Royal Match Blackjack

How do you determin how many Royal Matches someone can be dealt using one deck, playing 3 hours, with 5 players at the table?

Quote: Bongo777

How do you determin how many Royal Matches someone can be dealt using one deck, playing 3 hours, with 5 players at the table?

In single deck the probability of hitting a royal match (any two suited cards) is p = (12/51) = 0.235294118. Simply multiply this number by the total number of hands dealt during the time period to get the total number of royal match wins. For example, if 70 hands per hour are dealt to 5 people, that's 350 hands per hour, times 3 hours gives 1050 hands. So, the expected number of wins is (.0.235294118)*1050 = 247.0588235, or about 247 such wins for the entire table.

Now, if you are wondering about hitting KQ suited, then that happens with probability (8/52)*(1/51) = 0.003016591. Multiply this by that same 1050 hands and you get 3.167420814, so roughly 3 such hands should be dealt. If you're talking about the expected number of hits by any one of the 5 people, the expected number of KQ suited is 0.633484163. That's not the whole story.

Now, the standard deviation for the KQ suited is 0.0548406, so over 1050 hands the standard deviation is sqrt(1050)*0.0548406 = 1.777038548. So the first standard deviation is up to about 2.410522711. If you want to know what would be considered very abnormal, that would be anything beyond the third standard deviation, or any number over 5.964599806.

So, roughly 7 or more KQ suited by one player in a 5 player game during a three hour period dealt at a pace of 70 hands per hour would be out on the tail.

The only piece of variable data you need to know to do these calculations is the total number of hands dealt.

Since you asked *how* to do it, and not for the answer, I've shown you how to do it for one specific case. You can take it from here.

--Dorothy

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This absolutely answered my question completely and thoroughly.

Thank you