Is it ever correct to fold a guaranteed split?

In the past I have always snap called guaranteed splits with the logic: "Guaranteed split = Nothing to lose, Only to gain = Snap call".

Of course, I wasn't considering the rake...

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Let's say we are playing a game with 5% rake (6bb).

Preflop (100bb starting stacks): SB limps and BB checks Q 2 .

Flop: AK Q
Check, Check

Turn: J
Check, Check

River (2bb): T
SB shoves 99bb, BB?

EV of folding: 0bb
EV of calling: [(200bb - 6bb) / 2] - 99bb = -2bb

EV(Fold) > EV(Call) so BB must fold.

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So based on this I guess this is true:

1) The GTO play is for OOP to shove and IP to fold.

2) Versus a human that does not understand the rake trap and will call the river if SB shoves, the right play is for SB to check and fold to a shove, right?

3) Versus a human that may understand the rake trap and fold or may misread the board and fold, shoving may be the best option.

How often must BB fold for SB to shove?

x% of the time, BB folds and SB wins 2bb.
1-x% of the time, BB calls and SB loses 2bb (+1bb in split - 3bb rake)

2/(2+2) = 50%

Have I got it right?

Folding The Flopped Nuts

A similar scenario with 5% rake (6bb).

Preflop (100bb starting stacks): SB opens 4bb, BB calls JT

Flop (8bb): 987
SB shoves 96bb and turns over JT, BB?

EV(Fold): 0bb
EV(Call): [(200bb - 6bb) / 2] - 96bb = +1bb

EV(Call) > EV(Fold) so we call.

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But what if villain has JT, so a 4.5% BDFD to go along with his straight?

EV(Call): 1bb * 95.5% - 96bb * 4.5% = -3.4bb

EV(Folding) > EV(Calling) so we must fold the flopped nuts.

Is this correct?

It is correct.
It's one of those spots where even if you play GTO you can lose money, if your oponent is not playing equilibrium.

That's why gto sucks :/

I guess it's much more common in MTTs, in situations where you're supposed to shove super wide and the opponent is supposed to call super tight,
but human opponent is a fish who calls wide and ends up spewing your ICM EV all over the table.

Yes it's correct to fold. I've written an article about this concept - the rake can force you to fold.

In the repeated game, it may be correct to sometimes spite call (both players lose EV) in order to disincentivize your opponent from stealing next time. The optimal strategy in any repeated Prisoner's Dillema is called "Tit For Tat".

In poker, these chopped spots occur so rarely that there's probably no point in spite calling or setting up retaliatory threats.

Interesting article and video! Gonna read/watch it more in-depth later.

Speaking of the prisoner's dilemma and the research done around it, I saw this interesting video a while back: