Odds of Being Dealt a Royal Flush

I am not an expert on the laws of probability, so I am confused by your statement that there are four royal flushes in 2,598,960 hands, and therefore your odds of getting a royal are one out of 649,740. Is this a correct statement, or is it something totally different, that never changes, four out of 2,598,960?

The reason I ask is that I know if I buy one lottery ticket, and my chance is 1 in 29,000,000 of winning the grand prize, if I buy 10, my chance is 10 out of 29,000,000, NOT 1 out of 2,900,000. Obviously, following the odds you specify for the royal, if I bought 1,000 lottery tickets, I would dramatically increase my odds on the lottery to 1 in 29,000. I have always been told "sorry, mathematically if you buy 1,000 lottery tickets, your odds are only 1,000 out of 29,000,000, which is very different from 1 out of 29,000."

Can you clarify this for me?

Thanks,
David in Florida

Hi David,

The mathematical equations used to calculate odds of being dealt a royal flush or for winning a lottery allow for simplifying the result. Stating the odds of being dealt a royal flush as four out of 2,598,960 is equivalent to one out of 649,740.

Regarding the lottery example, 1,000 out of 2,900,000 is equivalent to one out of 29,000. It is possible when purchasing 1,000 lottery tickets to get exactly the same numbers on more than one, however, and that would slightly lengthen the odds of winning the jackpot. I am not sure why you were told the 1,000 out of 2,900,000 is very different from one out of 29,000. The math doesn't say that.

Jerry "Stickman"