I want to know how to work out the probability that someone left to act has cards in their calling range when there are multiple people left to act. Say you're shoving from UTG, theres 8 people left to act and for simplicitys sake say everyones calling range is 10%.

I thought that you could just do 10% x 8 but 80% seems like way too high a probability that someone left to act has a hand in the top 10% since thats A10+, 88+. Also if their calling ranges were higher say 15% then the probability would be over 100% which is clearly wrong.

So how do you figure out % of times you're getting called if everyone is calling with a range of 10%?

I'm interested so I can calculate what my fold equity is from various posistions if I can get a good estimate of the ranges of the villians left to act. I think I'm missing something really simple here.

You asked this question earlier, here:

http://forumserver.twoplustwo.com/sh...postcount=8033

and zumby answered it for you afaics.

Working is in the dumb questions thread but the simple bit you're missing is that you need to multiply the probabilities by themselves not by the number of players.

So for 3 players it's not "probability multiplied by 3 players" but "probability multiplied by probability multiplied by probability"

Hopefully Statmanhal or someone will swing by and confirm the equation

If Zumby's formular is correct, then
1 - Pr(villainFolds)^NumberOfVillains
= 1 - 0.9^8
= 1 - 0.43
= 57%

This approach is okay as a first order approximation. The problem with it is that it is based on the assumption that all the folds are independent, which is not likely.

For example, if UTG opens and 5 players fold, then it is more likely than 10% that the button will call -- that is, he expands his 10% calling range. If he also folds, then despite the positional disadvantage one or the other blind may call at a higher calling range because of the reduced investment.

So, the general formula P(all fold) = 1 - (100-C%)^n for n players each with calling range C% should be considered as a upper bound IMO -- that is, it is somewhat optimistic.