This past week I sat down to play some Deuces Wild video poker. About a dozen times, I was dealt a 4-Card Straight Flush, 4-Card (Wild) Royal or Four of a Kind. I missed getting my desired hand all 12 times.
The odds of hitting the hand vary a bit on the above three hands. I have a 4 in 47 chance of hitting the Five of a Kind, a 6 in 47 chance of hitting the Straight Flush and a 4 in 47 of hitting the Royal while still having a shot at pulling a Straight Flush instead.
For the sake of simplicity, we’ll say that on average I should hit the big hand 5 in 47 or just over 10 percent of the time. The probability of not hitting over 12 tries is just over 25 percent.
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Clearly things were not going my way, but we’re not exactly talking about questioning if the machine was fair.
Come to think of it, I forgot to mention that my very first hand dealt was a 4-Card Wild Royal and I actually did hit that one. So, I guess I actually went 1 for 13. The probability of hitting 1 of 13 is more like 35.9 percent. This is the most likely outcome for 13 hands. It is less likely that I would hit 0 or 2.
So essentially, given the small sample size, I’m exactly where I would expect to be. Of course, since I hit the first and missed the next 12, I wasn’t feeling very good about how I was doing — even though financially I was pretty close to even.
When playing video poker, however, how you are ‘feeling’ must be thrown away. You must play like a Vulcan — by pure logic. In the cases I’ve described, there really isn’t much choice to how you play your hands.
But suppose after missing out on the Straight and Royal Flushes you decide to hold only the Deuces? Two Deuces is worth 3.27 on our strategy table, while a 4-Card Royal is worth 4.52. That’s a big margin. If you only have 1 Deuce, the expected value is 1.03. a 4-Card Straight Flush is 2.23, more than double, while a 4-Card Royal is 3.25, more than triple.
What if the situation is reverse? You hit a bunch of these hands in a row and you decide to start holding a 4-Card Straight Flush with 2 Deuces figuring you’re likely to get the Straight Flush. In this case, the 4-Card Straight Flush isn’t on our strategy table because its expected value is below that of the Two Deuces.
What happened on the past hand, the past 100 hands or the past 1 million hands is completely irrelevant. Yes, machines have hot streaks and cold streaks. To be more accurate, the math tells us there will be hot streaks and cold streaks. The machine plays no part in it.
That math essentially also tells us what to expect going forward, but it does so without taking into consideration what happened in the past. This is because the past is irrelevant to the next hand. The expected value of the next hand is the payback of the machine.
If you are dealt Four of a Kind, you have a 6 in 47 chance of getting Five of a Kind. It does not matter if you hit the last 10 of these or missed the last 100 of them.
It’s O.K. to be (reasonably) emotional while you are playing. You just can’t let it dictate your strategy.