Losing at Dice

When six dice are rolled, the number of different numbers which can appear range from 1 to 6. Suppose that once every minute, the croupier rolls six dice and you bet $1, at even odds, that the number of different numbers which appear will be exactly 4.

If you start with $10, roughly how long will it be, on average before you are wiped out?


Update (11/12/09): Solution in comments!!


  1. sorry guys...

    Not the correct answer :(

  2. sahi hai jaadu...

    badhiyaan :)

    @junta... probability that the even occurs is > 0.5, and so, he would expect his money to grow :)

  3. I am not able to figure out how many cases would it take to arrange - 123412 and 123411 types of cases (this no*360) should be the total possible cases

  4. Hmm, Got it - 6C4(4C1 * 6!/3! + 4C2 * 6!/(2!*2!))/6^6

    Hmm good one.


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