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Royal Flush odds

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The Royal Flush is the biggest, meanest kid on the block. The absolute bully which cannot be matched by any of the other monsters, it is naturally quite illusive. Quite literally speaking, you can play on for years and years, and never even see a royal flush, let alone hit one yourself. As such, making a royal flush is not really part of any poker strategy guide, nor is it ever discussed how to play a royal flush for maximum value. Due to the fact that it’s simply way too infrequent, you may as well completely exclude it from your list of monsters. If you do happen to hit one though, be happy with it, make sure you recreate the poker hand in which it occurred through software dedicated for this task and post it on youtube. What exactly are the odds of a Royal flush coming by though? It’s not like you really have to know your royal flush odds by heart, but it’s an interesting thing to contemplate that you have an approximate probability of 0.000154% of hitting a royal flush. That translates into 649,740 : 1odds which are quite self-explanatory I assume.

The frequency of the Royal flush is 4. That means there are 4 possible royal flushes that can be made from a standard 52-card deck (one 10,J,Q,K,A straight flush for each suit: hearts, spades, diamonds and clubs), but don’t get yourself worked up about it: because of how Texas Holdem is played (you get two hole cards and 5 community cards) only one royal flush can be made in every hand. If you have the Js, Ks in your pocket for instance, and the board lands As, Kh, 10s, Qs, Qh, you have a royal flush but none else can make another one because taking away your three suited cards from the board, there will be only 2 cards left, and every royal flush needs a minimum of 3 cards off the board.

To put your royal flush odds into perspective, compare it with the next best hand, the simple straight flush: while the royal’s frequency is 4, the straight flush’s is 36, and it carries an approximate probability of 0.00139%, coupled with poker odds of 72,193.33 : 1.
Your regular everyday monster, the set (three of a kind) has a frequency of 54,912, approximate probability of 2.11% and carries odds of 46.3 : 1.

Now then, if you do manage to hit a royal flush, does that mean you’ll end up taking down a jackpot or at least all the other player’s stacks? While some poker rooms do reward such hands with a bonus as part of a promotion, the royal flush doesn’t carry any sort of guarantees otherwise.
You may well end up frustrated out of your mind as the entire table quietly folds to you while you’re sitting on the most impressive poker hand you’ve ever gotten together, but that’s just how the game is. If you make a royal, you’d better hope for another guy to make a flush, or chances are you will not get paid.

Example for Royal Flush in Seven Card Stud:

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Example for Royal Flush in Texas Hold'em in a PokerStars cash game:

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