Probability Question (what were my odds of winning?)?

Question

Hi I have a probability question. And it can be related to Poker (cause thats what I need it for =). My question is ...

I have 1100 chips and my opponent has 1900 chips. We are all-in and my odds of winning the pot (doubling up) was 81%. I win.

In the same game, my opponent has 750 chips left and I have 2250 chips. We are all-in again and I am 67% to take the rest of his chips. BUT instead, HE wins and doubles up thereby we now have 1500 chips each.

We go all-in again and I am 61% to win and I do and I win the tournament. The question is ... WHAT WERE MY OVERALL ODDS OF WINNING THAT GAME? I was 81% to double up then I was 67% to win the game (but lost), then I was 61% to win the game (and won).

What is the equation you use to figure this out?? Would there be any variation if the stack sizes above were different? (Supposing I had 1400 chips on the last all-in and won and he was left with 200 chips, how would that affect the outcome?).

Thanks so much for info !!!!!

Answer 1

Well if you assume that these were the only 3 hands of consequence...(not that great of an assumption), then you can determine your overall chance of winning given the preflop all-in matchups.

#1
you are 81% to double up and continue
you are 19% to lose

#2 of the 81% of the time you make it to this point:
you are 67% to win
you are 33% to continue the match

#3 of the 81%*33% of the time you make it to this point:
you are 61% to win
you are 39% to lose

So your overall probability of winning if these were the only 3 hands that mattered:

(.81)(.67) + (.81)(.33)(.61) = 0.706

You were 70.6% to win overall.

For the last part of your question, if he had a small amount of chips remaining, it would obviously reduce your chances because he still has a chance to make a miracle comeback, but it wouldnt change the numbers a lot if he only had less than 10% of the total chips in play.

Answer 2

Has nothing to do with chips and every thing to do with the cards. (when related to poker) What were you holding? what was the flop?... turn ?... river? percentage to win fluctuates throughout hands if you play you should know this already...