Hey pardon me, I am a beginner but are you saying that it will be easier to find a solution to games where there are more hole cards known to the person and that the bots will work these out first or that these games are more complicated because of more spots?

Also what do you mean by a pure strategy? Sorry for these beginner questions.

Pure strategy = given an information set (your hole cards, the community cards, the betting action and so on), you always take the same action. 'Always reraise Aces preflop in LHE' is a pure strategy. 'Reraise aces 70% of the time' is a mixed strategy.

I believe that the nash equilibrium any toy poker game with continuous, independent card distributions is pure. E.g. I get a random number from Normal distribution mean .5 variance 1, you get a random number from uniform distribution [0,1]. Whatever the betting rules you state, that game is going to have a pure distribution. To see that continuity is important, consider a game where we each ante $10 and I flip a coin. I have the option to bet $20, you have the option to call or not. Heads I win, tails you lose. Since we know that pot size bet --> 2:1 bluffing ratio, it follows that we should bet all heads and half of our tails. Let's say we get a random number from 0 to 1 and it is common knowledge that our opponent has .5. We should bet all number on the interval (.5, 1] and half on the interval [0, .5). Here it doesn't matter which half we bet, so we could play a mixed strategy here, but playing a pure strategy of betting on all hands bar (.25.5] is equally good.

The poker variants we play violate both the continuous and independent assumptions. Continuity is violated as we may have 8 high or 9 high, but not 8.1 high. I do not believe that is a big impediment to using a pure strategy. As we increase the number of cards in each suit towards infinity, we converge on a continuous distribution. Thus if each suit had 1000 cards, we would have essentially a continuous distribution. I believe that for almost all forms of poker that we play, the pure strategy is implemented because it violates the independence axiom, rather than continuity.

Independence is violated because my hole cards affect the distribution of my opponents hole cards. If I have AA on an A72r board, my opponents range is weaker than if I have a random hand. If we call a king high board with KQ but not KJ our opponent may find it profitable to bluff all hands containing a Queen. So Nash might say we should call half our KQ and half our KJ, as long as our opponents. Here, if we played say 10 deck hold'em, we are converging on an independent distribution. I'd love to hear Fullycompletely's thoughts on this, but I suspect that if his job for 100 deck hold'em would be significantly more simple than for 1 deck hold'em. You'd have to take in to account the possibility of a tie in certain spots, but this would easily be countered by the ability to ignore any card removal effects.

I think that Omaha is harder to mathematically solve than Hold'Em because it's a 'bigger' game. However, I suspect if you kept giving players more and more hole cards, eventually the game would get easier to solve. E.g I think that HU 23 card Omaha, so that there is one unknown card once the river is dealt, is easier to solve than 6 card Omaha. I'd love to hear others thoughts on this. Perhaps it's harder to solve for a de facto nash equilibrium, but I'm pretty sure that it's much easier to solve for an 'almost unexploitable' strategy.

****

Any base whole number. (I thought I was forgetting something...)

well played

Would both players have the nuts some huge percentage of the time... except when a flush is the nuts?

makes sense that the fewer the unknowns, the easier it is to solve. But the 6 hand combinations available from the standard 4 card Omaha hand presents 6x the unknowns compared to a 2 card HE hand.
It doesn't seem that the knowledge of just 2 extra cards would make solving simpler. I'd suspect a bell curve where it gets more difficult until your hand has maybe 14 cards, and then it gets easier from there on up.

Party Girl, I follow your logic on the 23 card Omaha being easier to solve.

With regards to Pure strategy's you mentioned. If you know a player always does something with a particular hand in a particular situation, it is easy to exploit, which seems contradictory to a GTO strategy.

Speaking in terms of specific hands was confusing. He meant range. A pure GTO bot could tell you it's exact and honest range in any given spot - and you wouldn't be able to do anything about it. Most players know the toy game of shoving the river for a pot sized bet with a [exclusive] nuts/air ratio of 2:1. That's an obvious and intuitive unexploitable spot. What a GTO bot would do is essentially turn every single spot in poker into that. I'm not going to speculate on whether a mixed or pure strategy would converge on this more easily. The one thing I've learned from studying GTO play in poker is that it's far from intuitive - so intuition/"educated guess"-based speculation is pointless.

The only difference in the above for mixed vs pure strategy would be the mixed strategy bot would give you his exact range along with frequencies.

games solved. everyone should just give up imo

not sure if serious

not sure if serious

Someone (i belive it was ike) said that a gto bot will look like a fish. Id say he will look like the biggest fish of all times.

Dont know if this was discussed before but, as i see it, the GTO basically dictates to never re-raise (a raise) or raise a bet!

Imagine this scenarios:

1) bot in bb gets raised by sb. The bot will basically have no 3betting range because it could be a strategy outhere that only openraises with aces and limps or fold the rest - so the bot cant reraise anything else but AA - even more, it will not reraise even the aces because its supposed to "even if the opponent know the exact ranges he wont be able to exploit it"

2) anywhere in the hand when facing a bet the bot cant re-raise unless he holds the absolute nuts because then again it could be a strategy out there that only bets there with the nuts...

Violent Leaks, you seem to have no idea what GTO means.

This is wrong - you have to look at the strategy as a whole.

Yes, the "limps or fold the rest" or the "only bets there with the nuts" strategies will gain EV in the spot you've given vs a GTO opponent, but you've also got to look at the EV they are losing by playing so tight/passive in all the other possible spots.

If this isn't clear, then consider a player who only pushes AA against an opponent in the BB who calls with the push/fold GTO range: yes, the BB loses a lot of EV the tiny fraction of times (<0.5%) when he calls with his GTO range against the SB's AA, but the EV lost is dwarfed when compared to the ~99.5% of the time he gets a walk from the SB. Overall the BB will be making a lot more against the SB's "only push AA" strategy than he would had the SB pushed with the push/fold GTO range himself.

Juk

lol im so bad at theory.
Thank you for reply.

Chess is not solved yet, but no human can beat it no matter how hard they learn. So a poker bot not need to be perfect GTO to be able to kill the game.

What about 2-7 triple Draw. How good could a bot be at that game??

What do you guys think of pokersnowie ?

From their FAQ :

The IA is based on a neural network (who seems to be a dead end from what I understood reading this thread). They obviously haven't solved HUNL : 1/2PSB, PSB and AI are the only analysed betting patterns, the bot still make horrible calls like calling with a pure drawing hand (8hi) without the needed odds. Anyway I was wondering how usefull/close to the GTO/good such a software can be ?

this is kinda scary cuz the tone of ur post suggests that u know what ur talking about and u obv have no clue.
If a bot only opens AA and limps or folds rest of hands then I could have a 100% 3bet stat and still be +EV against it.

jukofyork already responded to that post (a lot more eloquently and a lot less dickishly), so I'm sure VL gets that by now.

idc if a dozen posters already responded to that post (a lot more eloquently and a lot less dickishly) im gonna respond myself, yo

interesting. where is this result from?

this is obvious

jungleman vs pokersnowie LOL :

http://www.pokersnowie.com/blog/2013...e#.Unqqxvlg_zE

only zeee limit version of zeee game