- Appendices
- Slots Analysis
- Miscellaneous
Introduction
Sittman and Pitt of Brooklyn, New York developed a gambling machine in 1891 that was a precursor to the modern slot machine. It contained five drums holding a total of 50 card faces and was based on poker.The machine proved extremely popular, and soon many bars in the city had one or more of them. Players would insert a nickel and pull a lever, which would spin the drums and the cards that. A SIMPLIFIED SLOT. To see how slots pay less than true odds to give the house an edge, let’s set up an example that’s as streamlined as slot odds can get, a game of the type used in the early decades after Charles Fey invented the three-reel slot machine in 1895.A hypothetical three-reel slot game with one 7, two bars, three cherries and four watermelons per reel would have 1,000 possible.
From time to time I get asked specifically how to calculate the return for a slot machine. To avoid breaking any copyright laws I won't use any actual machine as an example but create me own. Lets assume this is a standard three reel electro-mechanical slot machine with the following payoff table based on the center line:
Slot Machine
| Center Payline | Pays |
|---|---|
Three bars | 5000 |
Three cherries | 1000 |
Three plums | 200 |
Three watermelons | 100 |
Three oranges | 50 |
Three lemons | 25 |
Any two cherries | 10 |
Any one cherry | 2 |
There seems to be always 22 actual stops on each reel of a slot machine. The following table shows the symbol on each stop as well as the weight.
Slot Machine Three Bars Near Me
Weight Table
| Symbol | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
Cherry | 3 | 2 | 1 |
Blank | 2 | 3 | 3 |
Plum | 3 | 2 | 2 |
Blank | 2 | 3 | 3 |
Watermelon | 3 | 3 | 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.
Most of the symbols occur twice on the reel, and the blank 11 times. The following table shows the total number of weights of each kind of symbol.
Total Weight Table
| Symbol | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
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 pay table 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%.
Go black to slot machines.