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We have to call 51629 into a main pot of 79451 and a side pot of 60744. I put the BB on 99+, AK, AQs, and the Button on 55+, ATs+, KTs+, QTs+, JTs, T9s, AJo+, KQo. These ranges might be even be too tight. Good players are more likely to make a move if they haven't made one in awhile (which you said the Button hadn't).
equity win tie pots won pots tied
Hand 0: 45.946% 36.06% 09.88% 103746768 28425114.00 { AKs }
Hand 1: 54.054% 44.17% 09.88% 127070076 28425114.00 { 99+, AQs+, AKo }
Side pot equity: 27909
equity win tie pots won pots tied
Hand 0: 33.036% 27.36% 05.68% 6637931952 1377296978.00 { AKs }
Hand 1: 27.341% 25.75% 01.59% 6247338024 386245694.00 { 55+, ATs+, KTs+, QTs+, JTs, T9s, AJo+, KQo }
Hand 2: 39.623% 34.77% 04.86% 8434911456 1178621696.00 { 99+, AQs+, AKo }
Main pot equity: 26247
Total: 54K
I also disagree with the philosophy that "either option is OK" in spots like this. That's true in small pots in the early levels but I strongly believe that in push-or-fold situations there's always a right play and a wrong play. If a call is +EV by nearly 2 BB (or more) then folding is flat out bad IMO.
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