This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore the chance of hitting five cherries in a row is 1/5 x 1/5 x 1/5 x 1/5 x 1/5, or 1/3125, or 0.032%. Your odds of winning are better than this, as you can hit five bells, five whistles or five of any other set of symbols, so on this machine your odds of any set of five are actually 5 x 0.032%, or 0.16%. Slot machines are a very popular form of gambling in North America. For example, Ontario, Canada, has approximately 23,000 slot machines, which in the fiscal year 2002-2003 generated approximately three billion dollars “after prizes/winnings but before operating expenses” (Williams & Wood, 2004, p. This revenue is greater than that.
- Slot Machine Probability Calculation
- Slot Machine Probability Calculator
- Slot Machine Probability Of Winning
A slot machine is a gambling game with spinning reels. Most slot machine games have 3 spinning reels or 5 spinning reels. Each reel has multiple symbols on it. The spinning reels stop at random, and if matching symbols line up across a pay line, the gambler wins prize money. Early slot machines had a single payline across the center of the reels. Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you’re ahead. If you win $100, cash out $50 and play with the rest, for example.
- Appendices
- Slots Analysis
- Miscellaneous
Introduction
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 |
![Slot Machine Probability Slot Machine Probability](https://thumbs.dreamstime.com/z/slot-machine-numbers-16491714.jpg)
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.
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 | |
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 Slotocash no deposit coupon codes. | 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 .
Slot Machine Probability Calculation
![Slot Slot](https://lh6.googleusercontent.com/-i1hjAJy_kN4/UswKxmhrbPI/AAAAAAAAB1U/82wq_4ZZc-Y/DE6B0895-6FC1-48BE-AC4F-14D1B91AB75B.jpg)
Thus for every unit played the machine will return back 94.545%.
Slot Machine Probability Calculator
Go black to slot machines.
Slot Machine Probability Of Winning
Written by: Michael Shackleford