--- In vpFREE@yahoogroups.
>
> I see that 19,933,230,517,
> total possibilities.
>
> I see that it is done as comb(52,5)*47*
>
> What I do not understand is HOW is that formula derived.
>
> I started college as a Math major (switch to computer science), so
I am
> familiar with statistics and such, but cannot figure out how that
is
> derived.
>
> Thanks
>
> Jim
>
It represents a weighting factor being applied to each outcome for
the best way to play each hand, so that the probability of any
final hand being formed after the draw can be determined by dividing
by the same number.
First you need to determine the least common multiple of the number
of ways to draw replacement cards for each way to play. The least
comon multiple of 1, 47, 1081, 16215, 178365 and 1533939 is 7669695.
The number of outcomes for the best way to play a hand is multiplied
by the appropriate weighting factor to make its total number of
combinations equal 7669695. For example, if the best play is to draw
one card there are 47 results, so the number of combinations of each
resulting hand needs to be multiplied by 163,185 to make the grand
total equal 7669695.
Thus, the final number of combinations for the entire game becomes
2,598,960 * 7,669,695 = 19,933,230,517,
Using these weighted totals it is then possible to calculate the
probability, cycle/frequency, return, and variance.
Different deck sizes have different LCMs and therefore different
weighting factors.
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