On Mon, Jan 3, 2011 at 9:02 AM, Vegasvpplayer <vegasvpplayer@gmail.com> wrote:
> I've been trying to come with an average number of hands on 9/6 JoB or 8/5 BP to complete a Bingo card. The five hardest spots to fill are a royal flush and a straight flush in all 4 suits. I know the cycle for a RF is about 40k and a SF is about 10k. In the 40k royal cycle you will have an average of 4 SF's but probably not one in each of the 4 suits. My gut feeling is the normal cycle for all 4 suites of SF will be somewhere around 80k to 100k hands. Am I close?
yes, you're close.
obviously it'll take an average of one SF cycle to hit your first SF.
after you've hit your first, 1/4 of your SFs are going to be in the
same suit as the first one. so it'll take on average 1/(1-1/4) = 4/3
SF cycles to hit a second one in a new suit.
after you've hit two, 1/2 of your SFs are going to be in a suit you've
already hit, so it'll take on average 2 SF cycles to hit a third one
in a new suit.
after you've hit three, 3/4 of your SFs are going to be in a suit
you've already hit, so it'll take on average 4 SF cycles to complete
the set.
so, to get all four SFs, it'll take 1 + 4/3 + 2 + 4 ~= 8.33 SF cycles,
or about 75000 hands on average.
as for the average number of hands to fill out a card... you can use
your intuition and figure you'll probably but not certainly have the
royal within 75000 hands, and the quads certainly won't hold you up,
and bump it up to 85000 or so. or you can pull out your poisson
distributions and numerical integration and come up with a figure
of... 85000 or so. either way.
the promo stopped being interesting when they added the specific-suit
straight flushes. it was pretty monstrous on multiline quarters for
the first week.
cheers,
five
