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Best of Jerry Stickman

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Odds of a royal flush

24 February 2018

Hi!

On vacation, getting caught up on my reading, carefully reading your article about getting 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 is 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, a one in 29,000,000 chance of winning is really quite high. The current odds of winning the jackpot for the Powerball lottery game is one in 292,201,338. Regardless, buying 1,000 tickets to a lottery where the odds of winning a jackpot are one in 29 million is equivalent to one out of 29,000 chances of winning. While this is quite a bit better, you still have 289,999 chances of losing – or only a 0.00003448 chance of winning – still not a very favorable position.

It is also possible when purchasing 1,000 lottery tickets that you will get exactly the same numbers on more than one ticket 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.

May all your wins be swift and large and all your losses slow and small.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot machine play. He authored the video poker section of Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker! You can contact Jerry “Stickman” at stickmanjerry@aol.
Recent Articles
Best of Jerry Stickman
Jerry Stickman

Jerry "Stickman" is an expert in dice control at craps, blackjack, advantage slots and video poker. He is a regular contributor to top gaming magazines. The "Stickman" is also a certified instructor for Golden Touch Craps dice control classes and Golden Touch Blackjack's advantage classes. He also teaches a course in advantage-play slots and video poker. For more information visit www.goldentouchcraps.com or www.goldentouchblackjack.com or call 1-800-944-0406 for a free brochure. You can contact Jerry "Stickman" at stickmanGTC@aol.com.

Jerry Stickman Websites:

www.goldentouchcraps.com
www.goldentouchblackjack.com
Jerry Stickman
Jerry "Stickman" is an expert in dice control at craps, blackjack, advantage slots and video poker. He is a regular contributor to top gaming magazines. The "Stickman" is also a certified instructor for Golden Touch Craps dice control classes and Golden Touch Blackjack's advantage classes. He also teaches a course in advantage-play slots and video poker. For more information visit www.goldentouchcraps.com or www.goldentouchblackjack.com or call 1-800-944-0406 for a free brochure. You can contact Jerry "Stickman" at stickmanGTC@aol.com.

Jerry Stickman Websites:

www.goldentouchcraps.com
www.goldentouchblackjack.com