Royal Flush Odds - Discovering the Chances of Forming a Royal Flush!

The probability of flopping a Royal Flush when starting with two suited Broadway cards is about 0.005%, which translates to 1 in 19,600.

The Royal Flush A Royal Flush is technically a specific type of straight flush, formed when we possess the cards Ten, Jack, Queen, King, and Ace all in the same suit.

In order to flop a Royal Flush, one must begin with exactly two suited cards ranging from Ten to Ace. Regardless of which of these cards we hold, the chances of flopping the hand remains consistent. straight flush will be the same.

This is crucial, as we require the flop to yield three exact cards.

Chances of Completing the Royal Flush After the Flop

There are two main varieties of Royal Flush draws that we might encounter after the flop: the gutshot Royal Flush draw and the open-ended Royal Flush draw.

Gutshot Royal Flush draws give us 1 out in the deck, while open-ended draws present us with 2 outs.

Odds of Hitting on the Turn or River

The odds of hitting the gutshot Royal Flush on the turn stand at 1/47 = 0.0213, which is about 2.1% .

The odds of achieving the open-ended Royal Flush on the turn are 2/47 = 0.426, or roughly 4.3% .

The chances of successfully hitting the gutshot Royal Flush on the river is calculated as 1/46 = 0.0217, roughly equating to 2.2% .

For the open-ended Royal Flush on the river, the odds are expressed as 2/46 = 0.0435 or approximately 4.4% .

Odds of Hitting by the River

To determine the likelihood of completing the hand by the river, we will utilize a technique based on calculating the probability of not hitting it, followed by subtracting that figure from 100%.

The chances of failing to hit the gutshot Royal Flush on the turn are 46/47.

The likelihood of missing the open-ended Royal Flush on the turn is 45/47.

The probability of not getting the gutshot Royal Flush on the river is 45/46.

The odds of not finding the open-ended Royal Flush on the river stand at 44/46.

The probability of failing to catch the gutshot Royal Flush on both the turn and river amounts to 46/47 * 45/46 = 0.9574, or approximately 95.7% .

In contrast, the odds of not hitting the open-ended Royal Flush on the turn or river are 45/47 * 44/46 = 0.9158 or about 91.6% .

The chances of obtaining the gutshot Royal Flush by the river is therefore (100 - 95.7%) approximately 4.3% .

Conversely, the probability of getting the open-ended Royal Flush by the river works out to (100 – 91.6%) around 8.4% .

Analyzing the Implied Odds of a Royal Flush

Achieving a Royal Flush typically comes with excellent implied odds upon hitting. This is largely due to our opponents often feeling compelled to go all-in with strong but inferior hands, like weaker flushes or full houses.

A Royal Flush made with two cards from our hand usually presents better implied odds than a straight flush derived from one of our cards. When relying on just a single card from our hand, it implies that there are already four cards contributing to the Royal Flush on the table.

Such a situation diminishes the likelihood of our opponents calling our bet with less powerful holdings. Additionally, unless all five cards necessary for the Royal Flush appear on the board, we can never tie with it. The Royal Flush is undoubtedly the best hand, and we should aim to wager a substantial part of our stack—ideally all of it.

Basic Strategy Advice

Observing a flop with two suited Broadway cards