Gambling GuideSlot Machine Appendix 1
Introduction
Between October 28 and November 1, 2000, I played and recorded 3976 plays at a 25 cent Double Strike machine at the Silver Legacy in Reno. This particular slot machine is a flat top made by IGT and is Silver Legacy machine number 4533. Following is the pay table for said machine. Some sybmols were marked with the word "double", in which case the total prize was doubled, except for three red double sevens.Double Strike Pay Table
| Combination | 1 Coin Pays | 2 Coin Pays |
|---|---|---|
| Three red double 7s | 2000 | 5000 |
| Three red 7s | 200 | 400 |
| Three blue 7s | 100 | 200 |
| Three green 7s | 40 | 80 |
| Any three 7s | 20 | 40 |
| Three 5 bars | 20 | 40 |
| Three single bars | 10 | 20 |
| Any three bars | 5 | 10 |
| Any three symbols | 2 | 4 |
As I played I wrote down where the payline symbol on each reel. By also observing the symbols above and below it did not take long to piece together the exact order of symbols on each reel. Later I entered the outcome of each play into a spreadsheet and tabulated the results. The following table shows how often each symbol occured over the course of this experiment.
Double Strike Actual Results
| Symbol | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
| Blue 7 | 169 | 156 | 112 |
| Blank | 109 | 178 | 224 |
| Double 5 bar | 138 | 120 | 107 |
| Blank | 166 | 211 | 253 |
| Red 7 | 116 | 115 | 53 |
| Blank | 161 | 199 | 275 |
| Double single bar | 161 | 101 | 125 |
| Blank | 121 | 99 | 104 |
| Green 7 | 322 | 390 | 349 |
| Blank | 251 | 240 | 300 |
| Double blue 7 | 115 | 72 | 51 |
| Blank | 215 | 220 | 292 |
| Single bar | 403 | 353 | 163 |
| Blank | 250 | 248 | 291 |
| Double red 7 | 52 | 51 | 55 |
| Blank | 259 | 292 | 262 |
| Five bar | 392 | 332 | 372 |
| Blank | 139 | 182 | 227 |
| Double green 7 | 113 | 107 | 44 |
| Blank | 110 | 111 | 108 |
| Single bar | 125 | 104 | 102 |
| Blank | 89 | 95 | 107 |
| Total | 3976 | 3976 | 3976 |
The following chart displays the number in the sample at each stop and for each reel. This may better show visually the range in sample.
Assuming these were the exact weighting the following table displays the pay off per coin based on two coins played, the probability of each paying combination, and the contribution to the total return.
| Combination | Pays | Probability | Return |
|---|---|---|---|
| 3 Red 3 Double | 2500 | 0.000002 | 0.58% |
| 3 Red 2 Double | 800 | 0.000013 | 1.01% |
| 3 Red 1 Double | 400 | 0.000022 | 0.87% |
| 3 Red 0 Double | 200 | 0.000011 | 0.22% |
| 3 Blue 3 Double | 800 | 0.000007 | 0.54% |
| 3 Blue 2 Double | 400 | 0.000039 | 1.57% |
| 3 Blue 1 Double | 200 | 0.000075 | 1.50% |
| 3 Blue 0 Double | 100 | 0.000047 | 0.47% |
| 3 Green 3 Double | 320 | 0.000008 | 0.27% |
| 3 Green 2 Double | 160 | 0.000122 | 1.95% |
| 3 Green 1 Double | 80 | 0.000524 | 4.19% |
| 3 Green 0 Double | 40 | 0.000697 | 2.79% |
| Any 7 3 Double | 160 | 0.000136 | 2.18% |
| Any 7 2 Double | 80 | 0.001128 | 9.02% |
| Any 7 1 Double | 40 | 0.002992 | 11.97% |
| Any 7 0 Double | 20 | 0.002526 | 5.05% |
| 5 Bar 3 Double | 160 | 0.000028 | 0.45% |
| 5 Bar 2 Double | 80 | 0.000256 | 2.05% |
| 5 Bar 1 Double | 40 | 0.000771 | 3.08% |
| 5 Bar 0 Double | 20 | 0.000770 | 1.54% |
| Bar 3 Double | 80 | 0.000032 | 0.26% |
| Bar 2 Double | 40 | 0.000321 | 1.28% |
| Bar 1 Double | 20 | 0.001015 | 2.03% |
| Bar 0 Double | 10 | 0.001017 | 1.02% |
| Any Bar 3 Double | 40 | 0.000183 | 0.73% |
| Any Bar 2 Double | 20 | 0.001714 | 3.43% |
| Any Bar 1 Double | 10 | 0.005345 | 5.34% |
| Any Bar 0 Double | 5 | 0.005569 | 2.78% |
| Anything 3 Double | 16 | 0.001189 | 1.90% |
| Anything 2 Double | 8 | 0.010477 | 8.38% |
| Anything 1 Double | 4 | 0.030698 | 12.28% |
| Anything 0 Double | 2 | 0.029908 | 5.98% |
| Total | 0.097644 | 96.73% |
The bottom row in the above table shows a theoretical return of 96.73% based on two coins played. The return with one coin played is 96.62%. Note also that the player can expect to win anything 9.76% of the time. The standard deviation based on maximum coins played is 8.54. It should be emphasized that these statistics are estimates based on actual results. I am not implying that these figures are exactly right. The purpose of this experiment was mainly to illustrate the concept of weighted reels as opposed to providing an exact return or wheel weightings.
Based on the actual distrubtion and assuming 128 virtual stops it can be approximated what the actual wheel weighting are. Following is an educated guess of the actual reel weightings.
Double Strike Approximate Reel Weightings
| Symbol | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
| Blue 7 | 3 | 3 | 2 |
| Blank | 2 | 3 | 4 |
| Double 5 bar | 2 | 2 | 2 |
| Blank | 3 | 4 | 5 |
| Red 7 | 2 | 2 | 1 |
| Blank | 3 | 4 | 5 |
| Double single bar | 3 | 2 | 2 |
| Blank | 2 | 2 | 2 |
| Green 7 | 6 | 7 | 6 |
| Blank | 4 | 4 | 4 |
| Double blue 7 | 2 | 1 | 1 |
| Blank | 4 | 4 | 5 |
| Single bar | 7 | 6 | 4 |
| Blank | 5 | 5 | 5 |
| Double red 7 | 1 | 1 | 1 |
| Blank | 5 | 5 | 5 |
| Five bar | 7 | 6 | 7 |
| Blank | 3 | 3 | 4 |
| Double green 7 | 2 | 2 | 1 |
| Blank | 2 | 2 | 2 |
| Single bar | 2 | 2 | 2 |
| Blank | 2 | 2 | 2 |
| Total | 72 | 72 | 72 |
Based on the approximate weightings the hit frequency is 9.77% and the return is 95.53% with 1 coin and 95.66% with 2 coins.
Written by: Michael Shackleford
