If you have 11bb and antes-
To answer this question, you need to take a guess at what button’s range is. Notate it all out. Is it most likely going to be middling speculative hands? probably. so put the hands together.

Count how many combinations of hands that is. Now guess which of those will call your shove. Will he call KJ? Will he call A4s? Count the number of hands that will call and divide it by the number of hands total you guessed he could have by limping. That number (it’s a number between 0 and 1) is the % you get called. (1- the number you get) is the % you get folds. When you get folds, you win (1bb+.5bb+1bb+ .9bb+10bb). So you take the %Folds and multiply it by the pot (13.4bb).

After you figure out which hands will call, open up an equity calculator that allows you to put in ranges. I use …..imulations when not at my desktop, and equilab when at home. …..ab-holdem/

Find out what your equity against the calling range is. Now you multiply the %Call by the size of the pot when you’re called and multiply by your equity. (1bb+.5bb+.9bb+10bb+1bb+10bb) (23.4bb)

Your end result is %Fold(13.4bb) + %Call(23.4bb x equity) = the expected value of the situation.

Compare expected value to slightly more than 10bb. (I’m assuming you win make money post flop with 24o when youre in for a free limp. Even if you only put a single chip in when you flop two pair+ and nothing else, or even quads only, it’s still money you get for free since youre given the option of checking if you take it). 10bb is how many chips you have when you check with the intention of folding at any point in the hand.

Now here’s an example with the stack sizes we’ve given.
PLEASE NOTE THAT I DID NOT GIVE ANY THOUGHT TO THIS RANGE. I DONT WANT TO GIVE YOU THE RANGE AND DO THE WORK. I WANT TO GIVE YOU THE FRAMEWORK TO DO THE MATH YOURSELF WITH THE RANGES YOU GUESS.
villain limps 67s, 78s, 89s, TJs, 79s, T8s, QTs, J9s, QJ, KT-KQ, A2-AT (240 hands)
and calls a shove with A8-AT, KT-KQ (96 hands)

%CALL = 96/240 = 40%
%FOLD = 144/240 = 60%

Equity when called is 33.75% and amount of times you bust (lose the hand) is slightly less at 65.92% (54,949,714/164,381,184 games)
…..;s=generic

60%(13.4bb)+ 40%(33.75% x 23.4bb)
8.04 bb + 3.159 bb = 11.199 bb

This is actually more than you have, which is 10bb. When doing this, first I’d suggest seeing if a situation is profitable. Checking is infinitely profitable because it’s free and you have equity, no matter how small it is.

For this example, shoving would be profitable by slightly more than 1bb, and you’d be out of the tournament 26.37% of the time. (65.92% x 40% = 26.37%)

If you want help going through any of this, don’t hesitate to ask. I like math. If anyone spots any mistakes, please feel free to correct it. Now that I’ve given you the framework, you should try doing your own with your own guess of his limp range in that spot. Do it here too and I can check the math as you go.