ok, what's a mixed strategy in poker?

i've heard people talking about taking a line some but not every time (given a specific hand and situation) as an example of a strategy being mixed, but i don't really know what 'mixed strategy' means in poker.


edit: i think i understand what a pure strategy is in poker.

the existence theorem for nash equilibriums is for games with a finite number of pure strategies, right? (wikipedia says: '...in which each player can choose from finitely many pure strategies') . does NLHU have a finite number of pure strategies?

would these two ways of choosing betsize lead to 2 (different) pure strategies?:

1) if stacks allow, raise to 874/63 of villain's betsize to the nearest bb

2) if stacks allow, raise to 875/63 of villain's betsize to the nearest bb

if yes, does this example show that there are infinite pure strategies in nlhe? (cause there are of course infinite fractions like that)

A pure strategy is where you take some action 100% or 0% of the time, a mixed strategy is where you assign some probability to each pure strategy.

e.g.

AK on AK7 - bet 100% of the time (pure strategy)

AK on AK7 - bet 40% of the time, check call 30% of the time, check/raise 30% of the time (mixed strategy)

Sam,

I would be very curious to see an in-depth analysis of this hand.

How difficult would it be to produce Claudico's estimate of its opponent's range (specified as a probability distribution over N-choose-2 holdings) at each betting action, assuming Claudico is playing a copy of itself? My guess is that the weight that Claudico placed on Axdd/AdTx holdings (incorrectly?) approached 100% after Doug's last raise.

Might it be possible to apply your endgame solver algorithm to some of the turn decisions on that hand?

GTO discussions in a subforum of 2+2 where 70% of its readers think GTO is just a bitchin' muscle car from the 70's and another 15% are checking urbandictionary.com and coming up with the same answer...

Let's chat after the competition ends, I can't say anything about our strategies or approaches right now. Keep track of the session/opponent/hand # of specific hands you want me to discuss.

Every starting effective stack size is a different game. In your example if 874/63 and 875/63 of villain's betsize round to the same number of bbs (or lowest units you can vary your betsize by) then they are part of the same strategy just represented differently. If they round differently then they define different strategies.

Heads up NL (for a given stacksize, blinds and a finite list of possible bet sizes) has a finite number of pure strategies.

poker is a zero sum game with exact known payouts for all players and it allows for mixed strategies.

Every game that allows for mixed strategies has a nash equilibrium. What makes you think otherwise?

^ took me a second to figure that out

'zero sum' for those of you as slow as I am

fixed. ty dodgy

So this doesn't apply to online poker.

Except that we know the exact payouts.

wow, nice one


Back to g-p
I think you're bringing up bayes-NE because you're thinking about solving from some specific subgame/situation (this hand right now) but this isn't right. You need to zoom-out and view the entire game tree. You solve from the starting point where two players are fully aware of position, stacks, available options, and that both players are dealt from the same pool of finite starting hand combinations. Yes the game then branches off into subgames where Nature plays a role, but all of the exact probabilities (how often players gets dealt x,y,z hands) are known fully.

This is why you can't solve NE for a river game (or any non preflop pre-action state) on its own without any information about villains range - you don't know which game state you're in. This is a point inside of the full game where what you're saying would be right - but we don't approach solving the game from this point.

punter is right, bot is weak b/c he can't beat the top tops .... should play every hand like he has set, pm me if you want sauce code

i approve of this, even though he attacks me alot ! =)

Might be helpful to think of the following. Every imperfect-information extensive-form game/Bayesian game/etc. can be converted to a matrix game. E.g., http://www.sfu.ca/~haiyunc/notes/Der...rm%20Games.pdf.

I assume you accept that a Nash equilibrium exists in matrix (aka normal-form) games, by Nash's theorem. So one way to see that an NE exists in HUNL is that it can be represented as an extensive-form game, which could be converted to an equivalent normal-form game, which contains an NE. This conversion from EFG to NFG results in a huge game (the NFG has exponential size in terms of the number of states in the EFG representation), which is why we don't want to do this conversion in practice and want to run algorithms on the EFG representation. But we could do this conversion at least in theory, and the NE of the corresponding NFG would correspond directly to the NE of the equivalent EFG.

And they would be correct since GTO isn't a real game theory term.

Doug throwing out the passive-aggressive slam at Jason when, after catching the bot in a bluff, says something like "it must have thought Jason was still playing down here."

Question: Is the team getting frustrated with Jason bleeding money while they print it or is it all being rationalized to variance/card distribution?

he serves to show how much a normal poker player would lose vs a good bot

^ i wouldnt exactly call him normal player, since polk said all of them are in top 10

Btw, anyone knows how much is each player up/down vs the bot? Thanks

I thought that the match was set up with mirrored card distributions to try to minimize the impact of card distribution/"luck." Given that, how possible is it for just one of the humans to be down just because of bad card distribution???

cheet has already said itt that he thinks his results so far are a combination of running bad and not playing his best (by failing to adjust to the bot as quickly as he should have.)

Yes this, but man this has been very brutal run of poker lol

bold the "minimize"

there's still huge variance EVEN with mirorred hands. I'm sure you can understand why...

Even more when 200bb deep instead of 100, since there are more ways to diverge in how the hands (and especially coolers) play out

Cheet runs terrible vs this thing obviously