A friend of mine, Steve, is someone I know from square dancing. He is retired and recently decided that he wanted to increase his monthly income by gambling, so he asked me which game he should learn first. I told him Full Pay Deuces Wild for quarters. It’s a relatively easy game to learn and it’s available in a few places close to where he lives (specifically Sunset Station, Fiesta Henderson, and Sam’s Town — possibly other places as well). He will only make $6 an hour or so playing the game and he needs significant study to get good enough to even do that. Still, it’s a place to start.
Four months ago he got Video Poker for Winners software and the Dancer/Daily Winners Guide to Full Pay Deuces Wild. So far he’s read only 25 pages in the book and practiced less than a couple of hours on the computer. This is not a “he’s too busy” problem. This is a “he’s not really motivated” situation. Which is okay. Each person must decide for himself how good he wants to become and how much he is willing to study to get there.
So Steve was playing in a casino, held one deuce, and received four natural royal cards for a 125-coin wild royal flush in spades. This struck him as highly unusual and he speculated that perhaps it was one time in a half million or so that this could happen.
Figuring out the exact odds after-the-fact can be a slippery process. It so happened that he held the deuce of spades and was dealt A♠, K♠, Q♠, J♠. This particular draw is one time in 178,365. However, if he would consider A♠, K♠, Q♠, T♠ just as special, or perhaps a wild royal in any the other three suits, or even one with another deuce or two thrown in, the number can get as low as one time in 686. One number is about 260 times as big as the other. That’s a pretty wide range.
He then asked me what the odds would be holding W (which signifies a deuce), A♥, K♥, and filling in the wild royal. This one I could figure out in my head in less than 20 seconds and it’s about one chance in 72. Most of you don’t obsess as much about video poker as I do so you haven’t had as much practice doing such a problem in your head. Let’s go through that process.
The other two cards must be from the following pool: Q♥, J♥, T♥, and the other three deuces. Any of these six cards can be drawn first, and once that card is drawn, you have five remaining cards. Since the order is unimportant (that is, whether you draw the Q♥ and then the T♥ or first draw the T♥ and then the Q♥ doesn’t matter) the formula is 6 * 5 / 2 = 15 different ways to complete the wild royal with those three initial held cards. Since there are 1,081 different ways to draw two cards from that position, the answer is 15 / 1081 = 1 / 72 (approximately) or about one chance in 72.
I then commented that holding W, A♥, K♥ may well have been a mistake! He didn’t believe me. He assured me there was really nothing else in the hand to be held.
While W AK is eligible to be held some of the time, there are many situations where you are dealt W AK and you should hold just the deuce or perhaps some other combination. It’s reasonable to assume there was only one deuce in the hand and that no card was paired up (making 3-of-a-kind). Even a beginner could see that. Also, there was probably not a flush or straight dealt, or Q♥, J♥, orT♥. Recognizing that is well within Steve’s current capabilities.
But was there a lower heart dealt? Or how about an unsuited Q, J, or T? In all of those cases, strong players just hold the deuce. Even with an unsuited 3, it’s usually correct to just hold the deuce, and sometimes the correct play is to hold the deuce with other low cards, such as 45 or 46 (where it can even matter whether these last two cards are suited with each other or not!) Or how about 6♦, 7♦? Does he know that W 67 is superior to W AK? Experienced competent players see these things at a glance, but Steve very possibly ignored all of these considerations. He hasn’t practiced enough on the computer or read far enough in the Winner’s Guide for these to be second nature. But he has been playing in the casino (it’s more fun than practicing!) so he’s on the path to becoming an experienced not-so-competent player. At this rate he’ll simply learn to make his mistakes faster!
Was holding W AK a mistake in the actual hand Steve played in the casino? I have no idea. He has no recollection of what the other two cards were. Possibly he’ll learn enough some day to understand that all five cards are important in making his decisions! He has the right tools for the job. All he has to do is to use them.
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