How can I find Villains calling range and calculate $EV for shoving.
Using the program ICMizer. To simplify things a bit I just used a standard 9 man SnG, where the pricepool is split 50/30/20, which is close enough to the actual payouts in this event. Then I plugged in the stack sizes and action and pressed "ICMize". ICMizer now calculate the NASH equilibrium, which is the ranges for all players, where noone is winning or losing. This is often referred to as GTO ranges.
Now there are some caveats in this, mainly that ICMizer cant calculate spilt ranges. It assume, that when BTN limp, he either limp or fold, so he has no raising range. It then also assume, that SB either move all in or fold, so again no completing range. And finally it assume, that BB either knock his option or move all in, which in this case is pretty much also his only options. The program then runs a simulation, until equilibrium is reached. These are the ranges, ICMizer came up with:
BTN limping: 40% of
hands
SB (Hero) jamming: 17% of hands (any pair, AT+, KQ, QJ, A7s+, A3s-A5s, T9s+)
BTN calling SB jam: 7,6% of hands (77+, AJ+, ATs)
Expected EV for Hero of jamming QQ: 3,54% of the price pool
Personally I would jam here, because its just so easy, and its massively profitable. Raising small creates an extremely awkward spot, if a K or A comes on the flop, and I would rather avoid that spot. Most of the time they are both going to fold, and thats totally fine. You chip up, and now the short stack only have 5BB left, so he is a fairly significant step closer to being out of there in third place.
Around one in five times BTN will call you, if he is playing optimally (very unlikely given the stakes but lets just go with that assumption), and then you get it in with 63%
equity. Which is totally fine even with ICM implications. Yes it sucks, when you bust and give the short stack a free payjump, but it happen so rarely, that its not a reason to do anything other than jam preflop. The hands, you can select to just complete, are the marginal ones in the suggested range like suited rag aces, low suited connectors and QJ. With QQ and frankly a lot of other hands its an easy jam.