[switters]

oops. the math from the previous posts was off - in most cases by a factor of three. The process I used was sound, but I was miscomputing the choose function throughout.

apologies for the confusion -- I knew I shouldn't have rushed through that post without a good calculator so many years since my last probability class... [img]/forums/images/icons/frown.gif[/img]


anyways -- here are the important numbers, FIXED:

number of flops containing precisely two [img]/forums/images/icons/heart.gif[/img]s:
(11 choose 2) * 39 = (11 * 10 / 2) * 39 = 2145

number of possible flops:
(50 choose 3) = (50 * 49 * 48 / 6) = 19600

percent of flops containing precisely two [img]/forums/images/icons/heart.gif[/img]s if you hold two [img]/forums/images/icons/heart.gif[/img]s :
2145 / 19600 = 10.94%

number of flops containing AT LEAST two [img]/forums/images/icons/heart.gif[/img]s:
(11 choose 2) * 39 = (11 * 10 / 2) * 48 = 2640

the percent of flops containing AT LEAST two [img]/forums/images/icons/heart.gif[/img]s if you hold two [img]/forums/images/icons/heart.gif[/img]s (this counts the times you flop a flush)
2640 / 19600 = 13.47%

number of open-ender flops:
3 ( 4 * 4 * 40) + 2 (4 * 4 * 4) = 2048

percentage of open-ender flops:
2048 / 19600 = 10.45%

percentage of flopped straights (four ways, 789, 89Q, 9QK, QKA):
(4 ( 4 * 4 * 4 ) = 256) / 19600 = 1.31%

now, we can't just sum up the percentages of flopped 4 flushes and flopped 4 straights, because there is overlap between those possibilities...

percent of time you will flop precisely a four-flush or four-straight:
[ 2145 + 2048 - (3 * (33 + 24 + 24)) ] / 19600 =
[ 2145 + 2048 - 243 ] / 19600 = 3950/19600 = 20.15%

percent of time you will flop AT LEAST a four-flush or four straight (inludes flopping straights and flushes, but doesn't count flopping trips, boats, or quads, for example):
[ 2640 + 2048 + 256 - 264 - 4 - 12) ] / 19600 = 4664/19600 = 23.80%

-switters