Hello,

i have a question about the calling range against a shove. For Example, someone pushes 40% from cutoff with 15bb. On a nash calculator, they say it to me for example we should call with 25% of hands against this push. But why is it not profitable to call wider? Is there a rule, how we can calculate(without calculator) a calling range against a pushing range(here 40% percentage). I hope you understand my question

Because we are calling all hands which are individually+EV against his range - so the top 25% of hands will all be +EV but below that they will be -EV so we should fold.

I think the mistake you are making is thinking about equity of our range against V's - we need to be thinking about individual hands

When you shove you can win by making everyone fold or having the best hand at showdown. When you call your only option is to have the best hand at showdown.

Also, because the value of the chips is non linear in tournaments (first place gets 100% of the chips but only wins like ~15% of the prize pool) the survival aspect is very important in MTT's to a point where a chip added to your stack has less value than a chip lost from it.

All in all you always need a better hand to call than to shove.

As mentioned earlier in the thread you would call with any hand that wins you chips overall (excluding icm type, life type issues).
If it is Cc chips to call and the final pot (including call) is FPc chips

Hand Equity needed = HE = Cc/FPc

Op, I don't think there is an easy way to calculate a Nash calling range, you have to put in a fair bit of work with icm tools so you develop a 'feel' for a reasonable range.

In HU play there is a system that can help you get a close approx to Nash using the system called Sage (searching Sage poker will show some info). Unfortunately this is set for SB vs BB and will not be close for a Co vs BB push, even worse for earlier position shoves.

You could make your own adjustments to it to try to cope with the stronger ranges seen from earlier positions, perhaps using the ranges for a hand 1 or 2 bb deeper than is actually present. eg if 6 deep use 8 deep if push was from CO.

Personally I think just doing plenty of work with hand histories reviews using icm tools is better but this may be a short cut to knowledge.

Here is an example of Sage (remember it is for sb vs bb)

After paying blind you are in BB with 5bb holding A2s
Sage says you need a score of 28 to call, and you have a score of 2*15 (as A=15 in Sage) 2 (for the lower rank 2) + 2 for being suited. Sage score is 32, so this is a call.

If you had J4s the score is 2*11 (J=11), + 4, + 2 for suited, Sage score of 28, the exact score need or break even.

This is about right for Nash of 6bb vs 6bb and SB vs BB but it took a bit of work and as I mentioned doesn't take position (and antes if present) into account.

You could try to develop your own extension to Sage to get approximately right and in doing so might be able to develop a good feel for calls in the process. Even if you get good a Nash calling ranges don't forget you also have to adjust to player types or reads.