Lookie here:

http://www.foldorraise.com/outscalculator.php

I used to pretty much calculate my odds like this: 9 outs, 2% per out, 18% + 1% for the 0.1%s so 19% for each draw left(turn + river / 19% + 19% = 38%). But according to the link above, its 19% for the turn, 20% for the river (which I understand - because there is 1 less card in the deck, right?), but the chance of hitting either is 35%. The higher up you go, the less accurate the turn + river method is. For example, with 22 outs, 47% on the turn, 48% on the river, the chance of hitting either is only 72%.

After thinking about it a minute I realized why. If you flipped a coin, you would have a 50% chance of hitting or "drawing" a heads, and in two flips a 75% chance (because you can't have a 100% chance even after a million flips, just a 99.999999999999999% chance). Or if you had a 33% chance of hitting/flipping/drawing/rolling SOMETHING, you would have a 1 in 3 chance of hitting it. If you missed, probability just used up 33% of a 100%, so you have 67% left...33% of 67% is ABOUT 22% ... 33% + 22% is 55%. A 55% chance of hitting/flipping/drawing/rolling SOMETHING in two 33% hits/flips/draws/rolls. The best example is the flush draw. You have 9 outs, so 18% on the turn, 19% on the river. 100% - 19% = 81%, 19% of 81% is 16%...19% + 16% is 35%.

This math is hard to do everytime you are on the spot, my question is, is there a simpler formula (besides memorizing every % of every out, on the turn, the river, and the turn AND river?)?

http://www.pokerforums.org/probabilities explains it

There was a thread here about this and there seems to be 2 schools of thoughts outs x 4 for the turn, then outs x 2 for the river. Or basically just outs x 2 post flop.

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Actually, you're not really adding chances to hit your outs. You're multiplying your chances to miss hitting your outs.

19% chance on the turn = 81% chance to miss on the turn

20% chance on the river = 80% chance to miss on the river

81% x 80% = 65% chance to miss on both turn and river

Subtract that from 100%, and there's your 35% chance of hitting on either fourth or fifth street.

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outs x 4 is ONLY for when you will either be facing no more bets on the turn or when you ca n accurately calculate your implied odds for the turn.

So for like 99% of the time in LImit, and 95%(?) of the time in NL, you should use Outs x 2% + 2%.

I did a little math a while ago, and if you have 5 or less outs, you should use Outs x 2%, for 6 or more, use Outs x 2% + 2%. And if you are going to see 2 cards, then for 10 or less outs, use Outs x 4%, for 11 or more, use Outs x 4% - 4%. I worked out all the numbers and this system is the most accurate.

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