On the annual town's fair you see the following game setup:

There is a table with 6 fields on it, numbered 1 through 6 (see picture). You can place money on the fields (however much you like, on however many fields you like), and the game master will then roll three dice. For every dice showing the number of a field you placed a bet on, you'll double your placed amount. So you'll quadruple your bets if two dice point to fields with your money, and sextuple them if you managed to guess all three dice's results. 

The game master claims that his game is completely fair: a single die has a 1:6 chance of landing on any of its faces, meaning that with three dice you have a 1:2 or 50% chance of winning. You are pretty confident this is not true, why exactly?

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