ok, i posted this hand in hopes that someone would give me some in-depth reasoning as to why or why not this would be an ok spot to shove with atc. I feel i was short with my op and in return received short answers. So, im reposting and will delve into my (incomplete) thought process. Maybe i have a fundamental misunderstanding somewhere. Hopefully you can help me fill in the gaps and/or correct my reasoning so the next time im in a similar situation i will be prepared.

Im live in a large field re-entry on day 2. the re-entry period has long passed. we're not in itm yet; the bubble is probably an hour or so off.

blinds: 3k,6k, 500

average: 170k?

table is snug. im utg with roughly 32k. is this a shove with atc?
my hand was 56o.

my thoughts:
if i shove and get folds im risking 32k to win 14k or 32k to win 46k when called. lets say im going to get called by the top 15% of hands- i think this is more than generous considering how snug my table is playing. so im roughly a 70:30 dog when called.

14000x + 46000*.30 (1-x)- 32000*.70 (1-x)=0
-or-
14000x + (1-x) (-8600)= 0
x=.38

so if the table folds anymore than 38% its +ev. yes?

now, to my understanding, **when shoving into 1 random hand we have a 15% chance of being called while opponents range is the top 15%.** so obv this would be a no brainer. But what i do not understand is how to calculate the odds of being called when more than one opponent is behind. The % of calls must increase along with the number of players left to act even if their calling ranges remain the same. This is why our shoving range changes along with our position. If the % of calls remained the same with any number of opponents behind us then the shove would be unexploitable regardless of calling ranges.

I would like to know the math behind this. I just cant seam to wrap my head around it. How does the % of calls change with the number of players if theyre all calling the same %? What is the formula to calculate this?


The **asterisks** above denote my uncertainty. If this is incorrect it could be throwing off my whole line of thought. Is this correct? If not, what is the correct way to calculate?

Just as an aside, i would also like to point out that calling ranges are generally going to be tighter in early position than they are in late position. So to be very accurate we would have to use some type of sliding scale. Maybe starting at around 5% for ep and working our way up to 20% in lp. I'm curious to see a formula for this calculation as well.

thanks 2p2