Bert hamminga  Roulette   The Capital Asset Pricing Model   Control Questions

Roulette is played with a disk on which a ball falls into one of 37 holes marked 0-36, at random.

1. Betting on 1 number (blue) yields 35 times your money if yours is the number resulting from turning the disk.
2. Betting on 2 numbers ("� cheval", yellow) yields 17 times your money
3. Betting on 3 numbers ("transversal pleine", green) yields 11 times your money
4. Betting on 4 numbers ("en carr�", black) yields 8 times your money
5. Betting on 6 numbers ("transversale six", red) yields 5 times your money
6. Betting on 12 numbers (column, purple) yields 2 times your money

The "column", "transversal six" and "carr�" bets can obviously never include 0.
Of course, if the number resulting from turning the disk is not in the range of your bet, you will loose your money.

Questions:

1. What is the expected rate of return of "investing" 37 Euro in each of these 6 types of bets? (Remember every number results one time in 37 turns of the disk on average).
2. If these six investment opportunities were the only ones open to investors, would any of them be inferior to another independent of what is the investor's utility function (risk aversion/preference), and hence certainly be chosen by noone? Or does it all depend on the investor's utility function (risk aversion/preference)?
3. If there are absolutely inferior bets, and you see people in a casino making such absolutely inferior bets, would that constitute an empirical falsification of your theory?