Jerrod Ankenman (![[info]](http://p-stat.livejournal.com/img/userinfo.gif){kind=small} hgfalling) wrote,@ 2005-03-01 19:09:00 |
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Headsup on the button
extempore posted the following question:
</span>When if ever should you fold your button preflop in a no-limit heads-up match?
Case 1: Small stacks (<10 BB)
Just play jam or fold. It's really, really hard to do better than this, and really easy to do worse.
Case 2: Larger stacks (10-25 BB)
Now the game moves from 1 bullet to approximately 2.
I think at this stack size you should probably be raising to either the minimum or 2.5, depending on your particular preference: if you like raising to 2.5, then you should probably play jam or fold up to about 12 or 13, lest you wander into the realm of "I've raised and I can't give up!"
The reason is because the blinds here represent a significant portion of all the chips in the (second-order*) match.
*second-order because of course we're only considering the match to be of stacks N where N is the minimum of the two stacks. Maximizing equity for the second-order match maximizes equity for the supramatch.
You should /clearly/ fold quite a few hands here. Take the extreme case, where you raise with all hands. The opponent can now treat this as a reverse jam or fold game with blinds 1 and 2.5 and totally smash you.
I think what actually happens optimally (though we have no methods for proving it) is that you play jam or fold up to some stack size, and then you switch to raising a little bit with quite a few more hands, and folding those hands as well as the bottom of your jamming range to a jam.
But even if you add 20% of hands to your raising range when you pass out of jam or fold, that leaves about 20-25% which should be folded preflop. Evidently your opponent can simply call the raise, so you want to add hands which flop hands which play well in two stages. That means suited hands, connectors, and the like. If you folded T5, 94, 84, 74, 64, 54, 42, and 32 (all offsuit), that's about 20%. I think after these if you add more they should be the weakest suited hands and things like J2, J3, etc.
Of course, raising 80% of your hands preflop means you have to call jams a lot, like with any ace, any king, pairs, and good suited connectors.
Case 3: (25+ BB)
Well, obviously above 25 blinds, categories aren't so clearly defined: playing at 25 blinds is much different than at 75 blinds. But the concepts about folding preflop are basically these:
1) Exploitively, your strategy preflop should be designed to create pots that are the size you want to play. So some people you play against are overaggressive and make big bluffs. Against these hosers, you want to keep the pots small so that you can pick them off with real hands. Other people you play against are tighter and more passive, tending to give up when they don't pair. Against these people you wat the pot to be bigger preflop so that when you both miss on the flop, you make money.
2) That leads to what I'd call the two balanced strategies preflop: limping in with every hand you are going to play and raising to some fixed amount with every hand you're going to play.
The former is stronger against:
Overaggressive types
People who have tells
The latter is stronger against:
Patient tight types
People who don't call enough preflop
It's probably possible to create a balanced strategy that involves both limping and raising, but as with all things of this nature, the gain isn't that large and the work, time, and thought that has to be put into that is large.
If you're playing 1), then as you play more and more hands your opponents should raise more and more often; you, too, should reraise more and more often. You should probably reraise with about as many hands as you fold to a raise after limping. So as you play more and more hands, you commit yourself to playing more and more bigger pots in position with weaker and weaker hands. At some point, just folding preflop and taking -.5 on the hand is worth more than the equity of playing your distribution out. I would guess that this point is probably around 10% of hands or so. Then you can do some kind of strategy like: limp-reraise with about 15% of hands, limp-call with 60%, limp-fold with 15%, and fold outright with about 10%.
If you're playing 2), it's the same thing except that you're committing more money when you play a hand preflop. Now you're going to raise and fold to a reraise more often, but you can't realistically play the same amount of hands as in 1) because your opponent can just smash you by reraising very liberally. But on the other hand, unless you want to end up putting in the third raise with like 20% of your hands, you have to fold more hands on the button. So I figure something like:
Raise-reraise with 10%, raise-call with 30%, raise-fold with 30%, and fold around 30% on the button creates some balance.
