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This week I’ve been reading The Mathematics of Poker
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“In the toy game, the out of position player bets every hand, even one like 0.99 which is beaten 99% of the time when called. The out of position player often should bet for the sole purpose of denying to the in position player the right to choose when the money goes in.”
I don’t get it. If my in position opponent has 0.98 which he is not going to bet, making this blocking bet just makes me lose 1 bet.
Jively-
You’re thinking about this one “hand”, instead of the game as a whole. If you check, you allow the in-position player to get bets in when he is a favorite and save a bet when he isn’t. By always betting, not just the current hand but every hand, you guaranteed to break-even in the long run.
So let say you have a crappy number. If you check, either your opponent will check, or he will bet, but then you you might as well have bet because nothing is saved. If he checks, it then you break-even on the hand, just like if you bet every hand. But sometimes (if you don’t have the worst possible hand) he will check when you have the better hand. In that case you will have lost that bet. Now you will no longer break even.
Also, if I understand correctly, you can’t ever have the “worst possible number”. If the set is all real number between 0 and 1, but does not include 0 and 1, then there is an infinite number of numbers and you can always find a larger number by tacking a 9 on then end.
That’s true if your strategy is to bet with 97% of hand or or less. However, your opponent is still always able to value bet you more (assuming he knows your strategy) unless you bet every hand.
For example, if you bet 98% of hands, your opponent WILL bet .98.
jively,
What niffe9 said is the basic idea.
Say your strategy as the OOP player is to bet all hands 0.9 and better and check everything worse than 0.9. Then your opponent will adopt the strategy to bet every hand better than 0.95 if you check.
So if you have 0.99 and check, and your opponent has 0.98, he will indeed check in this scenario and you will not lose a bet. But if he has 0.94, then he will bet, and you will pay off, and you lose a bet.
Now reverse the numbers. You have 0.94 and he has 0.98. You check, and he checks, and you don’t get anything. So when your opponent has 0.94 and you have 0.98, you lose a bet. When you have 0.94 and he has 0.98, you win nothing. So the pairing (0.94,0.98) is a net loser for you because of your strategy.
Compare to 0.98 and 0.99. There, both players will check according to these strategies in either situation, so no money is won or lost.
The reason betting all is the correct strategy for the out of position player is because it eliminates all pairs of hands like (0.94,0.98) where one player wins a bet but the other player wins nothing when the hands are reversed.
Betting every hand is guaranteed to break even because the distributions are equal. And, if you think about it, being out of position with equal distributions, break-even is the best you could possibly hope for out of a strategy.
I’m not really sure there’s much of an analogy between the mandatory OOP bet in this toy game and blocking bets.
Blocking bets are part of an exploitative strategy, not a game-theoretically optimal strategy. As you say yourself, they depend on your opponent’s unwillingness to bluff raise as often as he should.
If you look at the optimal strategy for toy games that allow folding, you don’t see anything that really looks like a blocking bet IMO.
EGJ,
I disagree. For one, check out the AKQ spread limit game starting on p. 165 of MoT. I don’t have time to describe the whole thing b/c it’s complex, but basically you bet a half-bet with hands OOP that have no chance to win if called for the purpose of preventing position player from bluffing as effectively. That’s largely what blocking bets are for. (FWIW, in MoT they call it “preemptive betting”.)
Interesting. I confess I did not read that far in MoP (it’s a tough slog!). I was thinking of the 0…1 toy games in, e.g., chapter 11.
Hi Ed,
I’m very pleased you read that book. It’s very theorical but I think you can have a lot of practical ideas from it.
I hope you will answer my question I posted on board about auto-check (”Chapter ‘Play on the flop’, page 272). I don’t understand why raiser’s range is much more stronger than BB’s range.
Now that’s a real engineer’s article.
And the book sounds like it was written by a real engineer too. It frequently happens that you want to create a computer simulation of a complicated system in order to try to understand it better. But building everything into the simulation would make it too large and unwieldy. So you pick out the most important aspects of the system and build a simulation of those. The simulator ends up being a lot simpler than the system, but if done correctly it can give you valuable insights into what the system does.
We do things like this all the time. It is very interesting to see someone applying this to poker.
I might have to buy this book.