Help me with a toy game - Impossible rake

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Help me with a toy game - Impossible rake

0% rake if no one bets, if anyone bets, it´s 100% rake (everyone always lose). Pot is 1, 100 bbs stack, only bet sizing allowed is the all in.

Board is 22223.

OOP range is KK. IP range is also KK.

My solver doesn´t accept absurd rake (GTO+), so I can´t check it.

OOP x, IP x: OOP EV=0, IP EV=0.
OOP allin, IP folds: OOP EV=1, IP EV=0.
OOP allin, IP calls: OOP EV=-100, IP EV=-100.
OOP x, IP allin, OOP folds: OOP EV=0, IP EV=1.
OOP x, IP allin, OOP calls: OOP EV=-100, IP EV=-100.

I believe a solver would always go allin here OOP, as it should always maximize his own EV, and IP would always fold for the same reason. Yet, when this came out on twoplustwo a few months ago, the consensus was that we should keep callin til villain knows we will always call if he bets, until he always checks, and we do too, and the nash equilibrium will always be both players x for 0 EV.

My understanding of the Game Theory topic (the broad one) is pretty much nonexistent, but from what they told us back then, a solver will in fact always bet OOP but this is not the true equilbrium, as it would require the, let´s say, future planning knowledge that GTO+, PIO etc don´t have.

Not sure if I stated correctly, or clearly enough, and if you guys understand what I wrote above. If not, but you´re still interested and wanna give your 2 cents, feel free to ask for clarifications.

What I´m trying to teach myself here with this toy game is if high rake environments really lead to high aggression levels in most nodes, as even optimally, villains need to overfold.


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