This doesn't really make sense in incomplete information games.

You can't pick an arbitrary information set S and then talk about the subgame rooted at an arbitary node in S. You can talk about the distribution on nodes in S induced by (x*,y*) and then ask for x* and y* to be best responses to these implied distributions (this is what is called a 'sequential equilibrium' when it holds for all S) but this is an even stronger property than being a Nash equilibrium.

I don't know enough to be able to tell whether everyone is making all of these terms up or not.

Oh right I don't mean an arbitrary node in S, I mean on the distribution. But I don't need x* at all, I can have whatever x, and I'm defining balance as "y*_S is a best response on the distribution induced by (x,y*)".

It's often used in more complex situations, too.

For example, I might say, "I think this guy has a pretty balanced 3betting game plan." By saying this, I would mean that I think all of the following things (and probably a few more things, too):

The range is strong enough that I have to fold enough hands preflop and on the flop that I think the weakest hands in his range are doing better than they would by folding or calling.

The range is not so strong that I think he could add lots more hands he's currently folding and have the above statement still be true.

The composition of his 3bet range and the way he reacts to a 4bet is such that 4bet bluffing him is neither totally hopeless nor wildly profitable.

His postflop play is sufficiently reasonable that I don't think I get to do anything wildly exploitive postflop after calling his 3bets.


This isn't any sort of precise game theory claim but it's a meaningful statement in terms of how I'm going to approach playing against the guy's 3bets. Contrast it with some things I might say about an unbalanced 3betting game plan:

"This guy's 3bet range is way unbalanced toward bluffs and I can exploit him by 4bet bluffing a lot."

"This guy's 3bet range is way unbalanced toward value hands. I'm folding a lot and he could get away with adding a bunch more bluffs but he isn't doing it."


Since we're not anywhere close to knowing what optimal preflop play looks like in HUNL, I have to be content with being "balanced" in something like the above sense.

I should revise what I said earlier. The "giving them a tough decision with a lot of hands" heuristic only really applies in situations where a lot of their range is composed of interchangeable hands. It's not possible to give my opponent a tough decision with a lot of hands preflop since he has a wide range of hands with varying values. If it's a close decision whether or not he should call my open with 86o, it's not going to be a close decision whether or not he should call my open with k5o. Instead the heuristic is something like "it should be a close decision whether or not he gets to play loose enough to make the weakest hands in my range lose."

Wow great insight Ike, thanks

Still really sounds like you're saying that villain's playing near-unexploitably.

Interesting post anyhow, thanks.

If we look at a half-street game, we are balanced if the ratio between bluffs and value bets is correct considering the pot and bet sizes. However we are free to choose how many hands we bet for value. Typically, only one of those choices has the highest expectation, and thus leads to a GTO strat.

So, finding a GTO strat is harder than finding a balanced strat.

Edit: oops, missed the page break

Unexploitable and balanced do mean roughly the same thing. Near optimal would be claiming something beyond that.

To go back to the river betting scenario, since these are easiest to talk about:

As long as you're betting valuebets and bluffs in appropriate proportion relative to your sizing, you're probably balanced. You also need to have correctly chosen your minimum valuebet and your sizing(s) correctly to be optimal.

+1
Thank you Ike for being so involved in the 2+2 community.
I undoubtedly prefer Ike to a guy like Ivey.

By the way, it should be pointed out, if it hasn't already, that the GTO head up holdem strategy, is actually two completely different strategies, one for the button, and one for the big blind. They are not balancing with each other (except for the fact that they break even if both players are using them). Neither one is a strategy that "at worst breaks even". The button strategy at worst wins x bb/100 and the blinds strategy loses at worst x/11bb.

Well, that's really a matter of definition.

Great poker players are more akin to great athletes (mindset wise) than great academics...(though I'm having to think carefully about this myself, since I believe great academics are just as competitive and driven as great athletes and poker players...)

Sauce? (Seeing as I saw you make a similar distinction)

That's kinda like saying that basketball is really two different games, offense and defense. But either way you're still playing bball.

And besides, where do you stop splitting into sub-strategies? Each street in each position could be considered a completely different strategy etc.

You can't look at different streets independently. You can (but don't have to) with different positions.

This reminds me of that Gigabet thread.

I can't get noooo, heads up action, but i try, buut i try , yeah i try, yeah i tryyyy, i can't get noooo

Makes sense. Thanks!

incorrect. the correct strategy on each street is heavily dependent on other streets, just like the correct strategy with various hands is dependent on the strategy with different hands. the button and big blind are two completely different games and are entirely independent of one another with respect to game theory. (though they can obviously be heavily dependent on one another with respect to exploitive strategies)

Wrong. I'll let others elaborate.

GTO doesn't care if it knows I have a bluff catcher, theoretically I could play against a GTO bot with my cards face up and it would still make the unexploitable play.

The great poker minds of 2+2 have no idea what a GTO strategy with AA is preflop, only God himself knows what GTO river strategies would look like.

Hahahahaha, this thread has everything.

Ike, thanks for your posts. Given how rare it is these days, it's always nice when guys as knowledgeable as you publically discuss strat.

In response to an earlier poster who asked about a good starting off book for learning about GTO, I would recommend "The Compleat Strategyist, Being a Primer on the Theory of Games of Strategy" by J.D Williams. The book is remarkably witty and well written in the old timey fashion as it was published in 1954. The book does a wonderful job of introducing game theory ("The Theory of Games of Strategy") in the most simplest of terms while expertly explaining all the intricacies of applying game theory to an array of real life situations and even offers practice problems.

Which brings up my response to another previous poster who claimed that research in poker game theory may be a waste of time. The author has you apply game theory to simple real life applications in which game theory can be utilized. Early on in the book we see how game theory can be used to determine an optimum strategy for an umbrella salesman who also sells sunglasses given certain probabilities that it will rain or be sunny (he must determine how much to invest in which product), we later solve a game theory matrix to determine an optimal strategy for a policeman chasing a villain. The policeman knows the villain will show up at his girlfriend's or mother's house with certain probability and can use game theory to decide the optimal strategy.

When modeled correctly game theory can be applied to a mind bogglingly large number of real life situations in which it can be used to our advantage as a society and as individuals.

there is a distinction between research in game theory in general, and research into game theory's relevance to poker, which I see as a subsection that has some qualities and does teach us some things but ultimately most solutions/conclusions can be achieved from gt research in other areas. there is a ton of research into game theory as it pertains to games of incomplete/asymmetric information (the market and modern wars being two main examples).

questions to all the GTO/computing experts:
how much more difficult would it be to construct a GTO bot for PLO than NLHE?
how much more difficult would it be to construct a GTO bot for tournaments than NLHE cash?
which would be more difficult (plo or tournaments)

GTO is always changing based upon types of opponents