Odds of Making a Royal Flush on the Flop
Since there are exactly 19,600 different possible flops that can be dealt, the odds of flopping the Royal Flush are precisely 1 in 19,600. (To learn how the number of different flops can be calculated, check out the 888poker article on straight flush odds in poker.)
Odds of flopping the Royal Flush with two suited cards between Ten and Ace =
1/19,600 = 0.00005 or roughly 0.005%
Odds of Flopping the Royal Flush Straight Draw
Flopping the Royal Flush is virtually impossible. A slightly more likely possibility is that of flopping the Royal Flush straight draw.
We’d only need two specific cards to fall for this to be the case.
For example, imagine we hold the TdJd.
Flops that give us the Royal Flush draw with TJs
QdKdx (47 possible flops)
AdQdx (47 possible flops)
AdKdx (47 possible flops)
The third card can be any one of the remaining 48 cards left in the deck (aside from the card that actually gives us the straight flush.
This means 141 different possible flop combinations give us the straight flush (47 * 3).
Odds of flopping a straight flush draw with two suited cards between Ten and Ace = 141/19,600 = 0.0072 or roughly 0.72%.
That’s still less than 1% chance of flopping a Royal Flush draw even after starting out with a suited connector, but it is 141 times more likely than flopping the Royal Flush itself.
Similar logic can be applied to calculating the possibility of flopping straight flush draws when starting out with a suited connector. Although there are typically more ways to flop a straight flush draw than a Royal Flush draw.
For example, starting with T9s, there are 9 different ways of flopping a straight flush draw, making the probability three times more likely than flopping a Royal Flush draw with a holding such as QTs