something maybe you SNG/MTTers can help me out with

[euphoricism]

You're at a table with 40bb behind.

You open to 4x with 66-JJ in MP and an LP player 3bets to 12x . You have 36bb behind. He has you covered.

When should you shove over? Is it mathematically solvable? How do I figure out what my equity needs to be in that spot to make it a +EV shove?

16x in the pot, 36x behind. Villain would have to call 24 more to win 56.

My stab:
80bb total at showdown
I have to win 36/80ths *when called* to break even on my shove which equals 45% of the time. And lets say villain always calls my shove with QQ+ and AK. My equity against that range is approx 35%. That means to break even on this shove I need 10% folding equity, in other words, I need him to threebet me (and fold) with 10% more hands than QQ+,AK right?
That would mean he would need to 3bet like 13% of the time.

Does that make sense? Did I do it right?

Thanks.

[taipan168]

Firstly, at least in a 1-table SNG, I wouldn't open raise 66-99 (and maybe TT), I'd limp with them and play for set value. Secondly, I don't think that, at least in the games I play, most players would ever 3-bet and fold to a shove. If they're good, they are almost always calling your shove because they would only 3-bet those hands that they'd call a shove with, if they're bad they won't fold their KJo.

That said, I think the step you're missing is that if you shove over and he folds, you don't double up, you just win the dead chips. I set out how a worked example of to do these calculations here.