Video poker odds are not always intuitive, with relative frequencies vs. payoffs of full houses, flushes and straights being prime examples.
In late May, I was playing video poker next to a husband and wife. He was playing 8-6 Bonus Poker Deluxe, with an average return of 98.5 percent with optimal play, while she was playing 7-5 Bonus Poker, a 98.0-percent game.
She was dealt 10 of hearts, 7 of hearts, 6 of spades, 5 of hearts and 4 of hearts.
Her husband looked over and said, “You have quite the dilemma there. I can never decide what to do with that hand.”
When she said, “The flush pays more. I’ll go for the flush,” he replied, “Yeah, the flush pays more, but you get the straight a lot more often. It’s a tough call.”
She held the four hearts and drew a Jack of clubs. No payoff, but she had the right idea. Per five coins wagered at 7-5 Bonus Poker, the average returns are 4.79 coins if you hold the four hearts and 3.40 if you hold 4-5-6-7 of mixed suits.
The 5-for-1 payoff on flushes vs. the usual 4-for-1 on straights is part of the reason. But at the time of decision, she had a better chance of completing a flush than a straight.
Of the remaining 47 cards after she saw the first five, eight would complete her straight — the four 3s and the four 8s. But there were nine remaining hearts, any one of which would have completed the flush.
She had a 17 percent chance of completing the straight and a 19 percent chance of completing a flush. Going for the higher-paying hand is no dilemma at all.
The specific case assumes five known cards, but even talking in general terms, the frequency of flushes and straights is a lot closer than most players think. You can add full houses to that mix, although full house draws don’t factor into the same decisions as flush and straight draws — if there’s a one-card draw for a flush or straight, there’s no reasonable path to a full house.
Given optimal strategy in 7-5 Bonus Poker, full houses occur about once per 87 hands, flushes once per 92 and straights once per 88. The most frequent of the three is the highest payer, and all three are close to the same frequency.
Her husband’s game, 8-6 Bonus Deluxe, which also pays 4-for-1 on straights, has hand frequencies that lean a little more toward straights. There, you’ll get full houses once per 87 hands, flushes once per 90 and straights once per 78.
If hand frequencies were perfectly in proportion to payoffs, you’d expect one straight for every 1.5 flushes and two full houses. Instead, it’s one straight for every 1.15 flushes and 1.12 full houses.
Strategy-wise, that affects us mainly on hands like the straight vs. flush decision I witnessed. In non-wild card games, the better call is to hold four to a flush vs. four to a straight. Flushes pay more, and you have a better chance of drawing the card you need.
Why wouldn’t game manufacturers change the pay tables to better reflect the true odds? Because the goal isn’t to pay true odds, it’s to make the games fun and interesting to play.
American Poker approximated true odds by paying the same 8-for-1 full houses, flushes and straights. It appealed to a niche, but most players prefer the more payoff demarcation. And if that’s what people will play, that’s what they’ll get.
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