In a RIO video I watched recently, Phil Galfond said he'd like to see some math on equities 3-way against AA** and another hand. As this situation occurs fairly often, and represents an interesting, albeit VERY risky opportunity to make money, I decided to do the math. I ran equity simulations on either a random hand, JJ77,TT76 or T987ds against AA and another hand.
Unless stated otherwise, the suits are randomly generated.
We are up against two AA** hands. This is our dream scenario: we are making money almost regardless of our hand!
AA: both 32,4%
AA: both 31,5%
JJ77 or TT76: 37%
AA: both 28.33%
The only hands we DON'T want here is a pair with uncoordinated side cards.
KK* has only 31,4%, QQ* has 32%,but QQJT has 35,7%
We are up against AA* and KK*. This situation is certainly much trickier; however, some money can still be made.
So the only EV-winning hand here is the premium rundown.
We are up against AA** and a double-suited hand:
This is the worst scenario. Only AA** makes money here - the other two hands are losers no matter what.