Question: What Is The Probability Of Spotting A Royal Flush And A Four Of A Kind In The Same Hand?
If you are someone who is new to learning how to play the classic game of Texas Hold’em, it’s understandable that you might get easily confused.
But don’t worry because this stage of confusion will not last forever. This game is pretty easy when compared to the other casino games. So, once you get the idea of the game and understand the tips and tricks, you’ll be able to master the game in no time.
One of the most common questions that people have about Hold’em is this: what is the probability of spotting a royal flush and a four of a kind in one round with 10 players? Let’s get to the bottom of this.
Breaking Down The Science
Let’s break down this possibility by working from the result.
The probability of one person having a particular hand is 1/221. It is absolutely necessary that the board should have the same hand, and in any case, 2 of the remaining cards should be suited. Now, there are 2 ways this odd hand might occur: there can ideally be 2 or 3. Now, let’s analyze this deeper.
While dealing a board, there are approximately 1,712,304 ways to split (48, you can pick 5). In total, there are 5 unique pocket sets specifically for your quads (10 10, J J, Q Q, K K, A A). Keep in mind that each of these pocket sets must have 4 remaining broadway cards. Out of these 4, 2 must be visible on the board.
This gives us 6 different ways that 2 of the 4 might show (The idea behind this being 4 suits which gives us 4 different ways the combinations can fall).
Let’s take one pocket set. Out of the 1,712,304 viable ways to deal a board, only 1120 will meet the correct basis that is required (the 6 broadways combos 4 suits 46 possible ways that the remaining card can fall). In order to conclude the royal flush, the secondary player must have the 2 particular cards. And the chances of that happening are 1/1980 (1/451/44) The overall combined chances for a specific pocket set is 7/4,682,937,402 (1/2211120/1712304*1/1980). And this is just for 1 pocket set!
When you total the possibilities for all 5 pocket sets, the chances are 35/4,682,937,402. Or, in simpler terms, 1 in 133 million! Amazing, isn’t it?
Summing Up
So there you have it, folks! The probability of spotting a royal flush and a four-of-a-kind in one round with 10 players is 1 in 133 million! You might feel that this could never happen. But that’s the beauty of the game. After all, card games also require a bit of luck, don’t they?
