We are playing heads-up Texas hold 'em poker. I want to find a situation where my hand is currently weaker than my opponent's (in the sense of hand rank if no more cards were to be drawn), but has the highest possible expectation of being the strongest hand after the river.
The set-up and constraints:
- There are two players, so no cards have been folded. Ignore any cards that may be burned during the flop, turn, or river.
- Player A has the highest ranked hand (not in expectation but in absolute rank at the moment).
- The situation may be at any point in the game - from pre-flop to pre-river.
The goal: Choose the situation (namely the hands of Players A and B and any community cards) so as to maximize the expectation that Player B has the strongest hand post-river.
I have played around with this and have a candidate answer where the expectation of Player B is slightly above 64%. I would welcome the results of a brute force calculation, a better example, or a better example with proof of optimality (I suspect a proof will be tedious...).
Played around at https://www.cardplayer.com/poker-tools/odds-calculator/texas-holdem a bit.
Pre-flop: The best cards against a pair of twos is not A-K same suit, but rather something more intermediate to allow more straights. The best I can find is J-10 same suit (and different suit from the twos). This has a win chance of $53.28\%$ and tie chance of $1.41\%$.
Post-flop: The best I can find is also somewhat obvious: a four card straight flush with both ends open. E.g. C2,D2 vs HK,HQ with the flop being HJ,H10,S6. This has a win chance of $72.32\%$ (and no chance of tying).