Obviously all of these are tempered by the particular stack situation; at 25 blinds you should be more willing to put in the third raise than at 75, etc. I also don't 100% stand behind all the off-the-cuff percentages here, since I haven't actually done any quantitative work on the problem (except for small stacks).
extempore posted the following question: </span>When if ever should you fold your button preflop in a no-limit heads-up match?
Case 1: Small stacks (<10 BB)
Just play jam or fold. It's really, really hard to do better than this, and really easy to do worse.
Case 2: Larger stacks (10-25 BB)
Now the game moves from 1 bullet to approximately 2.
I think at this stack size you should probably be raising to either the minimum or 2.5, depending on your particular preference: if you like raising to 2.5, then you should probably play jam or fold up to about 12 or 13, lest you wander into the realm of "I've raised and I can't give up!"
The reason is because the blinds here represent a significant portion of all the chips in the (second-order*) match.
*second-order because of course we're only considering the match to be of stacks N where N is the minimum of the two stacks. Maximizing equity for the second-order match maximizes equity for the supramatch.
You should /clearly/ fold quite a few hands here. Take the extreme case, where you raise with all hands. The opponent can now treat this as a reverse jam or fold game with blinds 1 and 2.5 and totally smash you.
I think what actually happens optimally (though we have no methods for proving it) is that you play jam or fold up to some stack size, and then you switch to raising a little bit with quite a few more hands, and folding those hands as well as the bottom of your jamming range to a jam.
But even if you add 20% of hands to your raising range when you pass out of jam or fold, that leaves about 20-25% which should be folded preflop. Evidently your opponent can simply call the raise, so you want to add hands which flop hands which play well in two stages. That means suited hands, connectors, and the like. If you folded T5, 94, 84, 74, 64, 54, 42, and 32 (all offsuit), that's about 20%. I think after these if you add more they should be the weakest suited hands and things like J2, J3, etc.
Of course, raising 80% of your hands preflop means you have to call jams a lot, like with any ace, any king, pairs, and good suited connectors.
Case 3: (25+ BB)
Well, obviously above 25 blinds, categories aren't so clearly defined: playing at 25 blinds is much different than at 75 blinds. But the concepts about folding preflop are basically these:
1) Exploitively, your strategy preflop should be designed to create pots that are the size you want to play. So some people you play against are overaggressive and make big bluffs. Against these hosers, you want to keep the pots small so that you can pick them off with real hands. Other people you play against are tighter and more passive, tending to give up when they don't pair. Against these people you wat the pot to be bigger preflop so that when you both miss on the flop, you make money.
2) That leads to what I'd call the two balanced strategies preflop: limping in with every hand you are going to play and raising to some fixed amount with every hand you're going to play.
The former is stronger against:
Overaggressive types
People who have tells
The latter is stronger against:
Patient tight types
People who don't call enough preflop
It's probably possible to create a balanced strategy that involves both limping and raising, but as with all things of this nature, the gain isn't that large and the work, time, and thought that has to be put into that is large.
If you're playing 1), then as you play more and more hands your opponents should raise more and more often; you, too, should reraise more and more often. You should probably reraise with about as many hands as you fold to a raise after limping. So as you play more and more hands, you commit yourself to playing more and more bigger pots in position with weaker and weaker hands. At some point, just folding preflop and taking -.5 on the hand is worth more than the equity of playing your distribution out. I would guess that this point is probably around 10% of hands or so. Then you can do some kind of strategy like: limp-reraise with about 15% of hands, limp-call with 60%, limp-fold with 15%, and fold outright with about 10%.
If you're playing 2), it's the same thing except that you're committing more money when you play a hand preflop. Now you're going to raise and fold to a reraise more often, but you can't realistically play the same amount of hands as in 1) because your opponent can just smash you by reraising very liberally. But on the other hand, unless you want to end up putting in the third raise with like 20% of your hands, you have to fold more hands on the button. So I figure something like:
Raise-reraise with 10%, raise-call with 30%, raise-fold with 30%, and fold around 30% on the button creates some balance.
Obviously all of these are tempered by the particular stack situation; at 25 blinds you should be more willing to put in the third raise than at 75, etc. I also don't 100% stand behind all the off-the-cuff percentages here, since I haven't actually done any quantitative work on the problem (except for small stacks).
