# Calculate probablity: all cards were dealt (13 cards each). We played 6 hands.

#### mendelejev

##### New member
Hello!

I have an question regarding probability! Help would be much appreciated.

In a scenario of 4 players, all cards were dealed (13 cards each). We played 6 hands.
In each game, I calculated that I "should" get jacks, queens, kings and aces to a sum of 4, since there are 16 of these in one deck, and 13*(16/52) = 4

Each hand I got the following number of jacks+queens+kings+aces per round:
3, 2, 1, 7, 9, 0

Now I want to statistically calculate if I got the amount that I'm "entitled to" or if I should accuse the dealer of hustling me?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello!

I have an question regarding probability! Help would be much appreciated.

In a scenario of 4 players, all cards were dealed (13 cards each). We played 6 hands.
In each game, I calculated that I "should" get jacks, queens, kings and aces to a sum of 4, since there are 16 of these in one deck, and 13*(16/52) = 4

Each hand I got the following number of jacks+queens+kings+aces per round:
3, 2, 1, 7, 9, 0

Now I want to statistically calculate if I got the amount that I'm "entitled to" or if I should accuse the dealer of hustling me?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

http://www.freemathhelp.com/forum/announcement.php?f=33

#### stapel

##### Super Moderator
Staff member
In a scenario of 4 players, all cards were dealet (13 cards each). We played 6 hands. In each game, I calculated that I "should" get jacks, queens, kings and aces to a sum of 4...
Usually, these cards are worth 10 or more. Should we assume that you're not talking about the sum of their values, but a total number of cards in a hand?

...since there are 16 of these in one deck, and 13*(16/52) = 4
Are these the only cards that "matter"? If not, then why are you concentrating on these only?

Each hand I got the following number of jacks+queens+kings+aces per round:
3, 2, 1, 7, 9, 0
This has an average of (3 + 2 + 1 + 7 + 9 + 0)/6 = 22/6, or about 3.7. That's fairly close to 4.

Now I want to statistically calculate if I got the amount that I'm "entitled to" or if I should accuse the dealer of hustling me?
What are your thoughts? What sorts of tools have you been given in your textbook or class notes? What have you tried so far? On what basis have you determined that 3.7 cards of the desired type, on average, over a very small data set, is questionable?