First of all....I hate Blogger. I had a lengthier post written that was for some reason deleted by Blogger when I tried to change the font color. Thanks Blogger.
Anyway, it seems like nobody's really interested in this Shortstack Game. But having come this far, I should give some sketch of a solution for equilibrium in the game. If you are enterprising and want to find it (or at least one of them):
1) Show that there is no equilibrium when player 2 shoves less than 1/3 of the time
2) Show that there is no equilibrium when player 2 shoves more than 1/3 of the time
3) Find an equilibrium where player 2 shoves exactly 1/3 of the time.
In the equilibrium I found, player 1 raise/folds 27% of the time, raise/calls 29% of the time, and open folds 44% of the time. Player 1's expected payoff in equilibrium is .42, while player 2's is 1.08, showing the disadvantage of having to act first.
I can also solve for an n-player game where two of the players have to post blinds, and the other players sequentially must raise or fold if no-one has yet raised, shove or fold if a player has raised already, and fold or call if a player has shoved already.
If you are interested, post a comment or email spritpot.
-BRUECHIPS
Episode 454: Jessica Vierling
1 week ago
2 comments:
I enjoyed your 4-piece write up! I'm still trying to digest some of it, very in-depth.
Honestly, your blog kicks ass, and makes me realize how much further I need to take my game to become a winning player (again).
Thanks a ton!!
Your blog sucks and BD who requested the link came here, saw some random equations, and left cuz his brain started hurting... wait, or was that me and not BD? Fuck, my head hurts!
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