’s fun to play, attractive to players and makes a profit for the house. Reflecting true odds in the pay table takes a back seat to all that.

On the player side, payback differences necessitate strategies that are more aggressive toward more lucrative hands.

Let’s set aside full houses for now and focus on flushes and straights.

In 9-6 Jacks or Better, you’ll see full houses an average of once per 87 hands, flushes once per 91 and straights once per 91. In 9-6 Double Double Bonus Poker, it’s once per 92 for full houses, once per 88 for flushes and once per 78 for straights.

In both games, flushes pay 6-for-1 and straights 4-for-1. And in both games, we treat a one-card draw for a flush with more respect than a one-card draw for a straight.

It’s easy to see the difference when we look at hands that include four cards to a flush as well as a low pair vs. four-cards to an open-ended straight and a low pair.

Imagine you’re dealt 3-4-6-9 of hearts along with a 6 of spades. In 9-6 Jacks or Better, your average return is 5.74 coins per five wagered if you hold the hearts and discard the other 6. If you hold the pair instead and discard the other three hearts, the average return drops to 4.12 coins.

In 9-6 DDB, the average return for holding the hearts also is 5.74 coins, but the average on 6-6 drops to 3.66. That’s because the two pair return on DDB is only 1-for-1 vs. the 2-for-1 on JB.

Now imagine you’re dealt 5-6-7-8 of mixed suits along with a second 6. In 9-6 Double Double Bonus, the average return for holding 5-6-7-8 is only 3.40 coins. Holding four parts of a straight is not as good a play has holding 6-6, at 3.66.

The difference is wider in 9-6 Jacks or Better. The average return on the mixed-suit 5-6-7-8 remains 3.40 coins per five wagered, but the higher two-pair return sends the average on 6-6 rising to 4.12.

There is a difference in the frequency of successful draws. Starting with four cards in the same suit, there are nine remaining cards that could complete your flush. Starting with four cards toward an open-ended straight, there are eight cards that could result in a straight. In the case of 5-6-7-8, any of the four 4s or four 9s would complete the straight.

Coupled with the gap in paybacks, that makes chasing flushes more lucrative than chasing straights.

It’s important to separate strategy for flush draws vs. straight draws when a low pair is involved, but there is no such conundrum when the alternative is a single high card. When either four cards to a flush or four to an open-ended straight is accompanied by a Jack or higher, the better play is to discard the high card.

Average returns on a lone Jack are 2.40 coins in 9-6 DDB and 2.43 in 9-6 JB. Averages remain 5.74 on the four-card flush and 3.40 on the unsuited 5-6-7-8 in either game,

So we hold either four to a flush or open-ended straight over a high card in either game, but there’s a separation where low pairs are involved. Hold four to a flush over a low pair, but a low pair over four to a straight.

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