Re: RANDOM thoughts
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This thread has left me with a nagging question:
1) Can a poker hand be characterized by random variables?
Wait, take a second to think about that. Consider bluffs, varying styles, human error and emotion, number of players, chance of seeing all cards on the board, etc, etc, etc.
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The answer to this for me is a clear "yes". Suppose you're playing against a player who will always call to the river no matter what his hand, then bluffing is always wrong. On the other hand, suppose you're playing a player who never calls without the nuts, then bluffing is always correct.
Most players will fall somewhere in the middle. If you can accurately assess the range of hands that a player would have played in the manner that he played them, calculate the probabilities that he has each of those hands, and calculate the chances that he will call a bluff with each of those hands, you can mathematically predict if a bluff is the correct play. It's true that a player might call or fold on a whim, but you can still use percentages to predict each of these events.
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Suppose yes: there should be some "normal" variance based on the combination of these random variables. How would our variance relate to this "normal" variance? What would it mean to have a variance above or below "normal"; would that reflect skill levels? Does this suggest the smaller the variance the better the player?
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Generally the ammount of variance a player has is determined by the game he is playing. In MTTs for example, a good player will have a much higher variance because he will be winning the tournaments much more frequently. STTs are the same, but less extreme. If you know that a place will place 14%/13%/12%/61% (1st/2nd/3rd/OOTM), then you can easily calculate that persons variance, and in general, it will be higher because of the fact that he's getting more firsts than average.
Many people confuse variance with the number of winning/losing sessions a player has, but this is incorrect. A player with a 20% ROI will have greater variance than a player with a 10% ROI. However, the player with a 10% ROI will have more losing sessions (assuming the same number of tournaments per session). Variance only refers to the deviation from the mean, so even though a player with a higher ROI will have fewer losing sessions, he will have a lot of sessions which are below average, but still winning.
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