-=> Quoting Robert Fortune to Bob Sewell <=-
 RF> With video poker, statistically one can only expect to get a
 RF> Royal Flush once every 40,000 hands (assuming one is at least
 RF> a semi-skilled player, haphazard play can result in haphazard
 RF> results and of course lady luck is always an indiscriminate
 RF> factor). I don't think I played quite that many hands before I got
 RF> a Royal Flush (40,000 hands), but I may have.
Is a royal flush limited to only one suit or any of the four? In
any case I believe your probability is off just a little. Let's
assume only the A, K, Q, J, and 10 of spades is acceptable, and that
we're dealing from the top of a full deck, to only one player:
The probability of drawing one of A,K,Q,J,10 is 1 in 52.
If one of those is drawn, the probability of drawing one of the
  remaining cards needed is 1 in 51.
The other three cards: 1 in 50, 1 in 49, and 1 in 48.
So the probability of drawing all five cards (in any order) is:
.01923 * .01960 * .02 * .0204 * .0208 = .000000003
which is approximately 1 in 313 million hands. Divide by 4 if any
suit will do, for odds of 78 million to 1.
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