Mini Slot Machine
Gambling is mostly a losing game. The most popular games in casinos are slot machines. Modern slot machines are electronically controlled; the spinning wheels, sounds, and other props are only window dressing.
In this unit we implement and play with a mini-slot-machine. You may pretend that you are playing for pennies, or if you are a gambler you may imagine that you are playing for dollars.
The probability of the payoff (for a 1¢ play) are:
| payoff | 0¢ | 1¢ | 2¢ | 10¢ (the jackpot) |
| probability | .65 | .2 | .1 | .05 |
So the average return for 10¢ is 9¢ (the payoff for 1¢ is.65*0 + .2*1 + .1*2 + .05*10 = .9, and the payoff for 10¢ is ten times more, or 9¢). This means that the expected profit rate for the "casino" is 10% per play. In real casinos you sometimes know the rate of profit, but you are never told the actual distribution.
Task 1.
Design a program for the TI-34 II that generates the values 0, 1, 2, and 10, with the probabilities .65, .2, .1, and .05
The key point is to create a step function, f:
This function f returns:
f(x) = 0, for 0 ≤ x < .65;
f(x) = 1, for .65 ≤ x < .85
f(x) = 2, for .85 ≤ x < .95
f(x) = 10, for .95 ≤ x < 1.
Now if we compute f(RAND), where
0 with probability .65,
1 with probability .85-.65 = .2,
2 with probability .95-.85 = .1, and
10 with probability 1-.95 = .05.
Implementation:
Define
OP1=
OP2=iPart(Ans+.35)+iPart(Ans+.15)+8iPart(Ans+.05)
Explanation.
1 - .65 = .35 is the probability that the payoff is bigger than 0.
So if Ans ≥ 0.65, then iPart(Ans + .35) = 1.
In addition, if Ans ≥ 0.85, then iPart(Ans + .15) is also 1.
And if in addition, Ans ≥ 0.95, then 8*iPart(Ans + .05) equals 8.
So payoffs of 0, 1, 2, and 10 are generated with the probabilities .65, .2, .1, and .05.
Remark.
Study OP2 carefully in order to see that for values x between 0 and 1 it computes f(x). Experiment with it as follows:
Enter
x [=]
OP2
Run the implementation of a mini-slot-machine,
Repeat,
OP1 OP2
Task 2.
Students work in groups of 4. Each student starts with 20 pennies. One student is the "cashier" (who gets 20 extra pennies) and keeps pennies on a paper plate. The remaining three students are "gamblers". A gambler pays a penny to the cashier and "plays" the calculator. If he/she wins, the "cashier" pays out the winnings.
The game ends when a "gambler" decides to quit, or loses all the money, or the total time allotted for the game by the teacher (for example 10 minutes) runs out.
All students (including the cashiers) record their winnings or losses.
After the game is played a few times, students discuss their strategies and the outcomes.