[mmbt0ne]

Sigh...that's what I was afraid of. [img]/images/graemlins/tongue.gif[/img]

Ok, here we go. First, I counted up the possible combinations of card that villian could have based on what we already know is out. Then, you can discount if you think he would've played something a different way. I'm assuming he could equally be slowplaying a flopped hand or have improved on the turn. This is probably wrong, but its still a good approximation. I knocked JJ down from 1 to 0.5 because I figure he'll raise it preflop from time to time. Similarly, we could discount TT, but a lot of people don't raise that from the blinds.

Now, we count the outs we have against every possible holding. Here's from the document file I was working with:

JJ - 0.5 (discounted) 4
TT - 3 4
99 - 3 4
33 - 3 4
J3 - 6 13
T3 - 9 12
J9 - 6 10
JT - 9 7
T9 - 9 12
(no 93, I can't see him with that)
87 - 16 4
Q8 - 16 3
QK - 12 1.5

total hands: 92.5

The second number is how many outs we have to improve to a winning hand. KQ I give 1.5 outs because when we hit one of the 3 remaining Qs we split the pot.

Now, here is how you get the outs number:

(hand combinations/total hand combinations) x (outs)

So, for 33 it would be:

(3 combinations/92.5 total combinations) x (4 outs) = 0.1297 outs.

Do that for every combination and add them together to get your total outs. That's called a weighted EV calculation. Of course, you can't do these at the table, but when you do enough of them away from the table, and practice putting your opponent on a range of hands you slowly become better and better at approximating your outs. For instance, now I know that if I have top pair with an over-kicker and a gutshot, and I get raised by someone with a made hand, I need a little better than 6:1 to call. I'm not going to commit that to memory, but I'm going to remember when it comes up that I shouldn't be folding in, say, a 7 or 8 BB pot.