Which poker variation is most exploitable by pure math strategy?

[jtollison78]

Sit n Go's. In particular, the old party NL SnG's.

John

[Whirlwind]

No peek has an unknown number of betting rounds which significantly increases the complexities of any analysis. Additionally, calculating the draw/win percentages based on the exposed and unexposed cards is no small task without the aid of a computer.

Indian chief does have an element of bluffing that needs to be addressed, but this is minor when compared to no peek's problems.

[Nsight7]

Hands down, the answer is Chinese Poker. Zero betting rounds, no bluffing, just showdown. If there was ever a form of poker that has a optimal strategy, it is Chinese Poker.

In fact, this would be a tie with Chinese Poker 2-7 in the middle for the same reasons as above.

[pokervintage]

I do not agree, but I might be wrong. Chinese poker is the simplest form of poker yet it is not exploitable by math for one reason. There are no options that a player has. One can theoretically set his cards optimally but that is all he can do. Of course if there is an optimil way of setting his hand that might be enough. I`m not sure.

pokervintage

[Nsight7]

The question was "MOST" exploitable by pure math. The fact is that aside from toy-games, most forms of poker are simply too complex to be analyzed with any depth. Once could theoretical develop a rigorous mathematical approach to Chinese Poker though because of its sheer simplicity (the fact that there are no betting rounds and that there is no bluffing makes it less complex and thus more mathematically tractable).

You are correct though, there is only setting up a hand optimally, but the fact that this is all that one has to do is exactly what makes it exploitable by a pure mathematical strategy. In other forms of poker one must mix up their play to optimize and the lines on how one should do so are rather fuzzy. This doesn't even consider the greater psychological aspects that come with NL/PL games.

Basically, the simplicity of a poker game is directly proportional to its solubility. This is why other forms are less exploitable by pure mathematics. This is of course without taking into account live play vs online play, wherein online play is inherently more mathematical. By yeah, simple = mathematically soluble.

[Nsight7]

I want to add something to my statement above (and I am no longer free to edit my post apparently).

With regards to Chinese Poker, it is explotiable in the sense I can develop a strategy that is optimal, meaning that any deviation from my strategy results in a loss of expected value. That is it. My edge will always be small and variance will always be high, but mathematically an optimal solution does exist (that could also be derived and/or approximated closely) and mixing up play is totally irrelevant (because as I have stated there are no betting rounds and nothing you do will allow your opponent to gauge your hand particularly well). Such is NOT the case with other forms of poker even if one can have a high-expected-value/low-variance on average. However, mathematical exploitable != highest EV. In those cases a very good strategy could be guessed at, but it isn't mathematically soluble.

[Jerrod Ankenman]

[ QUOTE ]
I want to add something to my statement above (and I am no longer free to edit my post apparently).

With regards to Chinese Poker, it is explotiable in the sense I can develop a strategy that is optimal, meaning that any deviation from my strategy results in a loss of expected value. That is it. My edge will always be small and variance will always be high, but mathematically an optimal solution does exist (that could also be derived and/or approximated closely) and mixing up play is totally irrelevant (because as I have stated there are no betting rounds and nothing you do will allow your opponent to gauge your hand particularly well). Such is NOT the case with other forms of poker even if one can have a high-expected-value/low-variance on average. However, mathematical exploitable != highest EV. In those cases a very good strategy could be guessed at, but it isn't mathematically soluble.

[/ QUOTE ]

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).

Anyway, solving the game for equilibrium purposes is stupid because there are like 10^21 hand matchups which is totally computationally intractable and you can just approximate down to really small nem-ev anyway. I'm comfortable with the idea that my opponents could exploit me for .0001/h if they knew my strategy.

Also, you seem to be confused about what is possible in other forms of poker. ALL zero-sum two player games have equilibria in the domain of mixed strategies.

[Nsight7]

I am thinking of full-ring games in general, nothing heads-up because I imagine that most of us don't play primarily heads-up games anyhow.

And yeah, I think that it would be computationally difficult to do outright, if not impossible. This is why I said something like "derived or approximated". It would be large otherwise I admit, but some Monte Carlo simulation would surely be able to arrive at some reasonable approximation of the best strategy for even multiplayer scenarios. Mostly I envision in this scenario dealing out the hands, then culling the non-legal hands from the combinations available, and then playing them against a statistically significant number of psuedo-random hand arrangements for opponents to yield some form of payoff-matrix, and then derive EV relations for the possible combinations your opponents could play against your arrangements. Still pretty far off from a total solution, but it could yield some reasonable information that is at least somewhat rigorous.

Also, I can envision combinations of hands that have approximately the same EV that would serve the purposes of mixing ones strategy here as well while still retaining optimal strategy (ex. playing strong in front and back but weak in middle vs strong front and middle with a weak back hand). So I suppose I messed-up above. I was really thinking of optimal strategy vs. deviation from optimal and I was approximating mixed play as non-optimal. That was just dumb thinking and wording on my part.

[Jerrod Ankenman]

It seems one of the points you were trying to make, which is a good one, was that in regular poker you can make more money by playing in a way that is really bad if they know what you're doing. But in chinese this isn't really true. Most of the possible exploitation in chinese comes in situations where you have two or more settings that are close against a broad range of opponent hands, but you choose the one that exploits their tendency. You would basically never set a hand in some bad way to exploit your opponents. But you might value bet superthin against an uber-calling station where you would never do that against a normal player.

Also, I think there is more room for exploitation in 2-7 chinese than in 3xhigh. I'll let others elaborate.

[MarkGritter]

[ QUOTE ]

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).


[/ QUOTE ]

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.