Bill,
A royal is usually called sequential if it is left to right or right to
left. That is why it is divided by 8.
=PERMUT(52,5)/8
···
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You're off by about a factor of 2. A dealt sequential royal has a
probability of .00000000012826, which if you invert it comes out to
be 1 in 77,968,800. I would guess this is a once in a lifetime event
for most VP players.
This is how you get the probability (you can use MS Excel to do this
easily).
There are 2,598,960 possible 5 card starting hands in a 52 card deck
[combin(52,5) in Excel] where order doesn't matter, i.e.,
combinations. Only 4 of these are RF. So, the probability of a RF
on the deal is 4/2,598,960 (or 1 out of 649,740).
For a sequential RF, order does matter. There are 120 different ways
to order 5 cards [permut(5,5) in Excel]. Only 1 of these ways will
be the T-A sequential RF. So, the probability of a T-A sequential RF
is 1/120.
To get the probability of a dealt, sequential T-A RF you just
multiply the two probabilities which is 4/311,875,200 or 1/77,968,800.
Combinations versus permutations can sometimes be confusing. Just
remember that order doesn't matter in combinations (which is the case
in VP) and order does matter in permutations.
Hope this helps.
Bill
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