have i calculated the odds correctly?

the first thing i have to say is; i only learnt how to calculate the odds of me winning a particular hand yesterday. therefore i could be totally on the wrong track.

i was playing in a game last night with some friends. it was getting late and i hadn't had a hand all night. i was also small stacked and therefore thought i had to make an all-in move soon. i was on the bb, holding a 7s 3h. everyone else folded apart from one person who called. the flop was qs js 7d. i checked, she made a small bet. (i called this bet, because i was pretty confident she didn't have anything-she was chip leader and had been limping in all night) the next card was 5c. i called, she bet.

Now this is where i need help: believing she still had nothing i went all in on these grounds; i figured at best she had two spades and was hoping for a flush. if not i thought she only had a ace or king. Now i had a pair of sevens and beleived that was the best hand. therefore i worked out that she had 9 out cards for a flush, and six out cards for a ace or king pair. (is this right?)

secondly, i then deemed everyother card in the pack as being my out-cards. is this right? (as it would of won me the hand)

as it happens she had as 2s and was looking for a flush. (which she got on the river-and i lost!)

[AaronBrown]

I would read this hand differently, but I wasn't there and don't know the players. You've shown absolutely nothing, you had the big blind and checked. With a flush draw she would normally check, and you have to give her credit for something on the preflop call. A small raise is probing, do you have nothing and will fold, are you slowplaying and will raise, or do you have another so-so hand like you do and will call. I'm inclined to go all in at this point, and fold if I don't.

But given your read, your calculation is almost right. She only has 8 outs for a flush, since you have a spade in your hand. You shouldn't add the 8 plus the 6, because you think she either has an Ace, a King or a flush draw, not both. Even if she has an Ace and any card higher than 7 that's fewer outs than the flush. The worst case is two spades higher than 7, that's when she gets the 14 outs. The other worst case is Ace King or Ace Ten, where she can win with a straight as well, six cards to beat your pair and four more to make the straight. If she has both of these, Ace/King of spades, for example, there are three Aces, three Kings, four tens plus 7 spades other than the 10. That's 17, you still have the edge (plus the rare opportunity to lose all-in to a royal flush).

So as long as you're pretty confident she doesn't have the Queen or Jack or 7 or a pair of 5's; you figure to win. Plus an all-in bet might well induce a fold if has, say, King Jack or even Queen-x.