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During the odds of getting a royal flush question, you didn't mention getting dealt a royal on the redraw after throwing your dealt cards away. I had that happen once. Quite a pleasant surprise.
If you're dealt five garbage cards, toss them, and draw five new ones, your chance of coming up with a drawn royal is 1 in 383,484.
And to answer a few similar questions you didn't ask, but really wanted to know, when you're dealt one card to the royal, your chance of drawing the other four is 1 in 178,365.
Dealt two cards to the royal, it's 1 in 16,215.
Three is 1 in 1,081.
And four, of course, is 1 in 47.