World Series of Poker Europe

Call or Fold? A Dilemma Caused by Small Sample Size

Call or Fold? A Dilemma Caused by Small Sample Size
  • Looks like that guy is a maniac -- but is he? In poker, a half-dozen hands usually isn't enough to confirm a read.

  • Successful poker requires seeing yourself through an opponent’s eyes -- specifically the one in the hand with you.

Last week I played a hand that looks on the surface to be so unremarkable as to be trivial, but actually reveals an important truth.

I was at Harrah’s Cherokee using their PokerPro tables, playing $1/$2 no-limit hold’em. In middle position, I was dealt {A-Diamonds}{K-Diamonds} and raised to $8. A gentleman three seats to my left then reraised to $25, leaving himself about $75 behind.

My stack was a little over $200. When action got back to me, I moved all in. He called, showing {A-Hearts}{9-Spades}. The board gave him no help, and I won the pot.

My two decisions probably don’t strike readers as surprising in any way. Those of my opponent, however, likely raise an eyebrow or two — and therein lies the story and the lesson.

The crucial information I have left out from the hand was suggested by what this other player said in disgust, to nobody in particular, after he saw my cards and while the computer was playing out the hand for us:

“He raises four out of six hands, so I know he’s just stealing, and I catch him the one time he actually has a hand.”

Eight players, including myself, had started the table as a new game about half an hour earlier. But this fellow — let’s call him Latecomer — had only joined us six hands before his confrontation with me. He was entirely correct about the six hands he had seen. Unfortunately for him, that constituted a very small and very skewed sample.

In the first 30 minutes or so, I had been completely card dead. If I’m remembering correctly, I had open-raised just once, and that was on the very first hand, with {A-}{Q-}. After that, nothing.

But right after Latecomer sat down, I got a mini-rush of decent hands. I raised first with suited connectors, figuring that I’d get credit for a bigger hand since I had been so inactive. Next was pocket nines, then {Q-}{Q-}, and finally the {A-Diamonds}{K-Diamonds} that saw Latecomer’s patience come to an abrupt end. Altogether that made for four justifiable raising situations in the span of six hands.

I’m confident that nobody else at the table would have played {A-Hearts}{9-Spades} the way Latecomer did there, because they all had important information that he lacked — specifically, a better read on my overall preflop raising frequency.

If you see a player fold hand after hand for half an hour, then raise four out of six times, you’ll be inclined to conclude that he finally caught a few good hands. But if those six hands are the first ones you see after joining the game, you get an entirely different impression — this player is a maniac.

In fact, I would not ordinarily just move all in against an unknown $1/$2 NLHE player with ace-king. That’s because the three-bet range of the average player in such games is heavily weighted toward medium and big pocket pairs, and I’m not thrilled to flip coins for meaningful sums if I can help it.

But that judgment was qualified here, first, by his relatively short stack. If I just called, we’d have a $50 pot, and I’d probably feel obligated to call a $75 shove from him on just about any flop. When that’s the case, I might as well get it in as the aggressor.

The more important consideration, though, was that I was fully aware of his likely perception of me. I had made a mental note of when he sat down. When he reraised, I realized that he had seen my entire flurry of raises in a short time, and knew that he likely concluded that I was getting out of line. That meant that his three-bet range would be much wider than usual, and suited {A-}{K-} had excellent equity against it.

Call or Fold? A Dilemma Caused by Small Sample Size 101
I decided to make my move as quickly as I could...

In fact, while waiting for the action to get back to me, I decided to make my move as quickly as I could, rather than take even a few seconds to contemplate. The reason was I wanted to help entice him into a call. I thought that if I took time to think before moving in, it might look like the kind of phony “what should I do?” hesitation that is so common in low-stakes games among players holding aces or kings.

On the other hand, a fast shove might look to him more like a bully with no real hand, trying to force him to fold. I have no way of knowing if that made a difference, or if he had decided in advance to go with his {A-Hearts}{9-Spades} no matter what he saw me do, but I think it was a worthwhile attempt to reinforce the erroneous image he had of me.

One part of the take-home lesson here is that you need to be aware not just of your overall table image, but of what each individual opponent has seen you do. Those who have played with you for a long time will have a different impression of you than those who recently sat down. Those who are paying close attention will have a different impression of you than those who are glued to the football game. Better players will probably have a more accurate bead on your playing style than newbies. And so on.

Successful poker requires being able to see yourself through an opponent’s eyes — and not just a generic opponent, but the specific one who is actually in the hand with you.

The other part of the lesson is about what Latecomer could have done differently. I can think of two things.

First, he could have thought about why I had won all three of my previous raises either preflop or with a continuation bet on the flop. At a full table, a true maniac or bully who is raising more than half of the time is likely to get a lot more push-back than that — a lot more “I don’t believe you” calls than that series of hands displayed. In other words, he might have thought, “Maybe these other players know something that I don’t.”

Second, he could have waited. Yes, {A-Hearts}{9-Spades} is pretty good against the raising range of a true table bully. If he had been short-stacked in a tournament, given the same information, it probably would have been the right move. But there was no reason for him to have been in a hurry. Just waiting another six hands would have doubled the number of observations he had on me — and it would have caused him to reconsider his first impression when I folded them all.

It’s true that in poker you want to extract all of the inference you can out of every scrap of information that you have. But that laudable objective must be tempered by the recognition of how badly distorted your impression of an opponent can be when it is based on a small sample of observations.

Photo (PokerPro table) via PokerPro.

Robert Woolley lives in Asheville, NC. He spent several years in Las Vegas and chronicled his life in poker on the “Poker Grump” blog.

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Call or Fold? A Dilemma Caused by Small Sample Size 102

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