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Does the house want everybody to win?

Does the house want everybody to win?

A shuffle through the Gaming mailbag:

Q. I’ve been thinking about the Joker’s Wild Kings or Better strategy problems you wrote about several weeks ago. One of the hands was 10 and Queen of diamonds, 2 and 4 of spades and 5 of clubs.

You recommended holding the Queen and 10 instead of discarding all five cards. That’s even though pairing a Queen won’t bring any payback since the table starts at Kings.

I’ve thought about it, and I guess I agree. You mentioned the long shot at a royal as one reason for the hold. Even if don’t hit that rare natural royal flush, I’d still be keeping my chances open of maybe hitting a wild royal flush. Did the wild royal cross your mind when you made the recommendation.

A. Yes, all possible outcomes are considered.

Per five coins wagered, the specific Joker’s Wild version discussed pays 4,000 for a natural royal flush, 1,000 for five of a kind, 500 for a royal flush with Joker, 250 for a straight flush, 85 for four of a kind, 35 for a full house, 25 for a flush, 15 for a straight, 10 for three of a kind and 5 for two pairs or a pair of Aces or Kings.

If you hold Queen-10 of diamonds, there are 17,296 possible draws in a 53-card deck that includes a Joker. Of those, 14,807 are losing draws that bring no payback.

Among the paying hands, there are 645 high pairs, 711 two pairs, 584 with three of a kind, 294 straights, 210 flushes, 27 full houses, eight with four of a kind, six straight flushes, three wild royals and one natural royal.

The paybacks on all those possible winners are added, then divided by the number of draws to get an average return of 1.79 coins per five coins wagered.

If you discard all five cards, there are 1,712,304 possible draws, including 1,344,068 losers. Among possible winning hands, there are 187,431 high pairs, 71,802 two pairs, 85,400 with three of a kind, 12,840 straights, 4,733 flushes, 3,942 full houses, 1,940 with four of a kind, 122 straight flushes, 15 wild royals, eight with five of a kind and three natural royals.

When the payoffs on all those winners are added and divided by the number of draws, the average return is only 1.65 coins.

That’s the way strategy evaluations work for every hand in every video poker game. All possible draws and payoffs are considered, and the average return per hand indicates our best strategy.

Q. You’ve written that the house gets its edge on casino games by paying winners less than true odds. Does that mean they’re happiest when everybody wins?

A. I get variations on this observation — or is it deliberate misunderstanding? — every few years. But to take it seriously, the house is happiest when a game plays at true odds. With a normal distribution of wins and losses, the house will make money because losers are paying full fare while winners get less than par.

Given a double-zero roulette wheel and 38 wagers of $1 each with one bet on each single number, the house will collect $37 on the losers and pay $35 to the winner. There is a normal distribution of winners and losers, and the house makes a $2 profit.

If the winner was paid $37 as per true odds, then the house would take in $37 and pay out $37. There would be no profit. The house makes money because it pays the winner less than true odds while collecting the full amount on losing wagers.

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