Flush draw odds
 

How come the odds of hitting your flush card on the river are 19%, but the odds for the same draw with both the turn and river remaining are only 30%? I thought it basically doubled, as one of the quick ways to determine approximate odds is to multiply your outs by 4 and then add 2 after the flop and multiply by 2 and then add 1 after the turn. Most of the time this seems to work out almost exactly to what the %'s are shown to be on television, but the flush draw odds don't seem to follow the same pattern. Please explain.

Re: Flush draw odds
 

It's 35% and 20%...

Re: Flush draw odds
 

On the river there are 46 unknown cards, 9 of which make a flush for you. Same 9 on the turn but 47 cards.

So, 19% of the time you make your flush on the turn, and 81% you don't. Of that 81%, 19% of the time you make your flush, for a total of 15.5%.

15.5% + 19.2% = 34.7%

In logic terms, it's an XOR instead of an OR. You frequently don't want to get your flush on the turn and then river another card of the same suit. If I have JT [img]/images/graemlins/diamond.gif[/img], I don't want that 4th diamond out there for anyone with Q, K or A to beat me. And the problem's even bigger for middle suited connectors.

Re: Flush draw odds
 

The simplest answer for whay it doesn't double for both is that by doubling the odds you're double counting the times *both* turn and river cards make your flush.

Re: Flush draw odds
 

Thanks guys. I love this site!