Which poker variation is most exploitable by pure math strategy?

[Jerrod Ankenman]

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No, this is wrong. Headsup Chinese could (I guess) be solved for an equilibrium strategy, but without some mixed strategies your nemesis EV will be higher than it would be if you were playing equilibrium (with mixed strategies).


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Not necessarily. I think it is an open question whether CP or CP2-7 require a mixed strategy at all. My initial feeling was that CP high does not while CP2-7 does. But I have been looking at solving increasingly greater subsets of CP2-7, and while all pure strategies have been exploitable so far, the number of hands with viable alternative settings and the benefit of shifting settings drops dramatically for increased subsets. At this point it looks like a pure strategy for CP2-7 is exploitable for no more than 1/100th of a point, and probably much less.

It's a work in progress so I don't have a good write-up, see these threads in 'Other Poker':
Initial results, looked promising for exploitative strategy:
http://forumserver.twoplustwo.com/sh...umber=10184435
Later results, more weighted toward pure strategies:
http://forumserver.twoplustwo.com/showfl...=0#Post10279827

Or this livejournal entry (there are more but they're friends-locked):
http://markgritter.livejournal.com/349690.html

I'm not sure CP counts as 'poker', though, absent any betting round. If you count it, it is certainly the most tractable.

If you don't, I think three-card lowball is probably within reach of a complete solution. I solved push-or-fold single-draw 3CL using only a modest amount of resources.

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OK, so I'm not claiming you can't play really strongly without mixed strategies, just that the equilibrium strategy will contain some mixing. Probably only a few hands, because really, how many hands are there that even have two settings that are really very close?

1/100th of a point is a lot. I suspect nem-ev vs max(purestrats) is a lot lower than that. If it were 1/100 of a pt, I would say that that strongly indicates that you need to mix to play optimally. 10^-6, maybe not.

Anyhow, is 635 million the equivalance class-reduced version of 52C13? How long have you been running this? It seems like some good work at a glance.