IS THIS % RIGHT WHEN DEALING W/ OUTS ?

[Acepimp05]

I had a guy at the poker table tell me every out is 2.1 % and i figued a flush draw 9 outs is 18% which is 36% to complete by river.So is this right that infact everyout is 2.1 % ?

[AaronBrown]

It's not a bad rule. When you see the flop you see five cards, so there are 47 unknowns, hitting one is 1/47 = 2.13%. After the turn there are 46 unknowns, hitting one is 1/46 = 2.17%.

You have to be careful, however, because you often know something about the distribution of the cards in your opponents' hands (including the ones who folded).

[John Bedtelyon]

"To complete by river"

You get two chances at approximately 18% to grab that fifth flush card.

Don't forget, on the flop there are two cards to come.

JMB

[AaronBrown]

That's a good point, I should have mentioned that. The 2.1% is per card dealt. With a small number of outs it's approximately correct to add them, so if there are two more cards to be dealt you have about a 4.2% of hitting one out. But with more outs you have to subtract the probability of hitting your out on both cards.

For example, with a nine outs to a flush after the flop, you might think you have 9 x 2 x 2.1% = 37.8% chance of hitting on one of the two cards. But the real chance is only 35.0%. 3.3% of the time you'll hit on both cards for a six card flush.

[Acepimp05]

So is 2.1% right? Yes i know a flush draw is 35 % so then is 2.1 wrong ? Or is there a better way to find out the exact precent?

[AaronBrown]

2.1% per out is good as long as there is only one card to draw. With two cards you can double it to 4.2% (4.3% would be a little better), unless you have a lot of outs in which case you have to subtract a little bit. 9 outs with two cards to go is not 37.8% but 35.0%.

[ajmargarine]

I have always multiplied my outs x two, and added one, giving me the percentage that I will hit my draw on the next card.

(9 outs x 2) + 1 = 19% to make on the next card. It's close enough to being exact that it works for me. If you add 2, instead of 1, when your outs get above 10, it's almost perfect.

[ChipWisperer]

In Harrington's Vol II (p. 201), he refers to a formula created by David Solomon from Boston which calulates winning chances from outs: multiply the outs by four, then subtract the excess of the outs above eight to get the winning percentage. For example, if you have 15 outs, the percentage is 53% = (15)(4)-(15-8). HOH Vol II is wonderful.