Ok let's break this down.
Live unknowns rarely have a draw/pure bluff in this spot given how much strength you've shown in this hand. Discounting this hand by 100% is a good approximation imo.
Live unknowns rarely have a one pair hand like AQ in this spot also, given how much strength you've already shown. Discounting this hand by 100% is a good approximation also.
Live unknowns are unlikely to show this much strength with K9s/K9o in this spot (and he may fold K9o preflop). This hand should be discounted significantly.
I would discount AA/KK 100% due to preflop action (no raise), and include all A9s/A9o in villain's range, and I would exclude all A2 hands assuming villain would fold to the flop raise.
I discounted AKo/AKs by 50% due to no preflop raise.
So here's where we are at:
Quote:
Board: Ac Kd 9d 2s
Dead:
equity win tie pots won pots tied
Hand 0: 40.909% 20.91% 20.00% 92 88.00 { Ad9c }
Hand 1: 59.091% 39.09% 20.00% 172 88.00 { 9h9s, AsKs, Ah9h, As9s, Ks9s, AhKs, AsKc, Ah9s, As9h, Kc9h }
If we just shove the turn and villain calls with 100% of his turn check/raising range, we are risking $760 to win $1435. We need 34.64% equity to make that play profitable. Based on the numbers above, it appears that's what you should do.
Now let's do some more worser case scenario analysis. Out of the AA/KK group there are 3 combos of KK and 1 combo of AA. Let's throw in just the one combo of AA (people like to be sneaky sometimes), and let's discount K9o/K9s by 100% (I only put in 2 combos of K9 originally). Everything else is kept the same:
Quote:
Board: Ac Kd 9d 2s
Dead:
equity win tie pots won pots tied
Hand 0: 24.242% 02.02% 22.22% 8 88.00 { Ad9c }
Hand 1: 75.758% 53.54% 22.22% 212 88.00 { AhAs, 9h9s, AsKs, Ah9h, As9s, AhKs, AsKc, Ah9s, As9h }
In this scenario, we should fold.
Bottom line, this is an extremely marginal spot you're in. Some shortcuts to use in the heat of battle that'll get you to the right decision the vast majority of time: If you don't think villain 3bets AK preflop oop then fold the turn. If you think villain always 3bets AK preflop, then shove turn. If you think villain is crazy enough to check/raise the turn with AQ, then shove the turn. More rarely, if you're knowledge on villain is precise enough that you believe villain will play K9o in this spot preflop and overplay K9 on this board, then shove turn.
That's a lot to take in. In the actual hand I would probably tank fold. I see too many live players that DON'T 3bet AK, especially oop preflop, and I see a lot of villains play mubsy with A9 postflop given that you raised the flop. And I see one pair/draw/air so rarely in this specific spot that it's barely worth mentioning.