Rare Streak Counts as Big Positive

Sometimes I'll count results each time through my money -- if I start with $100 and bet $5 a hand, I'll count 20 hands and see how much I have left.

Sometimes I get sidetracked and change counts in midstream. That's what happened one evening during a session of  8-5 Triple Play Bonus Video Poker. I wanted to track hands per hour. I still don't know just how much slower I play Triple Play than single-hand games, because along the way, I noticed something else.

At about play No. 150 -- the equivalent of 450 hands -- it occurred to me that I had not yet drawn a four of a kind. That's bad news in any video poker game. In the absence of a royal flush jackpot, the path to a winning video poker session usually is paved by frequent four-of-a-kind hands. Given expert strategy in 8-5 Bonus Video Poker, four of a kind should occur about once per 422 hands. Draw two sets of quads within 422 hands, and you have a good chance of being ahead of the game. With none, you'll be behind more often than not.

Here I was at the equivalent of 450 hands and still no four of a kind. I decided to change my focus from pure speed and track the number of hands before my first quads. Along the way, I also would track hands with three of a kind on the initial deal, and the results.

At play No. 178 (534 hands), I was dealt three Jacks, but the draw failed to improve any of the three hands. At play No. 232 (696 hands), I was dealt three 7s, and on one hand drew a pair of 3s for a full house. At play No. 257 (771 hands), I was dealt three Aces--a potential bonanza if I could draw a fourth Ace for a 400-coin jackpot. Alas, no improvement.

At play No. 316 (948 hands), three 9s, no improvement. At play No. 324 (972 hands), three Kings, one full house.
Finally, at play no. 362 (1,086 hands), I held a pair of Queens, and the other two popped up on the third hand. My first four of a kind.
How much money did I lose during this extreme quad-less streak? Oddly enough, I was ahead all the way and, in fact, more than tripled my original $100 investment.

Why? Because something even stranger than the four-of-a-kind dearth was happening. Sometime in the first 100 hands, I held 4-6-7-8 of hearts, and on one hand drew a 5 of hearts for a straight flush and a 250-coin payoff.

At play No. 277, I held 6-7-9-10 of diamonds and drew the 8, another inside draw for a straight flush. And on play No. 302, I was dealt 5-6-7-8-9 of clubs, a straight flush on the deal, meaning I had straight flushes on all three hands for a total 750-coin payoff.
That's five straight flushes in 302 Triple Plays, or the equivalent of 906 hands. On the average, we'll see a straight flush only once per 9,360 hands. I was seeing them more than 10 times as often. That'll make up for any four-of-a-kind dearth.

Video poker, and any other casino game, works that way. I can tell you that four of a kind should show up about once per 400 hands in most video poker games, that blackjack players should see two-card 21s about once per 21 hands and that in the long run, any number on a double-zero roulette wheel will turn up once per 38 spins. But those are long-term statistical averages.

In the short term, we won't necessarily get what we're looking for. But if we're very fortunate, we just might get something even better.