You are planning on going to the National Harbor casino to play roulette. The ro

Question

You are planning on going to the National Harbor casino to play roulette. The roulette odds chart tells you how much money you will win if the ball lands on one of the numbers you bet on. For example, if you bet $1 on number 17 (a) and the ball lands on number 17, you will win $35 and get back your $1 bet as well. If you bet on 24 numbers (h) and the ball lands on one of the 24 numbers, you will get back $0.50 = (1/2 * $1) plus not lose your $1 bet. If the ball does not land on any of the numbers you bet on, then you just lose your $1 bet.

Roulette Payoff Odds Chart

35-to-1 : One number

17-to-1 : Two numbers

11-to-1 : Three numbers

8-to-1 : Four numbers

6-to-1 : Five numbers (including 0 and 00)

5-to-1 : Six numbers

2-to-1 : Twelve numbers (1 column, 1 to 12, 13 to 24, 25 to 36)

½-to-1 : Twenty-four numbers (two columns of 12 squares)

1-to-1 : Red (18 numbers)

1-to-1: Black (18 numbers)

1-to-1 : High (19 to 36)

1-to-1 : Low (1 to 18)

1-to-1 : Odd (18 numbers)

1-to-1 : Even (excluding 0 and 00 for 18 numbers total)

The expected pay off value for roulette is

E = Payoff odds*bet* P(win) - bet*P(lose)

Let bet = $10.

Choose two different payoff odds from the above table and calculate what the expected payoff value is for each of your choices. (Hint: The expected payoff value has to be negative so that the house can stay in business over the long term!)

For your two choices of payoff odds, are your two expected payoff values the same (yes or no)? (Hint: It should not matter which numbers you play. Every choice should lose the same amount of money. Otherwise, no one would play the numbers where the losses are higher.)

Questions is in bold.

Explanation / Answer

For case (a):

Expected money = E = 10*(36/38 - 37/38) = -10/38

For case(h):

Expected money = E = 10*(1.5*24/38 - 14/38) =120/38

The expected pay offs are differenct in two cases

Case a can be selected over case h since negatuve expected payoff in first case

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