I once got dealt a royal flush.
That’s right. A “natural” royal flush. On a quarter video poker machine.
To make matters even more amazing, it was on the first quarter I gambled that day. (Can you imagine if the guy who had been playing that machine for hours just before saw me come over to “his” machine and hit a royal flush on one quarter?)
The probability of being dealt a royal flush is quite low. There are exactly four such hands — one for each of hearts, spades, clubs and diamonds — and there are 52!/(47! * 5!) different poker hands.
[Where does this number come from? Well, the first card has to be one of the 52 cards in the deck. The second has to be one of the 51 remaining, so there are 52*51 ways to get two cards. The third has to be on of the 50 remaining, so there are 52*51*50 ways to get three cards. Using this reasoning, there are 52*51*50*49*48 ways to get dealt five cards. But rearranging the cards doesn’t change what’s in the poker hand — that is, ace of clubs and two of hearts is the same as the two of hearts and the ace of clubs — so we have to divide by the 5*4*3*2*1 ways to arrange the cards.]
So there are 2,598,960 different poker hands, and exactly four of them are royal flushes. This means the odds of being dealt a royal flush are 1 in 649740.
Them’s not very good odds.
Here’s what happened. Several years ago, I was flying somewhere — I believe to Spokane to visit a friend of mine that lives just over the Idaho border in British Columbia. My plane landed in Las Vegas. I had to switch planes, so I got out and went to the gate. I had a good 45 minutes before boarding started, so I thought I would do some gaming. After all, how much can you lose in 45 minutes?!
I selected a quarter video poker machine. I put in my money and hit deal. It dealt out the cards pretty fast, then made the little happy note sound and highlighted the “Royal Flush” payout line. I was a little surprised (to say the least) and not too sure what was going on. It took me a few seconds to realize that I had actually been dealt a royal flush. I held every card (I was once dealt four deuces in a “Deuces wild” game and I was so flustered, I failed to “Keep” any of them, and thus failed to collect my $50), and hit “Draw”. Ta-da! For my one quarter, I won $75.
If I had put in five quarters, I would have won $1000. Yikes!! So of course I immediately started kicking myself for not having put in five quarters. But hey, what can you do.
Yeah, it was cool. But it was also a downer. I had hoped to kill 20 minutes or so. Now what was I supposed to do… keep playing? As a percentage, I was WAY up. And extremely unlikely to change that one way or the other.
I played a few more anticlimactic hands of poker, then cashed out my now $60-some odd dollar draw and went on my way.
It’s great that I got it. But also it’s a bit of a downer — not because I never CAN do it again, but because I probably never WILL do it again. If you play 450365 hands, you have a 50-50 chance of seeing a royal flush. I probably won’t play anywhere near that number, so I have much less than a 50% chance.
Of course, that’s just being DEALT a royal flush. The odds that it will happen with a draw are much higher, but it’s harder to calculate because it depends upon your strategy. Nevertheless, since I don’t play poker that much, I think it reasonably prudent that I don’t expect to see a royal flush ever again.
But that’s okay. I got mine.