Video Poker strategy is about the long run

Last night, I sat down at a five-play Double Double Bonus machine and had a mostly frustrating night. In the end, I hit a big four of a kind and only lost a few dollars, so it wasn’t a financially frustrating evening.
Just to be clear, I do not win every time I play video poker. Nobody does. If they tell you they do, well, let’s just say that they’re not telling the truth. Video Poker strategy is about the long run and given that I was playing a machine with a payback below 100%, I’m going to lose in the long run and probably win only about 30-35% of my sessions.
The night was frustrating because I just couldn’t seem to draw any good cards. C’mon, we’ve all felt that way while playing. Just admit it. The question I’ve often asked of you is what do you do when you feel this way? If you start playing hunches, you’ve fallen into the trap. If you just stay the course and keep following the right strategy, everything will eventually even out.
On this particular night, it just seemed like I was dealt an overabundance of 4-card Flushes and just didn’t seem to draw that Flush very often. Unfortunately, these hands can frequently be all or nothing. Sure, I had some high cards in the hands and I’m sure I picked up some High Pairs, but when you hold a 4-Card Flush, you lose all opportunities for the big hands in Double Double — the Quads.
But, what choice does a player really have? When you are dealt a 4-Card Flush, the choices of what else you could potentially play is pretty limited. You might have a Low Pair. You might have 1, 2 or 3 High Cards. A 4-Card Flush is a winning hand in the long run with an expected value of over 1.0. The other hands aren’t even close. Do I really want to throw away my long-term winning hand to go for some of the worst hands on the strategy table just because I seem to be drawing fewer flushes than I expect?
While sitting there, I can quickly calculate (roughly) the number of flushes I expect to hit on each draw. With nine possible ways to draw the flush and playing five hands, I quickly multiply these together and say this is similar to having 45 possible cards out of the 47 available.
This means on average I would expect to hit one each time I have a 4-Card Flush. Of course, while the average may be one that doesn’t mean every time I have this I’m going to get exactly that amount. If only it were this easy. Then again if it were this easy, playing video poker probably would not be as much fun as it is.
This morning, I calculated the probabilities of getting none through five flushes from a 4-Card Flush. Well, as is no surprise, “1” is the most likely outcome and should occur about 41% of the time. The next most likely outcome is “0” with 34.5%.
I’m sure in my mind, this was occurring about 90% of the time, even though it was not likely anywhere near this. Perhaps on the evening, these numbers were reversed. Given the relatively small sample, this would not indicate a machine defect or the earth coming to an end. This would just be an example of a “cold machine.”
As we move up the chart, “2” will occur about 20% of the time, “3” about 4.5%, “4” about 0.5% and you’ll hit all “5” flushes about 0.026%. Somehow, I never recall this ever happening, despite it being only a 1 in 3,883 chance of success.
Given the math, I can’t tell you with certainty that by the time the night was over I didn’t get very close to these probabilities. Unless I had a little notebook in which I was marking down the results, it is all based on my best recollection.
Since I was not doing well for most of the evening, I have no doubt that this made me remember all the “0” occurrences while down-playing the “3”s that I had. I don’t believe I got any “4”s, but I can’t swear to that.
Even if I am remembering correctly, my alternative would have been even worse. I have no doubt that if I had played all those Low Pairs over my 4-Card Flush, or started to play 2-Card Royals instead of the 4-Card Flush that my overall results would have been far worse.
There is a good chance that my bankroll would have been depleted before I had a chance to hit my comeback Quads that left me just short of even. Sometimes, it is not about the hands you win, but about staying in the game long enough to get to the hand that’s the big winner.
Elliot Frome is a second generation gaming analyst and author, whose math credits include Ultimate Texas Hold’em, Mississippi Stud and many other games. His website is www.gambatria.com. Contact Elliot at ElliotFrome@GamingToday.com.

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