AA vs T9s

When AA and T9s get all in before the flop, AA wins 77.8% of the time and T9s takes 22.2%. Broken down, AA wins outright 77.6%, chops 0.3% and loses 22.0% — a margin of 55.6 points. Overpair against two undercards — about 80/20 for the pair.

The same matchup shifts depending on how the suits overlap. With no shared suit the number is 77.1% (for example As Ah against Td 9d); with one shared suit it is 78.4% (As Ah against Ts 9s). That is a spread of 1.32 points across the 24 distinct card combinations, and it comes almost entirely from whether the two hands are fighting over the same flush.

Add a third player holding a random hand and the split becomes AA 67.5%, T9s 20.5%, random 12.0%. AA gives up 10.3 points and T9s gives up 1.7, so the favourite loses more than the underdog does. Extra players always eat into the leader's share faster than into anyone else's.

Taken on their own, AA is worth 85.2% against a random hand (rank 1 of 169) and T9s is worth 54.0% (rank 65). The gap between them in the ranking is only 31.2 points, yet head to head the gap is 55.6 points — a reminder that a ranking table and a direct matchup are two different questions.

Framed as a run of one hundred identical all-ins, AA scoops roughly 78 pots, splits about one, and loses the remaining 22. Against eight random opponents rather than this one specific hand, AA would be down to 34.5% and T9s to 16.3%, so the shape of this particular confrontation matters far more than either hand's standing in the overall ranking.

From T9s's side, 22.2% is the break-even point for calling an all-in at 3.5:1 pot odds. Put another way, the call is profitable as long as the amount you have to put in is less than 22.2% of the pot you are playing for. AA holds the other 77.8% of that same pot.

Two caveats keep this figure honest. First, it is showdown equity across all 24 card combinations with five board cards still to come — there is no fold equity in it, so the value of shoving in practice is usually higher than the raw percentage suggests. Second, it assumes T9s really does hold exactly T9s; against the wider range a player would actually get all in with, AA's 77.8% moves. Use the individual pages for AA and T9s to see how each of them fares against all 168 other holdings before treating this single pairing as the whole picture.