Why a Video Poker Bonus May Be No Bargain

It seems like whenever you check out the video poker machines in a casino, you find a new twist. Often it's a bonus for particular hands. You're supposed to think you're getting some kind of bargain. And, sometimes you are. But not usually.

One hitch is that most bonus machines have the same payout rates as their plain-Jane cousins. The dividend for one hand is taken from the normal return for another. An example might be a jacks-or-better game with a premium on red flushes but 1-for-1, not 2-for-1, on two pairs. On balance, this neither helps nor hurts; it just skews results from more but small to less but large wins.

There's a worse problem. If you alter your strategy trying for a bonus, it may be the casino that gets the bargain.

I'll explain.

The other day, I was watching someone play jacks-or-better draw poker, nothing wild. The machine ordinarily paid 25-for-1 on four-of-a-kind. A bonus raised the payout to 80-for-1 when the four-of-a-kind were pictures or aces.

At one point, the player was dealt K-ª J-¨ 7-§ 4-§ 2-ª. She held the king, mentioning she'd ordinarily keep both pictures but thought this would give her a better chance at the bonus.

She was right about the higher odds of hitting the bonus. The chance of two different face cards yielding four-of-a-kind is one out of 8,107. Starting with only one, the chance of a bonus hand more than doubles, although it's still a scant one out of 3,879.

Where was she wrong? On a representative liberal machine, the pre-draw expected value of two unsuited high cards is $0.49 per $1 bet. For one high card, it's $0.48 per $1 bet. Given the various amounts and probabilities, a $90 rather than $80 four-of-a-kind bonus payout would be needed to overcome the $0.01 difference in expected values. Dumping the second face card raised the casino's edge by a tenth of a cent per $1 bet on this hand.

A few rounds later, the player was dealt 5-ª 5-© 9-© 10-¨ Q-§. She drew four to the queen to get a shot at the bonus, rather than hold the fives. Another weak decision. The expected value of a low pair is $0.82 per $1 bet. The expected value of a single high card - ignoring the bonus - is $0.48 per $1 bet. The four-of-a-kind payout would have to be $1,344 to make up the $0.34 shortfall in expected value. Going for the $80 bonus payout gave the casino about $0.32 for the $1 bet.

As I was leaving, the player was dealt J-§ J-¨ 8-¨ 8-ª 4-©. She held just the jacks, saying she'd be guaranteed 1-for-1 and was willing to sacrifice the two-pair 2-for-1 to get a shot at the bonus. Here's what she really gave up. The expected value of two pairs is $2.60 per $1 bet. The expected value of a high pair, without the bonus, is $1.54 per $1 bet. The bonus would have to pay $407 rather than $80 to overcome the $1.06 expected value gap between the two pre-draw hands. The weak decision was equivalent to giving the casino $0.88 per $1 bet on this round.

Figures vary slightly among machines, based on individual payout schedules. And, there are instances - especially on progressive machines - when a gigantic jackpot makes a switch in strategy statistically sound. Also, of course, what's to tell folks who go for bust because they won't be happy with modest profits? Or to say to solid citizens who think they can pick the machines that are "due," play strictly on their hunches, and win almost every time they visit the casino? Greed and anecdotal evidence aside, though, you maximize your chances by learning the optimum strategy for a particular game, then following it faithfully.

This philosophy was perhaps best captured by the immortal Sumner A Ingmark, visionary poet of video poker, who vividly pronounced:

The tortoise-hare fable,
Should have long ago shown us,
That steady but able,
Can beat get-rich-quick bonus.