Probability of Playing Cards?

Can anyone tell me how to work out the following:





A shuffled pack of 52 normal playing cards, each card is dealt face up in order, how long (on average) do you have to wait before (say) the Ace of Clubs is dealt?





Of course it is less than or equal to 52 because it has to come up, but how long on average?





Thanks





Also if anyone knows any good books that deal with such question s (and others that I have asked) I would be grateful for a recommendation!

Probability of Playing Cards?
The ace of clubs is equally likely to be in any of the 52 positions in the deck.





(1+2+3+...+52)/52 = (52*53/2)/52 (using 1+2+...+n = n*(n+1)/2)


= 53/2


= 26.5





So, on average, you would expect to go through 26.5 cards to get to the ace of clubs, or any other card for that matter.





edit: Well, you would have to find the probability of getting the first ace in the first, second, third, ..., all the way up to the 49th position.





Probability it is 1st is 4/52.


2nd is (48/52)(4/51).


3rd is (48/52)(47/51)(4/50).


4th is (48/52)(47/51)(46/50)(4/49).


and so on...





Then multiply each probability with each postion and add up. I'm sure it's around 13. There's probably an easier way to do it. I'm not familiar enough with the subject of waiting times to know it.





edit (again): Running this through R, I get 10.6 as the expected number of cards using my suggestion. This is likely less than 13 due to the fact that the first ace can't occur in the 50, 51, or 52 positions.
Reply:26 for any card on average
Reply:26
Reply:26 for any card on average. The wait could be longer if you have a slow dealer. lol
Reply:Havent time to work it out, but it's a very long equation as the probabilty increases with every subsequent card, ie 1/52, then 1/51, 1/50 all the way down to 1/1 for the last card. I'll leave it to others to work out the answer! A good book though is ...





PROBABILITY GUIDE TO GAMBLING: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets





http://www.amazon.com/PROBABILITY-GUIDE-...
Reply:26