THE
ONE-ARMED BANDITTHE
ONE-ARMED BANDIT
A typical slot machine has 3 dials, each with
20 positions or symbols. The dials are set in motion
by pulling the lever. Which three symbols are
showing when the dials stop moving determine
your payoff.
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|
Dial 1 |
Dial 2 |
Dial 3 |
|
Cherries |
7 |
7 |
0 |
|
Oranges |
3 |
6 |
7 |
|
Lemons |
3 |
0 |
4 |
|
Plums |
5 |
1 |
5 |
|
Bells |
1 |
3 |
3 |
|
Bars |
1 |
3 |
1 |
Built into the machine are payoffs for certain combinations.
|
Paying Permutation |
Payoff |
|
Bar Bar Bar |
62 : 1 |
|
Bell Bell Bell |
18 : 1 |
|
Bell Bell Bar |
18 : 1 |
|
Plum Plum Plum |
14 : 1 |
|
Plum Plum Bar |
14 : 1 |
|
Orange Orange Orange |
10 : 1 |
|
Orange Orange Bar |
10 : 1 |
|
Cherry Cherry Lemon |
5 : 1 |
|
Cherry Cherry Bell |
5 : 1 |
|
Cherry Cherry Plum |
3 : 1 |
|
Cherry Cherry Orange |
3 : 1 |
|
Cherry Cherry Bar |
3 : 1 |
Let R be a random variable representing your return on a $1 slot machine.
Then R = k where k = ___________________________________________________
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k
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P(R=k)
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What is the expected return ?