Does "Transparent GTO" exist?
Let's say that someone tells you all the information about the cards that will be in play, in the next hand (NLHE). You
Hmmmm, I think you know how opponents will play only if your play will be adapted to this scenario (that you do know). For example they can fold their hole cards if you jam pre-flop and you'll know that before, but you don't know what they will do if you just raise. Judging the strength of hole cards (for example pre-flop) can be a subjective thing and small details might come into play.
Yes it exists. You know what cards are coming, you know how your opponent's will play, so it's just a computationally trivial EV calculation to find the best line.
You're basically solving a much much smaller game tree.
No argument about the first part, that modified game is clearly still covered by Nash's proof of existence.
I don't think it's easier to solve though, assuming the opponents are aware of you knowing the cards to come.
Why?
- Calculating your strategy for one specific deal (board + hole cards) is relatively trivial if you have some static opponent's strategies, sure.
- But: Instead of having 2 cards as hidden info, you now effectively have 17 cards hidden info (with some cards shared w/ other players, making up for interesting removal effects). Your opponents' strategies are determined by your play over all your possible deals of hidden info, since they can't distinguish between these states. So you can't really take one set of hidden 17 card info in isolation and solve it, you'd have to solve over all possible configs.
I think you would need the HUD statistics and all that kind of info about each player and their style to be able to calculate this.
I think people don't use that kind of software anymore, I don't know. Like Poker Tracker, etc.
Sure it does? It just assumes you're at its level. Which is usually a tragic and costly mistake.
Sure it does? It just assumes you're at its level. Which is usually a tragic and costly mistake.
I don't believe it does. If you play perfect GTO (not actually attainable), your actions make you indifferent no matter what your opponent does. If they also play perfect GTO, you both break even. But the more they deviate from GTO the more you profit. Is this the most profitable strategy? No. That would be exploiting your opponents weaknesses.
No argument about the first part, that modified game is clearly still covered by Nash's proof of existence.I don't think it's easier to solve though, assuming the opponents are aware of you knowing the cards to come.Why?- Calculating your strategy for one specific deal (board + hole cards) is relatively trivial if you have some static opponent's strategies, sure.- But: Instead
Hmm... That's a good point. I guess it hinges on whether or not the other players know you're a superuser.
If they're unaware, it's a simple exploitation problem. We can model them as playing a fixed strategy, whether that's a fixed GTO strategy or a specific "player style" like deuces mentioned. As long as their strategy is defined, finding the max EV line is computationally straightforward.
But what if your opponents know that you can see all the cards? Solving the equilibrium strategy in this case is indeed way more complicated than I initially thought. The superuser's "range" can no longer be represented by a simple 2-dimensional grid of hole cards, instead it's this massive 17-dimensional object(?!)
I guess it would shrink as the cards are revealed. From villain's perspective, their two hole cards would shrink your range down to 15 dimensions, and the community cards would shrink that down to 10 dimensions. But it's still unreasonably complex.
There was an interesting discussion about this topic right after the Mike Postle scandal broke, but I can't find the thread now.
I think opponents should be aware. It could then be a rule that DB sees all future cards, so all players can get their chance. If they didn't know, it couldn't be seen as a rule then, but cheating instead.
