Hi all, I love this forum and read all the time but just registered to ask a couple of questions about GTO theory.

1) I want to understand the indifference principle more. I'm wondering how we are able to achieve profit if we put our opponent in spots that they are indifferent as to which play they should make. It seems like if it doesn't matter what they do, they are unable to make a mistake, meaning no way for us to profit. If we are perfectly balanced, what is stopping our opponent from calling with all their bluff catchers, assuming we don't adjust? If we compare to rock paper scissors for instance, playing a GTO strategy guarantees we will break even no matter how "bad" the other player is. Where exactly does the profit come from against weak opponents. Obviously it is there, I'm just trying to understand it better.

2) Is it possible that there are multiple "revolving" GTO strategies (I made that term up). For example, one strategy beats another which beats another strategy which beats the first strategy.

Any input much appreciated.

1) When we're making opponent indifferent with our bet, we're making sure that we're getting the most money possible out of him on average, when he's playing optimally. Basically, we're making all of his options +10EV instead of making one of his options +8EV and another +12EV.

2) It's impossible to have the "one strategy beats another which beats another strategy which beats the first strategy" situation in HU, since the same player would be using both 1st and 3rd strategy. The "even number of revolving strategies" situation is possible though, the strategies just wouldn't be GTO, since they are by definition exploitable.

In a game theory sense the indifference principle simply states if any player in a Nash equillibrium has some strategy where they select different options with positive probability, then all of those options have the same EV vs the opponent's equilibrium strategy.

Now, I don't think you were specifically asking about the general indifference principle but something more along the lines of the AKQ game where the betting player bets A's and Q's with a certain frequency and a player calls K's with a certain frequency.

With the latter indifference scenario we often only look at the solution and become disconnected from the context.

If our opponent is making a clear mistake (i.e. calling too frequently or folding too frequently) then we would not choose to bet to make them indifferent. We would choose the highest EV option (i.e. betting only value hands or bluffing more frequently respectively).

So when we don't yet know how a villain plays or we are playing against a tough opponent that calls correctly we can minimize our losses or maximize our gains by playing with the balanced strategy.


The profit comes from understanding HOW they are weak compared to the perfect counter strategy. If they aren't weak, then our only choice is to play the balanced range.


It is possible for games to have multiple Nash equillibria because the only qualification is that in a Nash equillibrium no player can improve his or her own EV by deviating from his or her current strategy. In that way equillibrium actually comes in sets of strategies (one strategy for each player at that point in the game).

So at equillibrium there are no better strategies to choose from because if there were it would create a contradiction and you would not actually be at equillibrium.

They'd be indifferent if they were playing something resembling GTO, playing nearly perfect poker, but in reality your opponents will be far worse than perfect players, and also you got it backwards, it's true that if you're playing something resembling GTO it doesn't matter what they do, but that doesn't translate to them playing mistake free poker, it means they'll be unable to gain an edge against you no matter what they choose to do if you are playing closer to GTO than they are. Betting with a balanced range does just that, opponents are screwed no matter what they do. Of course no human can bet with a perfectly balanced range but the person who plays closer to the mark can take maney, the f do.

Uh because if we're perfectly balanced we'll be betting plenty of strong hands too? Which renders his "call with all bluff catchers" strategy a losing one?

And GTO poker presumably includes some checking back of hands that would have called a bet, so the habitual bluff catcher misses value in that way too.

And GTO presumably includes checking back winning hands that would have folded to a bet, another leak in the habitual bluff catching strategy, not enough aggression and denial of equity.

The indifference principle only applies when the bettor has nuts or air and when the caller has pure bluffcatchers.

Not true.

Example please?

Pretty much every time we bet in poker, there are some hands in opponent's range that are indifferent between calling and folding/raising.

Also, when we have an option to CBet the flop, usually 90%+ of our range is indifferent between CBetting and checking.