eecounter wrote:
Other 50 play whiff hands that you'll see (perhaps someone can
calculate the probability of these)
Dealt 2 pair - no full houses.
(1) There are 4 cards that give you a FH, 43 don't.
(43/47)^50 ~ 1.2%
Dealt trips - no quads.
(2) There are 46 ways to pick the first card, 45 for the second.
[(46/47) X (45/46)]^50 ~ 11.4%
Dealt trips - no quads and no full houses!
(3) P(getting a quad) = 46/C(47, 2) ~ 4.3%.
P(getting a FH) = [10 X C(4, 2) + 2 X C(3, 2)]/C(47, 2) ~ 6.1%.
(There are 10 denominations that have 4 suits remaining and 2
denominations that have 3 suits remaining.)
4.3% + 6.1% = 10.4%, so the probability of NOT getting a quad or FH
is about 89.6%^50, or (.896...)^50 ~ 0.4%.
4 to a wild royal (deuces wild) - no wild royals.
(4) There are 5 cards that give you a WRF, 42 don't.
(42/47)^50 ~ 0.4%
···
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To all: I would be interested in seeing any alternative approaches
to these, or corrections if that is the case. Please reply here or
privately. Thanks,
Jeff