Rick,
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.
RP>Is a royal flush limited to only one suit or any of the four? In
RP>any case I believe your probability is off just a little. Let's
    A Royal Flush is comprised of AKQJ10 in any order. They must of
   course all be of the same suit for the hand to be considered a
   Royal Flush. Otherwise if they are of different suits they are
   considered a straight. Un-ordered cards of the same suit are
   considered a Flush, etc... Keep in mind, and for the record, we're
   talking video poker only. Regular poker is another beast.
RP>assume only the A, K, Q, J, and 10 of spades is acceptable, and that
RP>we're dealing from the top of a full deck, to only one player:
RP>The probability of drawing one of A,K,Q,J,10 is 1 in 52.
RP>If one of those is drawn, the probability of drawing one of the
RP>  remaining cards needed is 1 in 51.
RP>The other three cards: 1 in 50, 1 in 49, and 1 in 48.
RP>So the probability of drawing all five cards (in any order) is:
RP>.01923 * .01960 * .02 * .0204 * .0208 = .000000003
RP>which is approximately 1 in 313 million hands. Divide by 4 if any
RP>suit will do, for odds of 78 million to 1.
     True, but your stats only account for hands where you are dealt a
   Royal Flush  straightout. One has to consider the hands where you
   are dealt less than a Royal Flush, say A, K, Q of hearts (a partial
   Royal Flush) and discard your 2 discards and are then dealt a J and
   10 of hearts (spades, diamonds, etc...) giving you a Royal Flush.
   There are numerous hands that can lead to a Royal Flush and they
   must all be considered when calculating the odds of getting a
   Royal Flush in video poker.
     Many video poker machines will pay the same for a Royal Flush that
   is dealt to you straightout as it will pay for one that you "earned".
   Some machines may pay extra for a straightout Royal Flush and for other
   rare hands. One should know the payout schedule before stuffing any
   cash into any gaming machine. All payout schedules on gaming machines
   are not the same.
     Maybe you were thinking of Video Slots where you get what comes
   up on the screen and there are no discards?
    If you really wanna see the math there are some pretty good books
   out there on Video Poker\card gaming. One is "Expert Video Poker - For
   Las Vegas" by Lenny Frome. He also does one for Atlantic City since
   each place offers slightly different machines\payout schedules.
   Card games are fun to program (in any version of BASIC, etc...) and
   the games are fun to play after you code em! Gotta have fun programming
   or you'll lose the mind! 
- Robert Fortune
 * OLX 2.1 TD * My mind is made up. Don't confuse me with the facts!
--- Maximus/2 3.01
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