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I don't see where they got 10^161 as the number of situations in no-limit. You can bet ANY amount, making it potentially unlimited. You also have to consider

by fsk 11y ago

I don't see where they got 10^161 as the number of situations in no-limit. You can bet ANY amount, making it potentially unlimited. You also have to consider the ratio of the size of your stack to the size of the blinds, which means the number of situations is unlimited (arbitrarily deep stacks). I.e., if the blinds are $1-$2, you follow a completely different strategy when you have $10 as when you have $100 or $10000.

learnstats2 11y ago
> You can bet ANY amount, making it potentially unlimited. Not really. The minimum bet size is fixed by the blinds/antes. The maximum bet is fixed by the total number of chips in the tournament (or that the player holds). The bet amounts are limited by the size of the smallest chip - in bricks and mortar tournaments tournament managers will 'chip up' the small chips whenever it becomes sensible to do so. In digital tournaments the smallest chip might remain at $0.01, but it still exists.
- fsk 11y ago
  Suppose again the blinds are $1-$2 and the stack is $10000. I can bet $2, $4, $6, $8, $10, $12, $14, any amount up to $10000. Each of those is now a separate game tree. A couple of bets, and now we're way past 10^161. It may never be optimal for me to bet $132, but a perfect computer player should be prepared for that bet.
  - cardprophet 11y ago
    While you are theoretically correct that the game tree is massive, the difference in tree between betting 1bb vs 2bb in a 50bb pot is marginal; the algorithm they use considers an abstraction of the game.
    - fsk 11y ago
      So they're just doing an approximate game tree. Small differences in bet size can matter, because professional players will sometimes try to give you the pot odds to make a bad call.
TylerE 11y ago
Nope. All that matters is the ratio of bet size to the blinds. Basically you normalize everything into "BBs". Actual $ amounts aren't relevant.
- fsk 11y ago
  False. The strategy is different based on the size of your stack relative to the blinds. If the blinds are $1-$2 and you have $10, you're probably going to go all-in or fold. If you have $10000, then you can think more about trying to trap an opponent and get all their chips, instead of just trying to take the blinds.
  - mbrameld 11y ago
    You're both saying the same thing except you're saying "if the blinds are $1-$2 and you have $10" and he's saying "if you have 5bb". You're saying "if you have $10000" and he's saying "if you have 5000bb".
    - fsk 11y ago
      What I'm saying is that I don't see how "all possible bet sizes" leads to a game tree of 10^161. It's got to be more unless they're taking some shortcuts, such as saying that a pot size of 24xBB and 25xBB are treated as equivalent. Also, it seems that they are only considering one stack size, where you have 100x or 200x the big blind. If the poker solver does all possible stack sizes, then it can't possibly be 10^161.
      - TylerE 11y ago
        In practical play the small blind is often the basic "unit", so usually the smallest delta between successive bet sizes are the size of the small blind, or half that (e.g. at $1/$2, allowed bets might be $2, $2.50, etc)
  - TylerE 11y ago
    Nope. Having a $200 stack at $1/$2 is the same having a $2000 stack at $10/$20. It's 100BB in either case, and the appropriate strategy is the same.

by fsk 11y ago

learnstats2 11y ago

> You can bet ANY amount, making it potentially unlimited. Not really. The minimum bet size is fixed by the blinds/antes. The maximum bet is fixed by the total number of chips in the tournament (or that the player holds). The bet amounts are limited by the size of the smallest chip - in bricks and mortar tournaments tournament managers will 'chip up' the small chips whenever it becomes sensible to do so. In digital tournaments the smallest chip might remain at $0.01, but it still exists.

fsk 11y ago
Suppose again the blinds are $1-$2 and the stack is $10000. I can bet $2, $4, $6, $8, $10, $12, $14, any amount up to $10000. Each of those is now a separate game tree. A couple of bets, and now we're way past 10^161. It may never be optimal for me to bet $132, but a perfect computer player should be prepared for that bet.
- cardprophet 11y ago
  While you are theoretically correct that the game tree is massive, the difference in tree between betting 1bb vs 2bb in a 50bb pot is marginal; the algorithm they use considers an abstraction of the game.
  - fsk 11y ago
    So they're just doing an approximate game tree. Small differences in bet size can matter, because professional players will sometimes try to give you the pot odds to make a bad call.

TylerE 11y ago

Nope. All that matters is the ratio of bet size to the blinds. Basically you normalize everything into "BBs". Actual $ amounts aren't relevant.

fsk 11y ago
False. The strategy is different based on the size of your stack relative to the blinds. If the blinds are $1-$2 and you have $10, you're probably going to go all-in or fold. If you have $10000, then you can think more about trying to trap an opponent and get all their chips, instead of just trying to take the blinds.
- mbrameld 11y ago
  You're both saying the same thing except you're saying "if the blinds are $1-$2 and you have $10" and he's saying "if you have 5bb". You're saying "if you have $10000" and he's saying "if you have 5000bb".
  - fsk 11y ago
    What I'm saying is that I don't see how "all possible bet sizes" leads to a game tree of 10^161. It's got to be more unless they're taking some shortcuts, such as saying that a pot size of 24xBB and 25xBB are treated as equivalent. Also, it seems that they are only considering one stack size, where you have 100x or 200x the big blind. If the poker solver does all possible stack sizes, then it can't possibly be 10^161.
    - TylerE 11y ago
      In practical play the small blind is often the basic "unit", so usually the smallest delta between successive bet sizes are the size of the small blind, or half that (e.g. at $1/$2, allowed bets might be $2, $2.50, etc)
- TylerE 11y ago
  Nope. Having a $200 stack at $1/$2 is the same having a $2000 stack at $10/$20. It's 100BB in either case, and the appropriate strategy is the same.