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Last Updated: August 19, 2016

# Slot 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.

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