Quote:
Short Stack Shoves
You can also glean a good deal of information from seemingly trivial cards that you do get to see. Suppose that the player in the above example moved in, got called, and showed down Ace-King offsuit. This may not seem significant. After all, virtually any player, even those who don't know what an M is, would move all in with AK and an M of 4.
The thing to understand is that AK is a much smaller part of the range of a good short stack player than it is for an overly tight short stack player. Suppose that a strong player would move in with any two cards, but a weak player would only move in with the top 33% of his hands in this spot. Before the hand, you thought there was a 50% chance that this opponent was strong and a 50% chance that he was weak.
Both players will move all in 100% of the time that they have AK offsuit. However, because the strong player is moving in three times as often as the weak player, he will have AK three times less often when he does move in. Thus, when you actually see the AK, there is now a 75% chance that this is a weak player and only a 25% chance that he is strong. In other words, the fact that this previously unknown player showed up with AK the first time that you saw him move all in makes it more likely that he is a weak player, as a weak player will have AK when he moves all in far more often than a strong player will.
This is complete nonsense. When the player shoves, before the cards are revealed, you rate him more likely to be strong. Every 6 actions we see, on average, are 3 strong player shoves, 1 weak player shove, and 2 weak player folds. Given a shove, he's a 3:1 favorite to be a strong player. Once he reveals AK (or a top 33% hand), it's back to even money. Every 6 actions will consist of 1 strong top 33% shove, 1 weak top 33% shove, and 4 outcomes where there's no shove or no top 33% hand. That's 50/50, just like you started with. It's Bayes' Theorem for the technically minded, and it's common sense that when everybody would play a hand the same way, seeing the hand played (that way) gives you no information about the person who played it.