Question

# At a dishonest backroom gambling establishment, they have a spinning wheel. The wheel has the numbers...

At a dishonest backroom gambling establishment, they have a spinning wheel. The wheel has the numbers 1 through 4. The wheel has 20 number places that are equally likely to be landed on by the spinner. However, there are an unequal number of numbers on the wheel. For example, there are only two 1’s on the wheel. For this problem assume you bet on the spinner landing on 1.
a. What are the actual odds against winning on 1?
b. What are the actual odds in favor of winning on 1?
c. In general, for this game, what payoff odds would favor the casino, what payoff odds would favor the players, and what payoff odds would benefit nobody?
d. If the payoff odds were 5:1 and you place a \$6 bet on the board, then what is the payout?

a) The actual odds against winning is computed here as:

= Number of places with no 1 on them / Number of 1s on them

= 18/2

= 9:1

therefore 9:1 are the required odds here.

b) The odds in favor of winning is the reciprocal of odds against winning that is 1:9

Therefore 1:9 are the required odds here.

c) Payoff odds of 9:1 would balance and would not favour anyone, but a payoff odds of less than 9:1 would favour the casino while a greater than 9:1 would favor the player here.

d) Given payoff odds as 5:1, the expected payoff for a \$6 bet is computed here as:

= 5*(1/10)*6 - 6*(9/10)

= 3 - 5.4 = \$2.4

Therefore \$2.4 is the expected payoff here for the player.

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