Years ago I read that the odds of being dealt a Royal Flush in poker are exactly the same a being deal any other hand. If we put the same significance on, say, Ace, 2, 5, Jack, Queen, we'd see that "special" combination was just as "rare" as a Royal Flush.
|Posted: 17 April 2018 at 10:22pm | IP Logged | 12
There's a little bit of wordplay here that's crucial.
Your chances of being dealt a Royal Flush in spades is exactly the same as any other hand.
However, there are four possible Royal Flushes (from four suits), so your chances of being dealt *a* Royal Flush (of any suit) is a little bit different.
For other hands there are more possible combinations making a 'lesser' hand of some combination more likely to be dealt.
As an example, there are 9 possible Straight Flushes for each suit (10, if you count the Royal Flush which is technically the highest Straight Flush). So you are 9 times more likely to be dealt a Straight Flush of any suit versus a Royal Flush of any suit.
I'll do one more with the next highest hand.
There are 13 possible Four-of-a-Kinds, each of these can have one of 12 possibilities for the fifth card that doesn't matter. You are 156 (13x12) times more likely to be dealt a Four-of-a-Kind than a Royal Flush of any suit.
But your chances of being dealt four 10s with a 3 of hearts is exactly the same as being dealt a Royal Flush in spades.