VIDEO POKER

Which Occurs More Often?

In 9/6 Jacks or Better, 2s, 3s, and 4s return 125 coins -- as do all other 4-of-a-kinds as well. What would you say is the frequency of hitting one of these hands in 9/6 Jacks?

a. Once every 1,925 hands
b. Once every 1,908 hands
c. Once every 1,897 hands

Simply translated, are these hands slightly more likely in Jacks or Better, slightly less likely, or equally likely than they are in Double Bonus?

The answer to this question isn't difficult once you correctly answer the following question first: Which hands (containing a single two, a pair of twos, or 3-of-a-kind twos) are played differently in the two games?

It is NEVER correct to hold a single low card in either game, so we just need to look at when we hold a low pair or 3-of-a-kinds differently between the two games.

One class of hands that contain a one of these low pairs that is played differently is "aces full", e.g., AAA22. But whether you hold the full house (as is the correct play in Jacks or Better) or just hold the aces (as is the correct play in Double Bonus), you are never going to end up with four 2s anyway. A similar type of hand is "aces up", e.g., AA229. Although the correct play in both games is to hold AA22, many Double Bonus players only hold the aces. But you are never going to get four 2s in either case, so these hands don't affect today's problem either.

One type of hand that IS played differently between the two games is 22345 "rainbow", meaning that there are no flushes or straight flushes possible. In Jacks or Better, you hold 22, while in Double Bonus you hold 2345. These hands don't happen very frequently, and even when they do it's a 1-in-360 shot to convert 22 into 2222, but at least it's possible.

Perhaps surprisingly, the low pair versus 4-card straight hands are the ONLY ones where you'd hold 22 in Jacks or Better and something else in Double Bonus. There are a few hands where you draw 5 cards in Jacks or Better but not in Double Bonus (such as 4h 5h 7s 8s Tc, or Th 9h 5h 3c 2d) or where you hold just a single high card in Jacks or Better but go for the inside straight in Double Bonus (such as Jd 9c 8s 7d 3s). Although it is not likely, it is at least possible to end up with special quads on these hands in Jacks or Better (because you are drawing either four or five cards and miracles do happen occasionally), but impossible in Double Bonus (because you aren't even trying for it). Once you realize that, it is easy to conclude that answer c above is the only one that could possibly be correct.

I was first presented this puzzler by Liam W. Daily (my co-author on both our strategy card series and our Winner's Guide series, of which Jacks or Better and Double Bonus are currently available at ). My initial thought was the special quads would occur more frequently at Double Bonus. After all, since they are paid over three times as much in Double Bonus as they are in Jacks or Better, it seemed to be plain common sense that you'd go for them more often. This was a case where my video poker common sense let me down.

A related question is how can you get an accurate answer? Getting the 1,908 figure for Double Bonus is easy. After all, you can go to the Double Bonus game on WinPoker and click on "analyze" and then "game" and the figure 1908.168 appears in the "occurs every" column. But how do you get this number for Jacks or Better? In the Jacks or Better game on WinPoker, all 4-of-a-kinds are lumped together. You can't assume they each occur equally often because the ones including jacks, queens, kings, and aces happen more frequently than the rest of them (because, among other hands, from Js Jh 9h 5h 3h you'd hold JJ but from 3s Jh 9h 5h 3h you'd hold the hearts.)