Last week, I was playing some Deuces Wild video poker and seemed to have hit a lot of cold streaks where I simply could not get a deuce. It seems like I would constantly go five or 10 hands without one.
For the moment, I’ll ignore those cases of selective memory all players have when we forget that we were dealt a deuce but we still lost the hand, so we ignored it. When playing Deuces Wild, the probability of having a hand without a deuce is 65.88%. So roughly speaking, two out of three hands will not have a deuce. This probably doesn’t shock anybody.
But, what is the probability that you go five consecutive hands without a deuce? We take this 65.88% and multiply it by itself five times. We get 12.41%. This, unfortunately, doesn’t seem so farfetched. What about 10 hands? We’re down to 1.54%. This is a bit more rare, but we’re not talking astronomical.
To put this in perspective, the probability of being dealt Three of a Kind on the deal is about 2.11%. You don’t think your machine is broken when you get dealt one of these, don’t think it is broken when you go 10 straight hands without a deuce!
Have you ever gone 20 hands without a deuce? Now we’re talking 1 in 4,210. Definitely longer odds. If you’re a regular player, it’s probably happened to you a few times, whether you remember it or not. You’ve played tens of thousands of hands. Maybe even hundreds of thousands or millions of hands over the years.
A few weeks ago, I was thinking about how I did not recall ever having a dealt Royal. Maybe I have, but I don’t remember it. Two weeks ago, on the deal, I was dealt four deuces plus an Ace. The odds of this is the same as being dealt a Royal — 1 in just under 650,000. I’m pretty much all set. I’ve done it all!
The reality is that if you’ve played hundreds of thousands of hands, having things occur that happen one in several thousand are simply not going to be that rare.
First of all, you can’t take your total game play (not that anyone knows this) and divide to say something should have happened a certain number of times. If I sit down and play 1,000 hands, I don’t have 100 sets of 10 hands, I have 990 sets of 10 hands. A new set starts with each hand except for the final hands because I don’t play the required 10. If I play for a couple of hours, I can expect to see several streaks of no deuces for 10 hands.
When you’re playing other forms of video poker, you don’t have deuces to count. So, you might turn to how many hands in a row that lose to help add to your frustration. Roughly speaking, when playing proper strategy, you will win 45% of your hands. This means that you will lose 55% of them. The odds of losing 10 in a row is 1 in about 395. Losing 20 in a row? 1 in 155,864. If you really lose 20 in a row, get up and take a walk. It’s not your day.