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Say someone goes all-in on you and you know what they have, so you know what your chance of improving to win the hand is. You have 9 outs once, let's say, so about an 18% chance to win (roundest of numbers). When should you call?
This appears to be the correct way to do the calculation:
Let Y = the pot size after your opponent's all-in
Let X = how much you would have to put in to call
(Note: this assumes you have the opponent covered. If you have less $ than the opponent does, then Y should be adjusted downward to reflect how much of the pot you will actually be calling!)
Here's the math:
X / (X+Y) = minimum percentage chance to win you should have in order to call.
This is important: the calculation is NOT just X / Y! (I thought it was X/Y. Wrong wrong wrong. Silly Kent. If you use X/Y, you will call much less often than you should.)
Say X = $100 and Y = $200. X / (X+Y) = 100 / 300 = 33%. You need at least a 33% chance of winning to call. Say 17 outs once or 9 outs twice.
Say X = $100 and Y = $250. X / (X+Y) = 100/350 = 28.6%. Say 14 outs once or 8 outs twice.
Say X = $100 and Y = $450. X / (X+Y) = 100 / 550 = 18.2%. Say 9 outs once or 5 outs twice.
Specific example.
Let's say you have flopped a set and are sure your opponent has flopped a straight. Your opponent is all-in and it's heads-up. What odds do you need to call?
You have 7 outs to make your full house on the turn and 10 outs on the river. (Always always always in this situation!). So a total of 17 outs, or about a 34% chance to win. (Confirmed via the poker calculator at twodimes.net: it's actually a 34.44% chance to win.)
If Y is double X, or more, then you have the odds. (If Y=2X, then X / (X+Y) = X / 3X = 33%.
So if it's $100 to call into a $200 pot, call. (Barely.)
$100 to call a $300 pot (or $67 into a $200 pot), definite call.
$100 into a $150 pot (or $133 into a $200 pot), fold.
$100 into a $190 pot, just barely fold by the math, but call in case he's bluffing.
Specific example #2.
It is the turn and you have only a flush draw against your opponent's made hand. Your opponent is all-in. When should you call?
9 outs once = about an 18% chance to win the hand. Make it 17% to be safe -- your opponent may have a set or two pair and 1-2 of your flush cards may give him a full house. (If your opponent has a set, you have only a 16% chance to win.)
If you have to call $100 into a $200 pot -- that would require a 33% chance of winning - FOLD!
If you have to call $100 into a $300 pot -- requires a 25% chance of winning -- FOLD!
If you have to call $100 into a $400 pot -- requires a 20% chance of winning -- FOLD!
If you have to call $100 into a $500 pot -- that's finally down to a required 16.7% chance of winning and you can BARELY make the call.
So if the opponent is all-in, the pot size has to be 5 times your required bet size in order to make it right to call with a flush draw only.
Just another way of saying that people chase their flushes way too much in this game.
If these numbers aren't intuitively obvious, I highly recommend running the numbers a whole bunch of times until you can do it in your sleep. I know I have a lot of work to do on this myself. It's hard enough to put an opponent on a hand in the time you have to make a decision online -- it's even tougher if once you've done that, you can't do the math fast enough!
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Not only do I lecture you, but then I also give you homework when I'm done.
