I think these numbers are too high. I posted a response to vkotlyar's similar post in the mid-high stakes section:
link to other post...
if you hold T[img]/forums/images/icons/spade.gif[/img]J[img]/forums/images/icons/spade.gif[/img], there are 11 [img]/forums/images/icons/spade.gif[/img]s left.
the number of flops that contain two of them are:
number of two card [img]/forums/images/icons/spade.gif[/img] combos = (11 choose 2) = 110
*TIMES*
the number of non-[img]/forums/images/icons/spade.gif[/img] cards remaining = 39
= 4290 ways to flop a four-flush.
there are (50 choose 3) possible boards, given whatever hand you have = 117600
which means you flop a four-flush 3.64% of the time.
I see now that I made a small error in my other post, in that there are more 8-out straight draws than I gave credit for...
ways to flop an 8-out straight:
true "open-enders": 89x, Q9x, KQx, where x doesn't complete the straight.
there are 4 * 4 * 40 of each of these (4 8's, 4 9's, and 40 remaining cards that don't complete the straight)
double-gut shots: 79K, 8QA
there are 4 * 4 * 4 of each of these
so:
3 * (4 * 4 * 40) + 2 * (4 * 4 * 4) = 1920 + 128 = 2048
dividing by the number of flops: 2048 / 117600 = 1.74%
also -- you can't just add these up to get
3.64% + 1.74% = 5.38%, because many of the hands are being "double-counted" (i.e., we have counted 8[img]/forums/images/icons/spade.gif[/img]9[img]/forums/images/icons/spade.gif[/img]2[img]/forums/images/icons/diamond.gif[/img] as both a flush draw and a straight draw). The real number works out to more like 5.10%
I'm pretty sure my math is solid here, but I'd love to hear about it if there are disagreements -- Cyrus, where did you get your numbers?
-switters