Re: Whats in a Range
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On a hypothetical level if one option is clearly "better" you take it. The point is that the majority of situations in which you start with at least a medium sized stack do not involve a specific "better" option. In those situations a mixed strategy is the "best" option.
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This is what I was getting at. I didn't mean to start a tangent about how to play a set out of position. In fact, I didn't even mention what hand Hero had in my example, because that was irrelevant. What I meant to say was, suppose there is some situation where you would advocate 70% check-raises and 30% leading out (maybe it's a set, maybe it's a combination draw, doesn't matter). There are at least three ways of interpreting this:
1. Check-raising is the 'best' way to play this hand, that's why we do it most often, but we don't want our opponents to catch on to our plan, so we have to lead out sometimes. But when I'm at a table that's going to break soon and I expect to be in this spot only once, I should check-raise every time, since it is on balance best and I need not worry about deception.
2. Check-raising is not 'best'. The combination of 70% check-raises and 30% leading out is 'best'. It sounds like this is what MLG is saying. How can this be the case? Because your opponents are always playing against a range of possible hands you could have, and you gain EV every time they either incorrectly estimate your range or incorrectly play their hand against a correctly estimated range. The latter occurs quite often at lower buy-in tournaments, which is why it is less important to use mixed strategies at those levels. Your opponents aren't likely to estimate your range correctly (though they are putting you on a range, even if they don't think they are), and they often misplay their hands even when their estimation is correct (drawing with improper odds, for instance). You ought to be able to exploit these mistakes without mixing up your play too often.
At higher levels, your opponents will estimate your range more correctly even when they have never played with you before. Conventional wisdom has it that an UTG raise is generally a big hand, maybe TT-AA, AQ-AK. Your opponents likely put you on a range such as this one the first time they see you raise under the gun. They don't assign you this range because they've studied your UTG raising tendencies, they assign you this range because there are mathematical reasons why you would not generally want to build a pot out of position with hands weaker than these. If you really do raise only these hands UTG, then your opponents can exploit you by folding, calling with good implied odds, calling with the intention of taking the pot away later, or re-raising their biggest hands, knowing you can pay them off.
Suppose you've just been moved to a new table deep in one of the big Sunday tournaments, and you decide to raise 87s UTG. If folds around to the BB, who mucks AJ, and you take the blinds. Has he made a mistake? Not if your range is 40% TT-AA, 58% AQ-AK, and 2% suited connectors. It doesn't matter that you had 87s this time, any more than it matters that Villain hit a two-outer after you made a great call. Although BB has never played with you, he's got a good idea what your UTG raising range is. The only way to combat this is to have a wider, less predictable range.
Similarly, if you have a draw 90% of the time you lead into the pre-flop raiser, but you have a set this time and he pushes, he still hasn't made a mistake. You need to make a guess as to what range he will put you on if you are unknown to him, and then you need to deviate from that range.
3. Some say you should mix up your play situationally, not randomly. Lead out on the 30% of flops that you think were most likely to hit a pre-flop raiser, check-raise otherwise. I don't think this is actually a separate alternative, since flopping a set on an AQ5 flop is a different situation from flopping a set on a T65 flop. Against a player who can make a reasonable estimation of your range and play correctly against it, you need to mix it up in both circumstances. If you know or have reason to think Villain will make a particular mistake, such as folding any flop he missed or jamming whenever he has top pair, then you can choose the play that best exploits that mistake.
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