Re: Whats in a Range
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The game-theoretic value is in the appearance of randomized play. A lot of times you don't have to randomize to have your play appear random.
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i think what your saying is absurd... isn't 2+2 the place where we have all decided that having a set with different variables should be played in different ways? i mean maybe having an Ace on board really should differ the type of play you make. i believe what MLG is trying to say is that for ever specific situation, there is a correct percentile way of playing the hand. the question of if it is possible for a human to do this is another matter.
to imply that your goal is just to appear random is not logical. if you just appear random, but are not accually random, a perfect player could beat you in those situations, a good player would be able to take advantage of the fact that you appear random, but are not atually random. randomness to some extent is what gives you the ability to make money when playing other good players.
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An attempted restatement of my point:
We often talk about game theoretic randomization as though it is an attempt to achieve an ideal ratio of different plays in a given situation, like "flopping a set vs. preflop raiser." There is a big difference between theory and practice, however. In theory, if we encounter a specific situation 100 times, we want to do x 60 times, y 20 times, and z 20 times. In practice, every one of those 100 situations is different, and there are often situational considerations that push you toward x, y, or z. Also, in practice, situations come up one at a time, not as part of some theoretical bundle of similar situations.
Another way to think about this is that any particular hand fits into several boxes within which you could choose to randomize your action. "Flopping a set vs. a preflop raiser" could also be "flopping a set on an ace-high board" or "flopping a set on a two-tone straight board" or "flopping bottom set with deep stacks versus a tight UTG raiser on an AQ5 board" or "flopping a set when I'm perceived as a maniac" or "flopping a strong hand when i've just checkraised two weak hands" or "flopping a strong hand versus a guy I know overplays medium strength hands when bet into."
When we say there are situational factors involved in decision-making, what we are really saying is that any given hand falls into several of these type of categories. In theory, you would want to randomize within every category. In practice, one or two of these considerations will usually dominate in a particular hand.
Even most observant players only go as far as to remember your actions with respect to the most straightforward of these categories. So you can check-raise with a set for a particular reason but the only mental note some observant players will make is "he checkraised a set."
Remember that the game theory goal when you randomize is to create a future situation in which an observant opponent will get your hand range wrong. An observant but not-too-sophisticated opponent may only remember that you checkraised a set 1 in 3 times, which is enough to confuse him when you get in a hand with him where you may or may not have a set. The better your opponents are at remembering details, the more likely it is they will properly evaluate the reasons you made certain plays in the past (that is, the less random your play will look to them). They will more accurately evaluate your hand range in a given situation b/c they understand better which pieces of other plays were related to your play in the current hand. Against the best of these, you do need 'pure' randomization to achieve the game-theoretic goal of masking your range. But bear in mind that the goal is to mask your range, not to be random for the sake of being random.
Finally, even though masking your range is a goal, it is not the only goal. You have to make decisions one at a time, and masking your range for the future by doing something other than what you expect to earn the greatest profit in a particular hand is only worthwile if you can expect to get back that profit and then some later. This is why people often focus on randomizing between options that have roughly equivalent EV.
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