[GTO] The absurdity of high resolution solutions - bunching effect - Page 3 - Poker Theory

Both folding ranges result in the same card frequencies in the remaining deck on average, i.e. there's one deuce and one three missing. The probability of SB holding 22 when BU folds is different in these two scenarios though. On average there are 3.5 combos to deal 22 for #1 while it's only 3 combos for #2.

Ah, that would mean there are multiple GTO ranges for BU (i.e. multiplayer NLH doesn't admit a unique Nash equilibrium, right?) -- is this a well known fact? I couldn't find anything googling but many papers refer to "equilibria" as if it's obviously true. I'm still catching up on the literature, sorry about these n00b questions

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09-20-2021 , 05:17 PM

#52

plexiq

veteran

Join Date: Apr 2007 Posts: 2,554

The example was just meant to demonstrate that specifying the average card frequencies in the remaining deck is not sufficient to describe all bunching effects. A folding range of {22, 33} produces the exact same card frequencies for the remaining deck as a folding range of {32o, 32s}, on average there are 3 deuces and 3 threes remaining either way. They actually produce different dealt frequencies for e.g. 22 though.

But this is really just a fringe point and not relevant in practice, don't worry about it.

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09-20-2021 , 05:35 PM

#53

brrrm

stranger

Join Date: Sep 2021 Posts: 6

for sure, I'm not incorporating this into my training or anything -- just an academic curiosity

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02-05-2022 , 08:41 AM

#54

mojo6911

veteran

Join Date: Feb 2008 Posts: 2,979

Pretty interesting subject. I guess the only thing that can fix this would be a full game tree solver that accounts for this starting from preflop. I suspect the new wave of GPU neural network solvers will be able to do this in a couple of years.

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