Lurking in the 2+2 forum archives I found this post I made more than a year ago. Hope you like it and provide some comments about it:
Stack size and calling an all in when reraised (essay). 05/31/05 01:38 AM
This is a usual question in this forum. What is the size of your stack such that you're in desperate mode, or basically commited to call all in when somebody reraise you.
Lets suppose the size of your stack is S = 12x, x = big blind; and you decide to open raise in MP to 4x, and somebody reraise you to 12x, should you call?
The analysis is pretty simple. You need to call 8x for a 18x (12x + 4x and lets suppose there are 2x in the pot to begin with, this varies from 0.5x to 2.5x). So you have odds of 8 to 18 or 1 to 2.25. So basically your hand needs to be 100/(1+2.25) = 30% or better against your opponent range. These are pretty good odds, even with a hand like KJo you're 34% against a range of AA-55, AK-AT, KQ. Even with a AA-88, AK-AQ range, you're 32%, so you need to call.
Now, lets suppose S = 24x, same scenario and you're reraised all in or close to it in practice, like somebody reraised to 20x, you know you're going all in anyway. Now you need to call 20x for a 30x pot, giving you odds of 1:1.5 , now your hand needs to be 100/2.5 = 40% or better; against AA-88,AK-AQ you can not call with KJo, what about AJs? Nope, just 35%. Even AQo is 36.5%, you need better than AQs (39.8%) in this spot vs such range.
Now, lets do the analysis in general for this situation, your stack = S, if you raise to 4x and need to call all in, you need to call S-4 to win a S+6 pot. Then your odds are 1 to (S+6)/(S-4) doing some elementary math, this is 1 + 10/(S-4). With this fraction is easy to see that if you want 1:2 odds, then S=14. Then basically, anytime you're behind the 14x mark, you need to choose a hand to go all in that is just better than 33%.
We can even generalize this result. Instead of raising to 4x, lets suppose you raise to Mx and reraised all in. Now you need to call S - M for a S + M + 2 pot; then your odds are 1 to
(S+M+2)/(S-M) = (S-M+2M+2)/(S-M) = 1 + (2M+2)/(S-M)
Now if you want to get 1:2 odds then (2M+2)/(S-M) = 1
this is 2M+2 = S-M this is M = (S-2)/3 !!! ... (sirio's raising factor )
Then you can manipulate the odds you're getting with your raise (how nice is that!!), if S = 14 then M = 4 is optimal to get 1:2 ; and if your stack = 17x, then M = 5 is the optimal raise to get 1:2 odds.