$27... another hand in push fold mode... AQ

[ZeroPointMachine]

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Here is my thinking process and tell me where i am wrong

Only 2 players have been eliminated so far... Last few hands have been allin and everyone folds...

If there are 4 hands in a row where it is push/fold then we know with the 100/200blinds we are getting to that stage with 7 still in. I need to find a hand soon and I may not see a better one than this for a while.

I only have 1200 chips left and after the next few hands will only have 900 left so i need to look for a chance to double up.

I put him on a range of any pair, Any ace with 9+ kicker, KQ and maybe KJ.

that makes me a conflip agisnt 10 hand
A big dog to 3 pairs
A dog to Ak
A fav to 5 other hands.

I think this makes it a true coinflip decision.

Now if i had thought about it like this before I made the call i would have folded... interesting... I figured I looked good.

I just need about 3 minutes to make decissions and i could make the right one.

I call, he shows 44 and it holds up

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You are thinking along the right lines, but this analysis is flawed. You can't just pick a range of hands and assume they are all equally likely. Unpaired hands can be made more wys than paired hands. Your cards also change the number of possible ways he can make each hand.

In this hand he is less likely to have AA or QQ than 66. Because you hold one of the aces.

AK can be made 16 ways and a pair can only be made 6 ways. When you hold an Ace then AK(or Ax) can only be made 12 ways, but it is still twice as likely as JJ.

Can you see how this reduces the chance that you are dominated and increases the chance that you are dominating him.