VIDEO POKER

An Interesting Question in Deuces Wild

Compare, in Deuces Wild, the two hands 2 3h 3s 9d Qc and 3c 3h 3s 9d Qc. In both cases you hold the trip threes. Here's my question: Which is more valuable? Your four possible answers are:

a. The first hand (trips including a 2)
b. The second hand (natural trips)
c. Both hands have equal value
d. It depends on the pay schedule

My guess is that most players are not certain of the correct answer. I could lie and tell you I knew it all the time, but in actuality I had to look it up to be sure. It isn't that hard to figure out when you do so systematically.

From 333 (without or without a deuce), the only way to improve the hand is to become a full house, 4 of a kind or 5 of a kind. Let's look at full houses first. Starting from 333 or 233, you simply need to draw a pair. A pair of 4s, 5s, etc. A moment's reflection should tell you that you are just as likely to draw a pair of 8s, for example, starting from 333 as you are from 233. You are less likely to draw a pair of 9s or Qs than the other ranks because there are only three of each left in the deck.

To end up with 4 of a kind from either position, you need to draw either a 3 or a 2. At the outset, there were four 2s and four 3s in the deck for a total of eight. You are looking at three of them, so there are five left. It doesn't matter which one of the five you draw. When you start with 333, there are still one 3 and all four 2s. When you start with 233, there are two 3s and three 2s. Similarly to end up with 5 of a kind, you need to draw two of the five (2s or 3s) remaining in the deck.

So the correct answer is c. Whether the trip is natural or wild makes no difference. In the 1,081 possible draws from either position, you end up with trips 801 times, a full house 60 times, quads 210 times and quints 10 times. And those numbers hold no matter what the pay schedule. I was surprised. Were you?

A related hand is next. Not worrying about suits, is there any difference between the value in Deuces Wild of 3333, 2333, and 2233? This is an easier question. Since it is a 1-card draw in all three cases, you have 47 possible draws. If you get one of the remaining 3s or 2s, (there are four of them in each case), you'll have a quint. Otherwise you'll keep the quad you started with. So each of these have equal value.

Is this information useful? I am not sure. I cannot think of a particular use for it offhand, but the more of these "little nothings" you know about video poker, the better able you are to understand how to evaluate and take advantage of various situations that come along.