texas shootout: A beatable game??

[AaronBrown]

If someone wants to do the math, I suggest starting out by assuming infinite decks and ignoring straights and flushes. You can add those refinements later. The dealer can either have a pair or not. If he does, you have have a higher pair, the same pair, a lower pair, two unpaired cards higher than him, one card higher than his and one equal, one card higher and one lower, one equal and one lower or two unpaired lower. If he has two unpaired cards you can have two higher than his highest, one higher than his highest and one higher than his lowest, one higher than his highest and one lower than his lowest, two between his two cards, one between his two cards and one lower than his lowest, or two lower than his lowest.

Given a strategy for picking your two cards, it's easy to figure out the probability of each of these things happening, and what your average odds of winning are in each case. That should allow you to pick an optimal strategy for this reduced game.

Next, I'd adjust that strategy by favoring suited hands and connectors, and set the weights for that by simulation. If I couldn't get close to even this way, I would give up. If I could, I would start working on counting algorithms and do a more exhaustive strategy search.