I'll put all correct solutions received by FRIDAY October 26 into a hat, and draw a winner, who will get a small prize.
The puzzle: An obvious way to use a dice to generate a random number between 1 and 6 is to roll it, and see what number is face-up. Of course, this way all six numbers are equally likely.
Here's another way, if you happen to have six dice with you: roll all six, and count the number of different numbers that are face-up. For example, if you roll three 3's and three 6's, you would count 2; if you rolled a 1, a 2, three 3's and a 5, you would count 4; if you rolled all 5's, you would count 1. This process definitely gives you a random number between 1 and 6, though it's very unlikely that all 6 numbers are now equally likely.
Here's the puzzle: If you could bet on one particular number being generated by this process, which number would you bet on to maximize you chances of being right? And is this bet in your favour or agianst you (i.e., are you more likely to win than lose, or more likely to lose than win)?
Solutions, together with the list of correct solvers and the prize winner, are here.