The GTO Blackpill
I've been working on an experiment recently that I think will fundamentally change the way you look at GTO.
A while back,
GTO is unattainable in practice, yet many players strive to play closer to GTO and reduce the exploitability of their strategy. This begs the question, does playing closer to GTO increase your EV against imperfect opponents? Well, if we exclude pure mistakes, then the answer is a resounding NO. That's my point.
I think there's a big difference. If you can play NE you minimise the amount your strategy can be exploited by, which is why it's how a lot of high stakes regs try to play. But if you replicate this approach in this thread that only has merit against an imaginary opponent who doesn't exist and I'd be confident a bot doing it above microstakes would lose
But you can't play NE in practice. It's too complicated to implement. You can only try to reduce the exploitability of your imperfect strategy.
My point is that a player who tries their best to reproduce GTO won't have the edge against a weaker player, so long as that player is not blundering.
I wouldn’t have predicted that result either but tbh don’t see why it would be a breakthrough. Since there are no players who play perfect equilibrium or this unbiased mixing strategy your own frequencies do matter
Yes you're right. People don't make unbiased mixing mistakes, their mistakes are always biased. But that doesn't change my point. The less exploitable (closer to GTO) strategy still does not have the edge against a player with biased mixing mistakes.
All that matters is which player just so happens to be exploiting the other player's mixing biases. The closer-to GTO strategy loses less when it gets exploited, but also gains less when it exploits.
Great read as always tombos. Thank you for keeping the GTO forum alive!
...The closer-to GTO strategy loses less when it gets exploited, but also gains less when it exploits.
Would it be too much of a stretch to infer from this that the highest EV strat would be the one that is closest to GTO when acting first with zero observation, but goes for max exploits when acting last with higher confidence in large data sample observation?
In case what I'm envisioning isn't clear, I'm imagining a continuum from being UTG pre-flop versus a complete unknown (pure GTO) to on the BTN on the river versus an opponent with clearly demonstrated leaks over a large volume of observed hands (max exploit).
Would it be too much of a stretch to infer from this that the highest EV strat would be the one that is closest to GTO when acting first with zero observation, but goes for max exploits when acting last with higher confidence in large data sample observation?In case what I'm envisioning isn't clear, I'm imagining a continuum from being UTG pre-flop versus a complete unknown (pu
I don't know how you would infer that from this thread.
But I agree that your exploits should scale with your information. A kind of Bayesian exploitative framework.
I don't know how you would infer that from this thread.
But I agree that your exploits should scale with your information. A kind of Bayesian exploitative framework.
Perhaps not the thread in total so much as this statement I quoted, "The closer-to GTO strategy loses less when it gets exploited, but also gains less when it exploits."
Logically, if we lose less when we get exploited, it would seem easier to exploit us when we have to act first, and if we have no info about our opponent, there wouldn't seem to be a reason to deviate from GTO. When we can act last and have more info, we have more of an incentive to deviate and go for max exploits.
I've been calling this player a "Bad Reg, " but this is actually a very high-level strategy lol.
I'm so glad you acknowledge this. I was in pure rage comic mode at the sheer nerve of taking a strategy that will never be attained by any human and naming it Bad Reg of all things.
Other than that, great read and thank you for posting!
My instinct is to try to ask a simpler question: what happens if you play “rounded” strategies where you just play every decision pure? It may turn out to be the case that in this framework, the pure strategies that appear in GTO mixes have equal EV against not just GTO but against each other. This is definitely possible (and even likely, since we’re mixing strategies that GTO has made indifferent), and if it is true it would immediately imply what you found in the OP.
This sort of result somehow doesn’t feel surprising to me. It seems like anytime there’s a pure strategy that does best in a solve, GTO would already be playing it as a pure strategy. It’s not immediately obvious that that has to be true but it’s not surprising to me if it is.
My instinct is to try to ask a simpler question: what happens if you play “rounded” strategies where you just play every decision pure? It may turn out to be the case that in this framework, the pure strategies that appear in GTO mixes have equal EV against not just GTO but against each other. This is definitely possible (and even likely, since we’re mixing st
I'm not sure I understand what you're saying?
I can round both player's strategy to a pure strategy easily enough. But they wouldn't be indifferent vs the rounded opponent.
Here's the root node of a CO vs BB sim, 100bb deep, SRP
GTO: Every hand in BBs range either has higher EV check, or is indifferent to checking:
After Rounding both players pure: Several hands in BBs range now have higher EV donk bets, despite always checking
There are many other examples like this.
