Download pokerstove to figure you equity against a range. In your examples I'm betting both and I'm VERY willing to get it in on either flop.
OK, I just downloaded pokerstove. That has got to be the coolest poker analysis program EVER. Wow! Thanks, I'll be using that one a lot.
OK, here's what it gave me:
With 9h Th Td on the board (the board that may have caused me a little concern), my equity was 53.815% and my opponent's was 46.185%.
With 2h 6h 9d on the board, my equity was 60.707% and my opponent's was 39.293%.
OK, but that's my opponent's range for getting to the flop. After the flop, let's say the board is 9h Th Td and it's my bet. If his range for calling tightens up to TT+,ATs,JTs then my equity drops to 43.553% and his increases to 56.447%. So against that particular opponent, right after the flop, a shove would be a bad idea, right? Because if he calls, he's the favorite.
To get my actual equity, wouldn't I need to factor in my fold equity as well? Let's say his range tightened up so much that he's only going to be in his range and call 5% of the time. Then 95% of the time, the pot is mine. So if my all-in is only a 5X pot bet, and I get the pot 95% of the time with him folding, it seems like all-in is a good move. (In fact, that sounds like my short stack game!) But if my all-in would be 100X the pot, then maybe not. Any ideas on this? And any ideas on working those numbers?
I'm thinking I would have to compute the probability of being dealt each of the
hands in his post-flop calling range and compare those to the probabilities of being dealt the hands in his pre-flop range. I'll give this some more thought (ugh, other duties call) but any additional thoughts would be appreciated.
Thanks again for all the help. I love trying to tie the various intuitions and theories to the math. Pokerstove is going to be a big help!