Recently had a thought about playing against a player/bot that 100% plays GTO. Might be interesting as bots will eventually find this strategy.
Wondering if my thought is right or where I go wrong.

I know if your opponent plays GTO then also playing GTO is the best counterstrategy. But aren't there multiple strategies that yield the same EV?

Look at he example below. In most situations the GTO strategy is a mixed strategy, I assume this implies that checking and betting with 78o gives the same EV against a GTO player. Normally always betting maybe is not good because you can get exploited by an opponent who calls or raises more, but a GTO player will not exploit you because he just plays his own mixed strategy.



Is it true that against an 100% GTO opponent it does not matter if you play a mixed strategy yourself? So in all the cases where GTO says you should sometimes check and sometimes bet you can also always bet because it gives the same EV?
Would this make playing against a 100% GTO relatively easy because in most difficult situations your GTO strategy is mixed? I don't have any experience with Pio etc so maybe I am wrong in this assumption. Maybe on river's GTO strategies are more pure so it does matter that you find this right strategy?

pedant mode/ In that example, Pio is almost always betting 87s with a BDFD, and almost always checking without it, and checking 87o almost always, so 87s and 87o are among the combos with the lowest amount of mixing. Hands like K8s and Q8s look much closer to 50/50.

When the solution is mixed, it doesn't actually matter which you choose, as all options have the same EV vs an opponent (like a bot) that never adapts.

As Arty has pointed out, when you drill down into the ranges, the individual combos are usually a pure strategy more often than not.

For instance, the A4o combos are about 50/50 and will likely be betting the two aces that are the best suits for card removal and checking the other two.

A truly interchangeable range would consist entirely of individual combos that are all individually equal EV between the two actions you are considering. Of course you could always bet these 100 percent, and no bot or human could ever exploit you. These actual combos that are mixed will be the exception, not the rule.

I don't actually agree with that. In many spots (possibly the majority??), a lot of combos utilize mixed strategies at equilibrium, even if the frequency of one of the actions is very low. (e.g. 87ss checking 2.4% of the time).
In my own c-bet range-building endeavours with Snowie, I was often disappointed that so few combos had pure strategies (e.g. 100% bet), since all the mixing makes it much harder for a human to learn what is correct.
All the mixing actually means bad players can "accidentally" play GTO some of the time, because it's quite often the case that it's correct to bet or check with a particular hand. In effect, a random button-clicker will often choose an option that is part of the GTO solution*.
When I'm studying frequencies, I focus on the few hands that are "pure", and then look for the ones that have frequencies that are near to 0% or 100%. Unfortunately, there are usually many more that have a number somewhere betweeen the two.

* A side-effect of this is that when I make a spewy play, I can laugh it off it a "low frequency balance play", as it often turns out that the solver suggests making that same spewy play about 3.50% of the time.

Checking a combo 2.4% of the time according to a solver is just noise. Clearly the solver is trying to teach you to not check that combo.

Do we really think there is a true GTO solver that computes GTO solutions?

With much respect, LOL

If you don't have low frequency low equity bluffs in your flop and turn range, then you will be value heavy on some rivers.

Well thanks for the comments, I was just trying to fall asleep when I had that thought.
And I knew I somewhere made a mistake but could not tell why, ofcourse not every 78o is the same.

And I also realise that with bet sizings it wil get much more difficult to beat GTO, because it wont happen often that every bet size is a part of the mixed strategy I suppose.

1) In pio, you are solving the situation such that your opponent's strategy is known and stagnant. In real life, our opponent's strategy is not inflexible, and therefore the game is more dynamic. What I mean by this, is if you are solving the game using PIO in a spot and it states an action with a hand is mixed (and solved completely), then that hand's action doesn't matter, as either action has the same expectation. However, in real life if we deviate all our mixed frequencies to one of aggression, then this opens us up to exploitation.


2) If you assume your opponent's strategy is set in stone and the game tree has been completely solved to give you that output, then sure.

3) No.

This is just wrong.

Yup, versus a GTO opponent you'll be indifferent. Versus a human it will make a difference since they aren't playing perfect. You are going to be playing against humans so if you are going to try this, then mixed frequencies are the way to go.

A good way that I use to randomize is using the orientation and suits of certain cards. Example: I need to 3-bet QQ 28% of the time. Approximate that to 25% and only 3-bet if Q of diamonds is the left card.

Hmmm. That approach generated a somewhat off-topic question, but here goes.

It is often recommended to use a second hand for randomization. So instead of using cards to randomize, which tells opponents nothing how you play, you check your watch. For 25%, if the second hand is in the first quarter of the minute, then do the action.

Okay, but knowledgeable players know that a frequent look at your watch before acting probably means a mixed bet frequency so they can figure that you are an aspiring GTO player.

Does an opponent knowing that mean a positive or negative for you?

I've never used a watch hand. One of the few places I've used GTO bluffing frequencies is nuts-or-air river situations. When the river card is unlikely to be a deciding factor, I tend to use the river card. When it is I guess I just estimate.