The Odds of Flopping, Drawing, Making a Royal Flush!

The odds of flopping a royal flush given two suited broadways → 0.005% or 1 in 19,600.

The Royal Flush is actually a type of straight flush. It is created when we hold T,J,Q,K,A all of the same suit.

To flop a Royal Flush, it is necessary to start the hand with precisely two suited cards between Ten and Ace. Regardless of which two of these cards, we hold the probability of flopping the straight flush will be the same.

This is because either way, we’ll need the flop to come down as three precise cards.

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

Odds of Making the Royal Flush Postflop

There will be two primary types of Royal Flush draw we’ll flop. The gutshot Royal Flush draw and the open-ended Royal Flush draw.

Gutshot Royal Flush draws have 1 out in the deck, while open-ended Royal Flush draws have 2 outs in the deck.

Odds of Hitting on the Turn or River

Odds of catching the gutshot Royal Flush on the turn 1/47 = 0.0213 or roughly 2.1%

Odds of catching the open ended Royal Flush on the turn 2/47 = 0.426 or roughly 4.3%

Odds of catching the gutshot Royal Flush on the river 1/46 = 0.0217 or roughly 2.2%

Odds of catching the open-ended Royal Flush on the river 2/46 = 0.0435 or roughly 4.4%

Odds of Hitting by the River

To calculate the probability of hitting by the river, we’ll employ the trick of calculating the chance of not hitting and then subtracting from 100%. 

Odds of not catching the gutshot Royal Flush on the turn 46/47

Odds of not catching the open-ended Royal Flush on the turn 45/47

Odds of not catching the gutshot Royal Flush on the river 45/46

Odds of not catching the open-ended Royal Flush on the river 44/46

Odds of not catching the gutshot Royal Flush on the turn or river = 46/47 * 45/46 = 0.9574 or roughly 95.7%

Odds of not catching the open-ended Royal Flush on the turn or river = 45/47 * 44/46 = 0.9158 or roughly 91.6%

Odds of hitting the gutshot Royal Flush by the river = (100 - 95.7%) roughly 4.3%

Odds of hitting the open-ended Royal Flush by the river = (100 – 91.6%) roughly 8.4%

Implied Odds Analysis of a Royal Flush

A Royal Flush always carries excellent implied odds when hitting. This is because our opponent is usually forced into stacking off with very strong worse hands - such as worse flushes and full houses.

Royal Flushes made with two of our hole cards always carry better implied odds than straight flushes made with one of our hole cards. When using just one of our hole cards, it means there will be four cards to the Royal Flush already on the board.

This scenario decreases the chance that our opponent will pay us off with worse holdings. It will be impossible for our opponent to make the nut flush since the highest possible card of the correct suit makes the Royal Flush, and we hold it ourselves.

Basic Strategy Advice

Unless all five cards of the Royal Flush appear on the board itself, it is impossible to ever chop with the Royal Flush. It is always the best hand, and we should be looking to invest as much of our stack as possible (preferably all of it).