I don't fully understand why GTOW recommends some negative ev decisions or am I just misreading it?
For example HJ vs BTN 3bet pot
flop AK7r
hj check
btn bet 2/3 pot
then looking at AQs for HJ it shows that calling is +0.1 ev and raising is always -ev but that is still recommended action about 30% of time.
please explain in simple terms why that is?
If you removed the option for HJ to raise to calling change ev? how does it work?
thanks

Understanding nash distance

Thanks. This is in the closing paragraph "Treat mixed actions as if they were the same EV. Any discrepancy you see can be thought of as the margin of error, (all hands are roughly +- that EV)." I do not understand. how can I know which ev they should be if they are different with some + and some -? image is AQs from my example

Maybe Tombos will chime in. He' a solver expert that works with GTOwizard.

At the risk of misrepresenting the way these things work, I think it is basically "solver noise." There is a margin of error when you select the nash distance for the solver to solve to. So if two actions are mixing the EV should be within those margins. If it was solved to a higher accuracy the effect you are seeing would likely vanish, or become such a small difference that it would turn into a rounding error.

GreatWhiteFish said it well, and thanks for linking my article, Zamadhi.

In Nash equilibrium, any mixed action a hand takes has the same EV (the indifference principle). In practice it’s fuzzier, because we don't solve to perfect accuracy.

We don’t actually know AQ’s exact EV here. To know it precisely, you’d need an essentially perfect solve. In that limit, every action the hand uses would be be the same EV: maybe it stops folding and call / small raise both land at +0.05bb; maybe it keeps mixing fold/call and the hand’s true value is 0bb. Without a perfect solve, we can’t pin down the exact number, we can only estimate it.

What we can say is that AQs is effectively indifferent between folding, calling, and a small raise (no larger raises are used). In the solve, the EVs of the actions it actually takes are within about ±0.1bb of each other, so the “true” equilibrium value is most likely somewhere around 0 to +0.1bb.

Practically, the moment I see blue, I just bucket it as a ~0bb hand. There’s nothing to be gained by sweating the last tenth of a blind. The strategic takeaway is simply that this hand is right on the continuation threshold, and makes an ok bluff. Everything beyond that is minutiae IMO.

Thank you.
I never quite fully understand, is GTOW actually solving these spots using an algorithm like cfr or it's pulling solves from a database somehow.. or something different?

Pulling it from a solved database... except for their ai thing.

It depends on the spot.

The library of solutions is pre-solved with a standard CFR algorithm, then stored in a database.
Custom spots are solved on demand using GTO Wizard AI.

https://blog.gtowizard.com/introducing-gto-wizard-ai/

correct GTO calculations should not include -EV moves

The last comment is essentially correct. In a true Nash equilibrium, any action you mix between should be indifferent, meaning equal EV. If GTO Wizard is showing raising as slightly -EV, that's almost certainly a solver convergence artifact rather than a deliberate design. The solver iterates until it gets close enough to equilibrium but stops before perfect indifference. The practical takeaway is that the raise frequency exists to balance your range, but if you're a human simplifying, just folding the raising frequency into calls costs you almost nothing.