A poker question.

[bangman]

Hello, me and my friend have had a discussion for a very long time. He claims that it is harder to get a royal straight flush in poker (Hold' em) if there are more people around the table. I think the opposite, the reason he thinks this is because of the possibility that another player around the table has a chance of having a card in their hand that you need to build up a royal straight flush. I'm convinced that it is the same odds of getting a royal straight flush wheter you are playing heads up or at a 10 man table. (This applies to getting 4 kind, flush, and pretty much everything). Thoughts?

 

[ksdhart]

Well, I think the answer to that question lies in how many decks of cards you're playing with. Adding more players to the table usually calls for increasing the number of decks, thus actually increasing the odds of getting a Royal Flush. So, by one interpretation, you and your friend are both wrong.

But, if we assume the game is always played with one deck, then you can perform a thought exercise and settle this matter. Imagine a game between two players. You know your own cards. Let's say you have two of the cards you need for a Royal Flush. Where are the other three at? Then imagine another game, this time with three players. Again, assume you have two of the needed cards. Where are the other three now? Continue imagining games, adding players until you reach ten players. Did you notice a pattern in where the remaining cards are? What does that tell you about the odds of getting a Royal Flush?