Not so Gene. Odds of two sequential Royal Flushs BEFORE YOU DRAW THE FIRST ONE is the probability of drawing one, squared.

An easy to see example, the odds of throwing a Six with one die are 1/6. The odds of throwing two sixes in sequence with a single die are 1/6 times 1/6 or one in 36, the same as the odds of throwing two sixes (a 12) with a pair of dice. The dice have no memory either.