Two natoral royal flush in a row is much more probable then 1/31,000,000,000.
Three natoral royal flush in a row is less probable, however........
royal flushes:
1: 1/40,000
2: 1/1,600,000,000
3: 1/64,000,000,000,000
(natoral royal flush has a probability of around 1/40,000 - depends on the game but it is almost always near that.)
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