1 bell, and 1 jackpot bar. The second reel has 7 cherries, reel has 4 walnuts, 7
ID: 3320839 • Letter: 1
Question
1 bell, and 1 jackpot bar. The second reel has 7 cherries, reel has 4 walnuts, 7 oranges, 5 lemons, 3 bells and 1 bar. The payoffs are: 3 walnuts, 7 cherries, 3 oranges, 5 lemons, 6 oranges, 1 lemon, 3 bells, and 3 bars. The third Reel 1 Bar Reel 2 Bar Bell Bell Bar Bell Bell Bell Lemon Lemon Bell Lemon Lemon Lemon Orange Orange Bar Orange Orange Orange Cherry Cherry Bell Cherry Cherry Walnut Cherry Cherry Any other Payoff in Coins 85 25 20 18 14 16 10 Reel 3 Bar (a) What is the expected payoff if each picture on each reel is equally likely to appear? (b) In the long run, what fraction of every dollar bet will this one-armed bandit (the slot machine) keep?Explanation / Answer
(A)
Reel 1
Reel 2
Reel 3
Payoff in Coins
Probability
(Payoff in coins)*(Probability)
P(X)
20
20
20
1
1
3
1
85
0.000375
0.031875
2
1
3
1
25
0.000375
0.009375
3
1
3
3
20
0.001125
0.0225
4
5
1
3
18
0.001875
0.03375
5
5
1
5
14
0.003125
0.04375
6
3
6
1
16
0.00225
0.036
7
3
6
7
10
0.01575
0.1575
8
7
7
3
5
0.018375
0.091875
9
7
7
4
5
0.0245
0.1225
10
7
7
13
3
0.079625
0.238875
Sum
0.7880
So the expected payoff if each picture on each reel is equally likely to appear is 0.7880.
(B)
1-0.7880=0.2120
So in the long run, the fraction of every dollar bet will this one-armed bandit keep is 0.2120.
Reel 1
Reel 2
Reel 3
Payoff in Coins
Probability
(Payoff in coins)*(Probability)
P(X)
20
20
20
1
1
3
1
85
0.000375
0.031875
2
1
3
1
25
0.000375
0.009375
3
1
3
3
20
0.001125
0.0225
4
5
1
3
18
0.001875
0.03375
5
5
1
5
14
0.003125
0.04375
6
3
6
1
16
0.00225
0.036
7
3
6
7
10
0.01575
0.1575
8
7
7
3
5
0.018375
0.091875
9
7
7
4
5
0.0245
0.1225
10
7
7
13
3
0.079625
0.238875
Sum
0.7880
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