1. What would be the fair market price for the right to play a dice rolling game where the payout is the square of the number shown?

There are six possible outcomes. These are 1, 4, 9, 16, 25 and 36. The average of these is 91 ÷ 6 = 15.167. This would be the fair market price if we ignore any transaction costs.

2. A game is played that involves rolling two dice. Competitors pay $1 to play. They are paid $5 if the combined score is seven but nothing if the score is any other amount. What is the expected value of playing the game once?

There are 36 different ways that the two dice can come up. Six of these will add to seven. So the player will win one sixth of the time. So if you pay $1 and have an expected payout of one sixth of $5 the expected loss is one sixth of a dollar.

3. A casino allows players to play the game from question 2. The casino has annual overheads of $1m and local gambling regulations limit its opening hours to just 12 hours per week while the fire regulations limit the number of gamblers in the building to 500. What would be the minimum number of games per hour that each gambler must play if the casino is just to cover its costs? What conclusions would you draw from this calculation?

The principle of value additivity means that the value loss to the player must equal the value gain to the casino. In theory, therefore, there is a gain to the casino owner of one sixth of a dollar each time the game is played. However, the casino has to incur high costs and only has limited access to gamblers.

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