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If I kept one player frozen to GTO, then the other player's mixes would of course be indifferent. But once both players are rounded the indifference argument goes out the window.
The surprising thing is that all the "accidental exploits" cancel out perfectly. Both players are making huge -EV blunders (exploitatively speaking), but over millions of decision points it washes out.
Here you can see the EV IP and OOP remain basically the same before and after rounding (within the margin of error of original sim)
The surprising thing is that all the "accidental exploits" cancel out perfectly. Both players are making huge -EV blunders (exploitatively speaking), but over millions of decision points it washes out.
The term that comes to mind is "information entropy".
If we think of the laws of thermodynamics:
1) The energy of a closed system is constant. Energy is neither created, nor destroyed -- only transferred/transformed.
2) Entropy tends to a maximum. A closed system tend to the most likely (most spread out) macrostate.
I guess the game theory equivalent would be:
1) The EV of a zero-sum game is constant. EV is neither created, nor destroyed -- only transferred.
2) Outcomes tend to the most likely (most spread out) macrostate. Good and bad luck tend to even out.
Example: A coin flip has a 50/50 probability distribution, but after one flip there is a 100% chance of finding it at all heads or all tails.
After 2 flips, there is a 50% chance of finding it at all heads or all tails.
After 100 flips, the probability of finding it at all heads or tails is: 0.5^(100-1) = 1.6 * 10^-30
This is the reason we get the bell shaped curve: because there's only one way each to get "all heads" or "all tails" over 100 flips, but there are many microstates that correspond to the macrostate of 50/50, or close to 50/50.
Veritasium made a good video about entropy. The part most relevant to game theory is between 10:20 and 14:50.
Thinking a bit more about it.
Just as the result after 1 coin toss is 100% guaranteed to be imbalanced (50% is impossible), we can create a toy game that is 100% guaranteed to lead to different EVs than nash.
Nash:
IP: 1 nut combo and 1 bluff combo (mixed at 50%), 1x pot. EV = 0.75.
OOP: 1 bluffcatcher combo (mixed at 50%). EV = 0.25.
If we round the bluffs/bluffcatchers to 0% or 100%, we get 4 possible strategy pairs:
* 100% bluff, 100% bluffcatch
EV(IP): 50%*2 - 50%*1 = 0.5
EV(OOP): 50%*2 - 50%*1 = 0.5
* 100% bluff, 0% bluffcatch
EV(IP): 100%*1 = 1
EV(OOP): 100%*0 = 0
* 0% bluff, 100% bluffcatch
EV(IP): 50%*2 - 50%*0 = 1
EV(OOP): 50%*1 - 50%*1 = 0
* 0% bluff, 0% bluffcatch
EV(IP): 50%*1 + 50%*0 = 0.5
EV(OOP): 50%*1 + 50%*0 = 0.5
If I'm thinking correctly: the standard deviation of the EVs are 0.25 away from nash EV, so to get the standard deviation down to 0.01 we would need this many more combos to randomly round to pure strategies: 0.25 / SQRT(x) = 0.01
x = (0.25/0.01)^2 = 625x more combos.
Similar to how diversification lowers volatility in investing.
Entropy is the best explanation, nice point Zamadhi.
My internal analogy is that exploits are kind of like magnets. You need enough charged particles pointing the same direction in order to create a magnetic field. But if you add some entropy (heat) the charged particles get shuffled and tend to cancel each other out.
Similarly, in this experiment we add an unbiased entropy (rounding), and the exploitative interactions tend to cancel out. And that's why I added condition #3 way back here. You need enough decision points for the law of large numbers to apply.
One clarification though: It's still wildly exploitable. Like in some lines it's way over-defending, or overfolding. In some spots it's bluffing way too much or not enough. Hugely exploitable patterns emerge, but neither side effectively punishes these deviations.
No need to suggest « to them », you ARE an employee of GTOWIZARD and r/Poker-Theory IS the dedicated forum for GTOWiZARd. Any other solver trying to post in there will get systematically banned.
If you want a real, open, free, no ban discussion on poker theory and ANY poker solver, there is a much better forum that started recently : r/PokerSolvers
See you there.
This entire post uses PioSolver, a competitor to GTO Wizard. I'm just trying to talk poker theory man.
You got banned from that subreddit for shilling a chatGPT wrapper pretending to be a solver. You broke the commercial spam rules and another mod banned you.
Why are you in here bothering me about it? Please take your victim complex elsewhere.
