I decided to analyze this spot imagining that villain did not bet on the turn but the pot remains the same on the river as it does in the hands history. I thought I had an easy shove on the river the way it played out but this way it was a more interesting decision because villains range changes somewhat. On the river, then, we are risking 13k to win half the pot which means we need 52% of folds.

I gave villain 61 value combos which includes 18 spade combos; the fact that we lose the other half of the pot outright when he turns up with those 18 combos clearly effects our math, but I'm struggling to find the best way to factor this into the equation. Can anybody solve this?

Assumed villain value combos: AhQh, AcQc, AdJd, AhJh, AcJc, AdTd, AcTc, Ad9d, Ah9h, Ac9c, Ad8d, Ah8h, Ac8c, Ad7d, Ah7h, Ac7c, Ad6d, Ah6h, Ac6c, Ad5d, Ah5h, Ac5c, Ad4d, Ah4h, Ac4c, AdTs, AdTc, AhTd, AhTs, AhTc, AsTd, AsTc, AcTd, AcTs, Ad9h, Ad9c, Ah9d, Ah9c, As9d, As9h, As9c, Ac9d, Ac9h. I removed AJo combos in our imagined scenario because he would bet them on the turn.

What do people think? I perceived villain as aggressive and defending a very wide range here OTB. I find this spot very interesting but difficult to solve. If somebody with a better insight into the math could give their input it would be greatly appreciated.

Cheers