Timeline for Does the optimal strategy converge in poker if the SPR tends to infinity?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| May 28, 2017 at 12:24 | comment | added | Will Sawin | @DouglasZare I am, yes | |
| May 28, 2017 at 4:00 | comment | added | Douglas Zare | It's not required to avoid infinite reraises. One common rule is that you have to raise at least the size of the last full bet/raise unless you go all-in. | |
| May 28, 2017 at 3:59 | comment | added | domotorp | @Douglas I thought we were, otherwise there's the issue of infinite re-raisings. | |
| May 28, 2017 at 3:41 | comment | added | Douglas Zare | Are you restricting bets to be integers? | |
| May 28, 2017 at 3:37 | comment | added | Will Sawin | @DouglasZare The one I'm thinking of is where we view strategies as a subspace of the product of spaces of distributions, and use e.g. the $\ell^1$ metric topology on the space of distributions of bounded expectation, which is compact because we can find a compact $\epsilon$-net consisting of all distributions on lines of total pot size $O(1/\epsilon)$. I don't think this is the best topology to use, but it's the best I've come up with so far. | |
| May 28, 2017 at 3:07 | comment | added | Douglas Zare | In the nut-blocker situation, I think the correct strategy may be to push with the nut flush and with nut blockers. Pushing a lot with a hand without the top spade is bad because you might run into the nut flush. Your opponent is playing the clairvoyant game, and might be able to call some of the time with hands between the nut flush and some hands involving just the ace of spades. The preferred calling hands might be hands that partially block you from having the flush, so it might be reasonable to fold a set but call with top pair with a king of spades kicker because that blocks AKs. | |
| May 28, 2017 at 3:01 | comment | added | Douglas Zare | What topology do you use on the space of strategies? I proved a similar result, that in the $[0,1]$ model of poker, the probability of betting at least $b$ is $O(1/b)$, and I wanted to use a compactness argument, but I have to add additional assumptions. | |
| May 27, 2017 at 23:52 | comment | added | Will Sawin | @domotorp What definition of convergence would you use where this issue would block convergence? | |
| May 27, 2017 at 20:52 | comment | added | domotorp | Oh, I see, of course. Anyhow, the real issue is what you describe in the last para. | |
| May 27, 2017 at 20:34 | comment | added | Will Sawin | @domotorp I will see if I can say something more substantial. | |
| May 27, 2017 at 20:33 | comment | added | Will Sawin | @domotorp It would be the probability distribution that is zero with probability one. | |
| May 27, 2017 at 20:25 | comment | added | domotorp | Yes, I was aware of most of this. I'm not sure I understand "the space of probability distributions on the natural numbers with expectation bounded by some constant is compact." What would be the limit of the distribution that takes $n$ with probability $\frac 1n$ (and zero otherwise)? | |
| May 27, 2017 at 18:40 | history | answered | Will Sawin | CC BY-SA 3.0 |