This week's topic comes courtesy of my own experiences this past summer. My son was visiting from the East Coast for a couple of weeks. This means some time spent on a video poker machine, in between shooting pool, bowling and some movies. I had one of those frustrating nights that could've been so much better "if only". I like to play Double Double Bonus Poker if I'm out playing for a short period of time. In all honesty, it's not the best play, but if you're looking for a quick significant profit, Double Double offers this opportunity. But, you have to get Four of a Kinds and preferably Quad A's, 2's, 3's or 4's. If you get really lucky, you'll pull the right kicker and have a big payout!
Well, within my first ten hands or so, I got dealt a Three of a Kind. It wasn't a bonus one, but any Quads pays well on these machines. I figured I could make a quick profit and be done in under 10 minutes. Needless to say, I didn't hit the Four of a Kind. I played for maybe 20-30 minutes and wound up getting about a dozen more Three of a Kinds dealt to me. None of them turned into Four of a Kind. Hence, the "if only" comment earlier. Had I hit even ONE regular Four of a Kind, the night would've been much better. Had I hit one Bonus (or Double Bonus) Quad, I would've left a winner. Had I managed to hit a few Four of a Kinds, the night would've been a mirror image of how it turned out.
I may know the math, but I still get frustrated when things like this happen. My son asked me the obvious question - how often SHOULD you get a Four of a Kind from a Three of a Kind? The answer is 4.26% of the time or 1 in 23-24 times. I had about 13 of these. So, the probability of me whiffing on all 13 of them was an incredible 56%. In other words, getting none of them was more likely than getting 1 or more. Or yet another way, I had an incredibly ordinary experience. The only thing that may have been unusual was the number of Three of a Kinds I was dealt in such a short period of time.
When my frustration abated, I remarked to my son that I really shouldn't be upset as it wasn't all that unusual for me to miss so many times (I didn't know the exact probabilities in my head, but I was able to make a good estimate and realize it was not so odd). Further, I went on to say that since a Player actually gets more Quads from Pairs than from Trips, I shouldn't be that upset about what happens on 13 hands out of the few hundred (or more) that I played.
This had my son a bit confused. How does one get more Quads from Pairs than from Trips? I had to explain it to him. IF you already have Trips, your odds of getting Quads is far greater than if you had a Pair, but this is not what my statement said. If you have a Pair, you will hit Quads only 1 in 360 times.
BUT, you will be dealt a Pair FAR more frequently than Trips. Of the 2,598,960 possible hands, 1,070,604 will be played as a Pair. 54,912 will be played as Trips. When we take this into account, we find that we'll be dealt a Three of a Kind that will turn into Four of a Kind once in every 1112 hands (approx.). We'll be dealt a Pair that will turn into Four of a Kind once every 875 hands (approx). Unfortunately, for me, on the night in question, I was getting Four of a Kinds this way either!
The point is that in regular jacks or better video poker, about 6% of the payback comes from Four of a Kinds. In Double Double, where the minimum pay for a Four of a Kind is doubled to 50 and go up from there, the Four of a Kind contributes about 15% of our payback, which is a huge portion of it. If you want to win at Double Double, you better get at least your fair share of Four of a Kinds. Roughly speaking, they should hit about once every 425 hands, which translates to every 30-45 minutes depending on how fast you are playing. If you play and hour and haven't hit one, you're probably not doing too well. But, don't fret if you're not getting them from your Three of a Kinds, because you are more likely to get one from a Pair then you are from a Three of a Kind. In the end, you don't really care how you get them, as long as you do get them!