a razz odds question

[RustyBrooks]

Of course I factored them into the equation. If you have a 57% chance of drawing 2 3 4 5 6 7, then you have a 43% chance of catching all the other cards (A 8 9 T J K Q). I'm just interested in the cases where you catch good and he catches bad. There are 4 branches to this probability tree and we're only interested in how often 1 particular branch happens.

And yeah, technically if he catches a T and you catch a 9 your hand looks better. But I don't know how often he'll fold there and you want him to, because his hand IS better.

But this is kind of balanced out by the fact that there are a couple cards each of you can catch that look good but aren't. If you want really comprehensive results, you'd probably need to enumerate all the cases and consider how often you'd get cases you like. The math I did above is kind of shorthand... like you're not going to be sad at all if you get a 9 and he gets a K even though he's still ahead, because he might fold.

The cases are enumerable but I don't think you'd want to do it by hand. There are 160-ish distinct 3rd streets (that's kind of just a ballpark guess, actually probably a bit fewer)

And yeah of course I am not factoring in known up cards. These can considerably sway the decision one way or the other.