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 The Dice Game (Posted on 2005-11-04)
In a game show, there is a certain game in which there are four hidden digits. There are no numbers greater than six among them, and no zeros.

You roll a die and then guess if the first digit is higher or lower than what you rolled. (If the die you rolled is equal to the first digit, you win no matter what you said.) You then roll and guess for each of the other three digits.

If you use the best strategy each time when saying "higher" or "lower", what is the chance you will get all four right and win? (Keep in mind you have no idea what the 4 digit number is.)

 See The Solution Submitted by Gamer Rating: 3.6667 (3 votes)

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 Worst Case Scenario | Comment 8 of 12 |
The worst case scenario for each roll is that you roll either a 3 or a 4.  In the case of a 3, the best guess in higher and with a 4, lower.  Either way you've got a 3 in 5 chance of being correct or 60%.  With 4 rolls you've got 60% * 60% * 60% * 60% = 12.96% chance of winnning.
 Posted by Morgan on 2005-11-16 17:45:00

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