Well, you'd have to clarify your question and make some assumptions first. Assuming a 40,000 hand royal cycle and assuming your question is the chance of hitting back to back royals after hitting one royal, the simple answer is 1 in 40,000. The odds of hitting back to back royals on any given 2 successive hands is, of course, 1 in 40,000 squared. So your question is probably more interesting than either of these. You mentioned a lifetime, so, even though you technically gave an estimate for its chance, maybe your question is the chance of one person doing this in his or her lifetime. An estimate for how many hands would be played would be necessary to make and then the chance of any 2 of them being back to back could be calculated. There may be a more sophisticated approach to the problem, but I'll take a stab at it and say that, assuming the player will play 8 million hands and hit 200 royals, the chance of 2 of them being back to back at least once would be 1 - ((39,999/40,000) ^ 199), which is the same as the chance of hitting at least one royal in 199 hands. Without doing the math, I'll guess it's about 1 in 200.
----- coachvee@aol.com wrote:
> My questions are:
> 1) Is it possible to compute the odds of this once-in-a-lifetime happening?
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