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Is jackpot size your criterion for choosing a video poker machine?23 November 2009
Make believe you're at a casino and notice something strange. Five double joker video poker machines in a row. They all look essentially alike but have different jackpots for natural royals.
You figure they're progressive games, where payoffs rise as action proceeds and nobody hits the biggie. But, no, not in this case. Perhaps payback percentage varies from one to the next, those with the highest jackpots having the greatest returns. You do the math, which you can in video poker because the statistics of the final hands are known. Surprise! The calculations reveal that all five machines have equal 98.1 percent returns.
Close scrutiny shows the bosses are robbing Peter to pay Paul. As returns for tough hands go one way, payoffs for some of the easier results go the other. And the changes (that darned math, again) are balanced so overall payback percentage stays constant.
Here are some examples. Say one of the five games has the standard payouts for 98.1 percent double joker poker. These include 800-for-1 on a natural royal, 100-for-one on a wild royal, 50-for-1 on five of a kind, 25-for-1 on a non-royal straight flush, 8-for-1 on quads, and 5-for-1 on a full house.
Two of the five machines have higher jackpots. One is over twice the usual amount, 1648-for-1; a scan of the payoff list shows everything else standard except that quads pay 7-for-1 instead of 8-for-1. The second highest jackpot in the row is 1142-for-1; here, quads return the regular 8-for-1 but a non-royal straight flush is reduced from 25-for-1 to 20-for-1.
The two remaining machines have jackpots below 800-for-1. The lowest is 328-for-1; to compensate, five of a kind yields 75-for-1 rather than 50-for-1. The second lowest jackpot is 360-for-1, with the return for a wild royal also trimmed – it's 75-for-1 instead of 100-for-1; on the rising side of the ledger, a full house is worth 6-for-1 compared with the customary 5-for-1.
Say you're faced with these options. You happen to know that return percentage is the same in all of them, and chances of hits on various hands don't change. The latter two points aren't strictly true. Modifications in payouts for alternate hands may affect the optimum strategy and therefore the probabilities of the game. But the offsets are negligible in the present context.
Given these considerations, many solid citizens would jump at the highest possible jackpot. Economists would say such folks value the utility of $2,060 much more than 1,648 instances of $1.25, even though the total amount of money is the same. A more analytical gambler might well make the same choice. However, a punctilious punter might also ponder two further factors before reaching a decision.
First, odds of busting out vary among the games. Cutting low-probability returns to get higher pay for more common hits improves prospects of long sessions. For the examples cited, the 360-for-1 jackpot game gives a $1.25 bettor with a $100 stake about 62 percent shot at being in action for at least three hours (at four hands per minute). The 1648-for-1 jackpot model gives such a player only 27 percent chance of lasting this long.
Second, the likelihood of reaching a specified profit level before going bust also changes with the different arrangements. Higher payoffs for infrequent hits with lower returns on hands that occur more often are helpful here. Betting $1.25 on a $100 bankroll, the promise of money doubling before running out is best at 49 percent with the 1640-for-1 jackpot. It's worst at 42 percent with 360-for-1 for natural and 75-for-1 for wild royals.
If you're bent on going for broke, none of these numbers matter. Play for the largest jackpot and pray for luck. But remember, this isn't the only criterion for gambling. Maybe you visit a casino for the action, the comps, or the tasteful decor. As the irascible inkmeister, Sumner A Ingmark, intelligently instructed:
Decisions made using impressions initial, May prove in their haste to be too superficial.
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