The odds of being dealt a Royal Flush
Even novice players know that a Royal Flush is the ultimate poker hand but even many experienced players might not realise just how rare getting the ten, jack, queen, king and ace of one suit actually is. Although movies like Casino Royale have made this most sought after hand seem within the realms of possibility the odds are truly stacked against you.
Of course, the chances of getting a Royal Flush no more difficult than getting any other 5 specific cards in a straight flush. A Royal Flush is 1 specific straight flush and there are 4 different ways in can occur, one for each suit. There are 2,598,960 different combinations in 5 card poker so there is a 4/2,598,960 or 1: 649,740 chance of getting a specific straight flush, including a Royal Flush using the formula (1/p) -1:1, with “p” being probability. The chances of drawing any straight flush, aside from a Royal Flush, are reduced to 1:72,192 since there are now 9 different hands which can be used to in 36 ways to make the hand.
To put that into context, you could be dealt 20 hands every day for a year (20 x 365 = 7300) from the time you were old enough to play poker (18 or 21 years old depending where you live) and mathematically speaking you would likely never get a natural Royal Flush (649,740/7300 = 89) unless you lived to 107 or 110 years old! It gets significantly easier of course to make a Royal Flush when you are discarding and picking up cards or have a flop as in Texas Hold’em. In a standard game of Texas Hold’em your chances of getting a Royal Flush improve to 1: 30,940 – so if you played 20 hands of poker a day, mathematically you’d get about 1 Royal Flush every 4 years. How about the chances of 2 players having a different Royal Flush in the same game? About 1: 1,516,060. What a cooler that would be!
There are worse odds however than getting a Royal Flush. In fact, if you think about it your chances of having any straight poker hand is only 1 out of the 2,598,960 possible combinations. Your chances of getting that hand again are exactly the same, meaning that it is very unlikely that most people are dealt the exact same hand twice over the course of their lifetimes! Other popular forms of gambling also offer worse odds. For example your odds of winning the lottery are only about 1 in 8 million at best – and with super-lotteries like Mega Millions your chances of winning the jackpot are a mere 1 in 259 million! With that said, if you did somehow manage to win the lottery you’d obviously make more a lot more money than you’ll ever make playing even the highest level of professional poker. With prizes worth hundreds of millions of dollars lottery is still by far the most popular form of betting, with millions of people buying tickets to each weeks draw, hoping that their lucky numbers come up despite the long odds.
Getting a Royal Flush is extremely difficult, even with a flop, so appreciate just how fortunate you are when it happens to you. And the next time that you hear a fellow poker player telling you about the number of Royal Flushes which they’ve had, take it with a grain of salt. A serious professional Texas Hold’em player will probably have a Royal Flush every year or two, a casual player maybe a handful in their lifetimes if they cards fall in their favour. However if you hear about a person who brags about getting a Royal Flush on the first five cards that they were dealt you should be wary – odds are that they are either dishonest, delusional or extremely lucky!
