Video poker design

17 March 2016

By John Grochowski

Video poker games aren’t designed to reflect the odds of poker. They’re designed to attract players and keep them in their seats, and to make a profit for the house.

In the case of big four-ace payoffs, that’s well-known. Games such as Bonus Poker and Double Bonus Poker pay more on four aces than on the rarer straight flushes because chasing the aces brings in players. The rest of the pay table takes care of the profit.

Less obvious is the relative frequency among full houses, flushes and straights. Each occurs about as often as the others, but pay tables separate them with disproportionate payoffs.

Take 9/6 Jacks or Better and 9-6 Double Double Bonus Poker. On each, full houses pay 9-for-1, flushes 6-for-1 and straights 4-for-1. Full houses pay more than twice as much as straights, and pay 150% of the payoff on flushes.

But look at how often they occur, given expert strategy. In 9/6 Jacks or Better, you’ll draw a full house an average of once per 86.9 hands, flush once per 90.8 and straight once per 89.1. Those are all very close, and the hand that occurs most often also is the highest payer.

The result of those disproportionate paybacks is that in 9/6 JoB, full houses account for 10.4% of our overall return, flushes 6.6% and straights just 4.5%.

In 9/6 Double Double Bonus, where our strategy is different, full houses are the least common of the three hands, but the disparity isn’t wide. You’ll draw full houses about once per 92.1 hands, flushes once per 88.0 and straights once per 78.3.

Again, the pay table differences are wider than differences in hand frequency, so that in 9/6 DDB full houses account for 9.8% of our overall return, flushes 6.8% and straights 6.8%.

If we were to convert to a ratio so that the four-coin payoff per coin wagered on straights is 1, then the full house : flush : straight ratio is 2.25 : 1.5 : 1. If we convert the frequency of the hands to a ratio with straights being 1, then on 9/6 Jacks or Better we get 0.98 : 1.02: 1. On 9/6 Double Double Bonus, it’s 1.18 : 1.12 : 1.

Our strategy factors into that. There are more straights in 9/6 DDB than in 9/6 JoB because we draw to inside straights a lot more often in Double Double Bonus. DDB pays only 1-for-1 on two pairs, while Jack or Better pays 2-for-1. That reduces the value of a complete redraw in Double Double Bonus, so we draw to a hand such as 6-7-9-10 of mixed suits that we’d throw away in Jacks or Better.

On both games, we preferentially draw to flushes as compared to straights. Dealt a hand such as 2 of hearts, 6 of hearts, 7 of clubs, 8 of hearts, 9 of hearts, we have a choice: Do we hold all four hearts, or do we hold the 6-7-8-9?

Any of the other nine hearts completes the flush, while there are only eight cards – four 5s and four 10s – to complete the straight. And the flush pays more. So we go for the flush without thinking twice, and that contributes to flushes occurring nearly as often as straights.

Gamemakers could have straights, flushes and full houses pay the same. It’s been done, in a game called All-American Poker. But player preference is to have that bigger full house return available, and player preference trumps having paybacks reflect the relative odds of winning.

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