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Payout Percentage Calculation
There are 3 reels, each with 10 symbols, so the sample space consists of 1000 equally likely outcomes. There is only 1 way to get three sharks. There are 9 ways to get a different three of a kind. To get two of a kind, there are 3 possible configurations **-, *-*, or -**, times 10 ways to choose the doubled symbol times 9 ways to choose the other symbol. To get 3 different symbols (worth nothing) there are 10 times 9 times 8 ways. These counts are summarized in the 'Number of Outcomes' column of the calculation table below.The probability of each event is the number of outcomes for the event divided by the total number of outcomes.
The values are taken from the pay table.
| CALCULATION | ||||
|---|---|---|---|---|
| Event | Number of Outcomes | Probability | Value | Expected Value Calculation |
| three sharks | 1 | 1/1000 | 200 | 200/1000 |
| other three of a kind | 9 | 9/1000 | 20 | 180/1000 |
| two of a kind | 270 | 270/1000 | 2 | 540/1000 |
| three different | 720 | 720/1000 | 0 | 0 |
| TOTAL | 1000 | 1 | N/A | 920/1000 |
The expected value of 920/1000 is found by multiplying each value by its probability and summing. The expected payout for this slot machine is 92%.
Random Number Generator
This toy slot machine uses a Lehmer random number generator The formula chosen is
Xk+1 = 1111 * Xk mod 3001.
Since 3001 is prime, and 1111 is a primitive element of the units of Z 3001, the formula cycles through all 3000 units: {1,2,3,...,3000}. The first element or seed is given by
X0 = (t mod 3000) + 1
where t is the number of milliseconds since January 1, 1970.
On each spin, the random number is taken mod 1000 so that the cycle of 3000 provides each number in {0, 1, 2,...,999} exactly 3 times. This then determines the spin. For example 123 -> (dog, crow, mouse). (Preceeding zeros are added when it is not a 3-digit number.)
Empirical Testing
It is one thing to calculate a theoretical payout percentage, but to see if that percentage is realized in practice, it is necessary to do a large number of spins. To this end, pressing the Generate Spins button bypasses the 3D model, and taps directly into the random number generator. The resulting spin history is displayed opposite the model as before.
One press of the button simulates starting with 100 coins, and playing until either there are more than 100 coins, or no coins left.
SPIN HISTORY
