tiltproof

It's not often that you see a one or two outer hit on the turn or river, but I recently had this happen on two consecutive hands. The first I won, and the second I lost. I want to discuss them really quickly, not so much to analyze the play but to talk a bit about odds and how they apply to actual results.

The first hand I limped in with T9s and picked up a flush draw on the river. There was a pot-sized bet which another player and I both called. The bet was pretty small in relation to our stacks, and I thought it was possible I could win more if the flush came.

I did hit my flush on the turn, and also picked up an inside draw to a straight flush. There was a bet of only about 1/3 of the pot in front of me, then a raise of the same size. I called, and then the bettor reraised for the same amount. The other player and I both called.

The river brought my miracle card and I made my straight flush. The player who reraised on the turn moved in. He had made the nut flush on the turn and was pretty amazed to see I had hit my one out on the river.

As we were talking about how lucky I had been, the next hand was dealt. I looked down at 88 and limped in. The flop came AJ8 with two clubs. I really liked this flop, I thought there was a good chance I could get some action. I bet the size of the pot, another player called, and then a third player put in a pretty good-sized raise. I was not very worried about AA or JJ as there had not been a raise preflop, and I moved in. The raiser called and turned over J8, he had flopped bottom two pair.

Now, someone in this situation who flopped top two would have four outs, since the board could pair with either of his cards, but since all the eights were out it meant that only the two remaining jacks could save him. I knew that I was in fantastic shape, but the turn card was a jack and I was drawing dead on the river.

So, the first hand I hit my one outer, then I immediately lost to a two outer. I don't know what the odds are against those two things happening on consecutive hands, but I'm sure it's a pretty big number. This is the sort of thing that could get someone who had never taken a statistics class to start grumbling about how the site is "rigged." I didn't do that, because I know that just about anything can happen in the short term.

Say that you're a 90% favorite in a hand. That means that if the hand is played ten times, you'll win nine out of the ten, right? Actually, it doesn't mean that at all.

When you look at real world results using statistical measures, a big thing to consider is the size of the sample (the number of events). The bigger the sample is, the more the results should approach the theoretical odds.

For example, let's say you flipped a perfectly balanced coin ten times. Even though there is a 50% chance of it coming up heads and the same for tails, you are not likely to get five heads and five tails in your results, and that certainly wouldn't happen each time you tried. You might even get all ten heads or ten tails, because such a small sample is not very accurate. Again, in the short term, anything can happen.

If you made that same coin flip a thousand times, or ten thousand, or a million, you would expect the actual results to more closely approach the theoretical odds as the sample size got larger. The bigger the sample, the more accurate it should be. This is called The Law of Large Numbers. (There is a cool Java calculator that demonstrates it here.)

Now, let's say that you're in a tournament, and all of the chips go in on the flop. You're a 90% favorite to win the hand. That's pretty much a lock, right?

Well, the first thing to consider is that even if the results held to the theoretical odds, you would lose that matchup ten times out of one hundred. Even a big underdog will win sometimes, and if the other player is not drawing dead they do have a chance. But let's consider this further in light of the sample size issue.

As we discussed, the results should get more accurate as the sample gets bigger, but in the short term with a small sample anything can happen. You might lose that hand where you're the 90% favorite, and then it could happen again within a short period of time, even several times in a row. Ths short-term results may not resemble the actual odds at all when you look at your play during an hour, or a day, or even a five day tournament. Those sample sizes just are not big enough to expect that you'll really win that matchup 90% of the time. You might win it every time, or not at all.

Of course that doesn't mean you should get your money in as the big underdog, thinking that the small sample size means you're more likely to suck out. We still use the theoretical odds to determine whether we should make a specific play or not, because we're playing for the long term.

In a cash game if you're a 4:1 dog to hit your draw and win the hand, but the pot is offering you 6:1 to call, that's a call you should make. You should call even though you know that you might not hit the draw this time, and you might not hit it the next ten times you're in that same situation. Over the long run, though, as the sample size gets bigger, it should be a profitable situation.

Ted

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