Mark Gritter (markgritter) wrote,
Mark Gritter
markgritter

Yay!

*  2016:   objval =   2.151221879e+00   infeas =   0.000000000e+00 (0)
OPTIMAL SOLUTION FOUND
Time used:   347009.0 secs
Memory used: 16418.3M


Recap: The game is 3-card push-or-fold single draw lowball using A-5 rankings (and a standard deck.) The SB pays a blind of $1, the BB pays $2. SB/button acts first predraw but second on the draw. Effective stacks after paying the blinds are $20.

If correct, this solution says that the game is worth about $0.15 to the second player, despite his drawing disadvantage. (Perhaps because the stacks are so large that it is pretty much never correct to draw.)


The solution appears to contain no mixed strategies. I need to work up a tool to extract the results in a more-easily-read form (I can't convert to base-4 in my head), but here are some I eyeballed:

AAA: push, 42 = 0222 (draw 2 if called, stand pat against a 3-card draw.)
AA2: push, 5 = 0011 (draw 1 if called but stand pat against 2 or 3.)
AA3: push, 53 = 3111 (draw 1 except against a 3-card draw, then draw 3?!?)
A23: push, 64 = 1000 (draw 1 against a 3 card draw?)
AA8: push, 22 = 0122 (draw two except against a two-card draw)
AA9: fold
A26: push, 224 = 3200 (pat except against 2 or 3?)
222: push, 58 = 0322 (more bogus behavior against 2- and 3-card draws.)
678: push, 1 = 0001 (draw 1 if he's pat, that makes sense at least)
679: push, 17 = 0101 (draw 1 against pat or 3-card draw.)

679 looks like the worst hand that is pushed. The solver does recomment complete pats with A24,A34, and a bunch of other hands up to 467,567.

It looks like the "what to do against a 3-card draw" field is either incorrect or a "doesn't matter".

I did find one mixed strategy, with A46: 79% pats and 21% 240 = 3300 (more with the drawing three garbage.)
Tags: lowball, poker, theory
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