Turn is the key
Hi Killah...
I think the turn play is the key in this hand. When he is raising You, he says "Im not afraid of You having a 6". That means either a) He has a 6, with a good kicker. Most likely K-6 or A-6. Likely, given his preflop limp. b) He has 7-6 (likely) or 2-6 (probably dumped pf). c) He has 77 or 22. Can be, but the combinations are fewer. d) He has played AA or KK in a peculiar way (he should then fold for your re-raise). I think, with hands like 8-8 to J-J, he just calls on the turn.
The river does the combinations of sixes less likely. After this i would say K-6, A-6, 7-6, 7-7 and 2-2 have 18 pts each, and other hands 10 pts (like AA or trash). I dont think he is folding any other hand than 2-2 here, so you will be called 72 pts of the time - plus maybe 5 pts of the remaining 10. Since you are risking less than a 2-oddser, you need to be called less than 50 pts of the time.
The push is therefore wrong, given my prespumptions.
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