[gaming_mouse]

[ QUOTE ]
I'm still not totally clear on the math for including multiple hands pre-flop, so I'm not gonna try to tackle the odds of someone flopping

[/ QUOTE ]

Since it is impossible for two players to both flop a royal flush, we need only calculate the chance of a specific player flopping one and then multiply that by 7. You have already correctly calcualted the chance that a specific player flops a royal as 1 in 649740, so the chance that 1 of 7 players flops one is 7 in 649740, or:

1 in 92820

Now, to answer the OP's other question, in a live game you will play about 35 hands/hour, or about 140 hands/4 hour session. After 663 such sessions, the chance that you will have seen another flopped royal is about 63%:

1 - ((92 819 / 92 820)^92 820) = 0.632122541

Note, also, that this is almost exactly 1-1/e, where e is the base of the natural logarithm.

Anyway, if you are playing 4 hours a day every day, expect to see this every couple years or so.

gm