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'Conquers' in the sense it always plays +EV hands. This is exactly what 'grinders' do -- you just play the hands that have a long-term positive expected value.

'Conquers' in the sense it always plays +EV hands. This is exactly what 'grinders' do -- you just play the hands that have a long-term positive expected value. You play that way long enough, your risk goes to zero and you normalize out at a regular return.

jib 12y ago
A good h2h limit strategy probably plays 95% of buttons and 70% of big blinds or so, so at least 30% of the hands you play are neutral EV at best (symmetrical game, so at most 50% are +EV preflop and you play at least 80% of all hands). Only playing hands you are +EV against a full range would be exploitable as it is way too tight in heads up.
- GoatOfAplomb 12y ago
  I don't agree with your 50% figure. Symmetrical, sure, but remember the blind bets. Once that money is committed, each player can have a higher EV in playing the hand than in folding. (Related thought experiment - consider a game where each player has $101 in front of them before the hand starts, and then post $50 and $100 blinds. 100% of hands should be played from each position.)
  - jib 12y ago
    Yeah that's fair. It was sloppy language from me. The point I wanted to make was that you play hands where your odds of winning is <50% a large amount of the time.
baddox 12y ago
So what happens if everyone plays that strategy? Presumably expected earnings approach zero?
- lukevdp 12y ago
  If everyone plays perfectly, in the long run everyone will have the same amount of money that they started with. In most games there is a rake (fee) taken by the house, so the house would slowly take everyone's money.
  - frinxor 12y ago
    The super-hard part is figuring out what 'perfect play' (GTO) is. Thats what the post is claiming
swyman 12y ago
I think, more accurately (and also more impressively), it plays nothing but +EV hands, while also not folding any +EV hands. Avoiding false negatives against a GTO player sounds like the really hard part.
deleted 12y ago
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gweinberg 12y ago
I don't think that's correct in heads up. I think optimal play includes "bluffing" a fair portion of the time.
- jchendy 12y ago
  Indeed. It's pretty easy to win against somebody who only bets with strong hands.
- thret 12y ago
  That's one way to put it. Often nobody has anything that would be playable in a full ring game. The button is paramount, almost like having the serve in tennis. Also, HU LHE is (much) more complicated than full ring. You have less knowledge about your opponents range, not more. You have to play more hands, a wider range of hands, and you frequently need to make marginal decisions.
DennisP 12y ago
This may not be what you mean, but it sounds like you're saying the computer just plays hands with favorable odds of getting winning cards. That's trivial and not at all what this is doing. It's finding the game-theory-optimal play, which means it bluffs in the most effective way possible. It does that with the assumption that the opponent is also very strong, so it doesn't attempt to exploit weaknesses. If you try to exploit weaknesses, you have to vary from optimal play, thus opening up your own weaknesses. The software doesn't do that, it just plays a perfect game.
- ikeboy 12y ago
  If perfect play is known, why not just use that? The article compared this program with perfect play, which means that perfect play must be computable. I'm confused.
  - DennisP 12y ago
    Perfect play exists but is extremely difficult to compute because it's such a large problem. But they've shown that this program comes very close. Perfect play also exists in games like chess and checkers. Checkers has been completely solved and computers can play it perfectly. This is not true for chess, though computers play quite well. Go is even harder and the best humans easily beat the best Go computers.
    - ikeboy 12y ago
      Do you mean they only tested it against perfect play for a subset of hands, but ran their program for all hands, and the "close to perfect play" is only statistical? Otherwise, how could they show it's close if they can't compute perfect?

jib 12y ago

A good h2h limit strategy probably plays 95% of buttons and 70% of big blinds or so, so at least 30% of the hands you play are neutral EV at best (symmetrical game, so at most 50% are +EV preflop and you play at least 80% of all hands). Only playing hands you are +EV against a full range would be exploitable as it is way too tight in heads up.

GoatOfAplomb 12y ago
I don't agree with your 50% figure. Symmetrical, sure, but remember the blind bets. Once that money is committed, each player can have a higher EV in playing the hand than in folding. (Related thought experiment - consider a game where each player has $101 in front of them before the hand starts, and then post $50 and $100 blinds. 100% of hands should be played from each position.)
- jib 12y ago
  Yeah that's fair. It was sloppy language from me. The point I wanted to make was that you play hands where your odds of winning is <50% a large amount of the time.

baddox 12y ago

So what happens if everyone plays that strategy? Presumably expected earnings approach zero?

lukevdp 12y ago
If everyone plays perfectly, in the long run everyone will have the same amount of money that they started with. In most games there is a rake (fee) taken by the house, so the house would slowly take everyone's money.
- frinxor 12y ago
  The super-hard part is figuring out what 'perfect play' (GTO) is. Thats what the post is claiming

swyman 12y ago

I think, more accurately (and also more impressively), it plays nothing but +EV hands, while also not folding any +EV hands. Avoiding false negatives against a GTO player sounds like the really hard part.

deleted 12y ago

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gweinberg 12y ago

I don't think that's correct in heads up. I think optimal play includes "bluffing" a fair portion of the time.

jchendy 12y ago
Indeed. It's pretty easy to win against somebody who only bets with strong hands.
thret 12y ago
That's one way to put it. Often nobody has anything that would be playable in a full ring game. The button is paramount, almost like having the serve in tennis. Also, HU LHE is (much) more complicated than full ring. You have less knowledge about your opponents range, not more. You have to play more hands, a wider range of hands, and you frequently need to make marginal decisions.

DennisP 12y ago

This may not be what you mean, but it sounds like you're saying the computer just plays hands with favorable odds of getting winning cards. That's trivial and not at all what this is doing. It's finding the game-theory-optimal play, which means it bluffs in the most effective way possible. It does that with the assumption that the opponent is also very strong, so it doesn't attempt to exploit weaknesses. If you try to exploit weaknesses, you have to vary from optimal play, thus opening up your own weaknesses. The software doesn't do that, it just plays a perfect game.

ikeboy 12y ago
If perfect play is known, why not just use that? The article compared this program with perfect play, which means that perfect play must be computable. I'm confused.
- DennisP 12y ago
  Perfect play exists but is extremely difficult to compute because it's such a large problem. But they've shown that this program comes very close. Perfect play also exists in games like chess and checkers. Checkers has been completely solved and computers can play it perfectly. This is not true for chess, though computers play quite well. Go is even harder and the best humans easily beat the best Go computers.
  - ikeboy 12y ago
    Do you mean they only tested it against perfect play for a subset of hands, but ran their program for all hands, and the "close to perfect play" is only statistical? Otherwise, how could they show it's close if they can't compute perfect?