Timeline for Does the optimal strategy converge in poker if the SPR tends to infinity?
Current License: CC BY-SA 3.0
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| Jun 1, 2017 at 18:53 | comment | added | Douglas Zare | @domotorp: There are several variations. My comment that the AQT player should bet big with every ace assumed that the AQT player acts second. If the AQT player acts first, then the possibility of a check-raise needs to be considered, and the player with KJ can't bet that much to avoid paying off too much if the AQT player checks an ace. My intuition is that AQT out of position would have a slight advantage, but I have not done the calculations. I don't have a reference for the AQT vs KJ game, although I think I have seen it considered before, but with a limit betting structure. | |
| Jun 1, 2017 at 4:30 | comment | added | domotorp | So with one street and large SPR, this would practically give away whether AQT has a Q or not, so the KJ player "becomes the Clearvoyant" and can asymptotically win the blind if there's a Q. This doesn't seem like a smart thing to do, but might be optimal, I don't know, it gives that AQT has $33\%$ blind advantage. Do you have some reference? | |
| Jun 1, 2017 at 3:46 | comment | added | Douglas Zare | @domotorp: If there are two or more betting streets, then on the first street, the AQT player can bet big (but not all-in) and the KJ player can't call. In just one betting street, there doesn't seem to be any point to betting with a queen, and the player with AQT would bet big with every ace and some tens, asymptotically all tens as the SPR increases to infinity. Some restricted continuous games are solved, and the bet size narrows a player's range, with smaller bets for more mediocre hands. The consensus of poker players is to bet just one amount, but I disagree with it. | |
| May 31, 2017 at 11:55 | comment | added | domotorp | I'm sorry, I shouldn't have called one of the players Clairvoyant - I wanted to ask what happens if none of them knows the card of the other. | |
| May 31, 2017 at 10:18 | comment | added | Douglas Zare | @domotorp: If you have a jack, the Clairvoyant knows this, and then there isn't any difference between a queen and an ace. If you have a king, there is no difference between the queen and the ten. So, the bet sizes could be unbounded with every hand. | |
| May 29, 2017 at 8:33 | comment | added | domotorp | Finally I've managed to digest (most of) your answer. Now that I know so much about poker, I wonder what other notion convergence could be replaced with to make a true statement. For example, suppose that in a one-card poker Clairvoyant has A, Q or T, while the other player has K or J (say, uniformly). Would the bet size be unbounded with a Q, or only with A (strongest) and T (used to bluff)? | |
| May 28, 2017 at 18:42 | history | bounty ended | domotorp | ||
| May 28, 2017 at 4:39 | history | answered | Douglas Zare | CC BY-SA 3.0 |