Dale, would you accept an exact value of 0.988438106?
For those who would like to be able to do this calculation on their
own, I believe the appropriate Excel method is with the Binom
function as follows: 1-BINOMDIST(F25,G25,H25,TRUE) where F25 = the
number of royals, G25 = the number of hands and H25= the prob of
getting a royal in one hand. The "True" variable says you want the
number of royals to be treated as a minimum number rather than
absolute. In other words, true= 11 or more royals and false = exactly
11, no more no less.
Now, what they are saying is with the odds of getting 11 or more at
about 98.84%, the odds of getting only 10 or fewer is 1.16%, and in
VP 1% odds come through all the time (that's the odds of getting a
full house).
But, of course, he didn't say he got 11 royals. He said he got 6. I
suppose Dan was looking at a chart rather than doing the calculation
himself and the chart didn't list the value for 6. But if you
calculate it out, 6 is much less believeable than 10: the prob is
0.99965903. That means, if he really played over a million hands, the
odds of getting 6 or fewer royals is only 0.03% or approximately 1 in
2931. Now, that's still possible because even long odds come through
once in a while, but that's a lot harder to believe.
That is part of why I believe the number of hands must be overstated
at one million, because the odds of getting less than 7 royals in a
million hands is 2930-to-1 against, while in 500,000 hands the odds
of fewer than 7 are only 4.4-to-1 against (those with excel, run that
same formula with 500K hands, then 600K, then 700K, etc), a much more
reasonable proposition. A million is certainly possible, but
something less is far more likely.
···
--- In vpFREE@yahoogroups.com, "rosspark100" <rosspark100@h...> wrote:
The normal approximation gives the following:
expected number of royal = 1019200/48048= 21.2121
the approx probability of 11 or more royals is .989989547
Dale Borowiak