Slot Mathematics
Centre Payline | Pays |
3 Bars | 5000 |
3 Cherries | 1000 |
3 Plums | 200 |
3 Watermelons | 100 |
3 Oranges | 50 |
3 Lemons | 25 |
Any 2 Cherries | 10 |
Any 1 Cherry | 2 |
Weight Table | |||
Symbol | Reel1 | Reel2 | Reel3 |
Cherry | 3 | 2 | 1 |
Blank | 2 | 3 | 3 |
Plum | 3 | 2 | 2 |
Blank | 2 | 3 | 3 |
Orange | 4 | 3 | 3 |
Blank | 2 | 3 | 3 |
Lemon | 4 | 3 | 3 |
Blank | 5 | 5 | 8 |
Bar | 4 | 3 | 1 |
Blank | 5 | 5 | 7 |
Cherry | 2 | 2 | 1 |
Blank | 2 | 3 | 3 |
Plum | 3 | 2 | 1 |
Blank | 2 | 3 | 3 |
Watermelon | 3 | 2 | 2 |
Blank | 2 | 3 | 3 |
Orange | 3 | 2 | 3 |
Blank | 2 | 3 | 3 |
Lemon | 4 | 3 | 3 |
Blank | 2 | 3 | 3 |
Total | 64 | 64 | 64 |
There are two interesting things to note at this point. First notice that the first reel is weight the most generously and the third is the least. For example the bar has 4 weights on reel 1 and only 1 weight on reel 3. Second notice the high number of blanks directly above and below the bar symbol. This results in a near miss effect.
Total Weight Table | |||
Symbol | Reel1 | Reel2 | Reel3 |
Bar | 4 | 3 | 1 |
Cherry | 5 | 4 | 2 |
Plum | 6 | 4 | 3 |
Watermelon | 6 | 5 | 4 |
Orange | 7 | 5 | 6 |
Lemon | 8 | 6 | 6 |
Blank | 28 | 37 | 42 |
Total | 64 | 64 | 64 |
Given the two table of weights and the paytable it only takes simple math to calculate the expected return. Following are the specific probabilities of each paying combination. Note that each virtual reel has a total of 64 stops so the total number of possible combinations is 643 = 262,144.
3 Bars: 4*3*1/262,144 = 0.000046
3 Cherries: 5*4*2/262,144 = 0.000153
3 Plums: 6*4*3/262,144 = 0.000275
3 Watermelons: 6*5*4/262,144 = 0.000458
3 Oranges: 7*5*6/262,144 = 0.000801
3 Lemons: 8*6*6/262,144 = 0.001099
2 Cherries: (5*4*62 + 5*60*2 + 59*4*2)/262,144 = 0.008820
1 Cherry: (5*60*62 + 59*4*62 + 59*60*2)/262,144 = 0.153778
The average return of the machine is the dot product of the above probabilities
and their respective payoffs:
0.000046*5000 + 0.000153*1000 + 0.000275*200 + 0.000458*100 + 0.000801*50
+ 0.001099*25 + 0.008820*10 + 0.153778*2 = 0.94545 .
Thus for every unit played the machine will return back 94.545%.
Courtesy of WizardofOdds.com