October 17th, 2012 at 12:15:55 PM
permalink
I have a doubt regarding the # of hits decided i.e. the number frequency of a particular pay in a slot machine. Suppose, I have 100 prize amounts and a million tickets to assign any one of those prize amounts then what strategy should I adopt to calculate that # of hit frequency or as I can say # of particular prize amounts. Also how can one decide how many hits should be provided to a specific pay in a game if suppose the payout percentage is to be say 95%.
With regards
With regards
October 17th, 2012 at 2:01:58 PM
permalink
Since apparently I'm bored, here are two examples for you that I created via trial and error on a spreadsheet. Both payouts return 95%, one of the machines has a hit frequency of 7.34%, the other, 8.59%. The first machine has a variance ~50% higher than the 2nd machine.
Machine 1: 7.34% hit frequency
Return 95.01%
Standard Deviation: 8.72 bets/spin
Machine 2: 8.59% hit frequency
Return 95.00%
Standard Deviation: 7.19 bets/spin
Machine 1: 7.34% hit frequency
Return 95.01%
Standard Deviation: 8.72 bets/spin
Payout | Probability | Inverse Prob. | Return | Variance |
---|---|---|---|---|
4000 | 0.000001 | 1000000 | 0.004 | 15.9924004388 |
2000 | 0.000002 | 500000 | 0.004 | 7.9924013415 |
1000 | 1.73913043478261E-005 | 57500 | 0.0173913043 | 17.3582745507 |
500 | 0.00002 | 50000 | 0.01 | 4.9810168928 |
300 | 0.00001 | 100000 | 0.003 | 0.8943086783 |
200 | 0.0001 | 10000 | 0.02 | 3.9620879422 |
150 | 0.0001 | 10000 | 0.015 | 2.2215885219 |
100 | 0.0005 | 2000 | 0.05 | 4.905445508 |
50 | 0.004 | 250 | 0.2 | 9.6235872522 |
30 | 0.002 | 500 | 0.06 | 1.6877982638 |
20 | 0.01 | 100 | 0.2 | 3.6290029131 |
10 | 0.0166666667 | 60 | 0.1666666667 | 1.3650241788 |
5 | 0.04 | 25 | 0.2 | 0.6560812175 |
0 | 0.926582942 | 1.0792341998 | 0 | 0.8363431667 |
Total | 1 | 1 | 0.950057971 | 76.1053608662 |
Machine 2: 8.59% hit frequency
Return 95.00%
Standard Deviation: 7.19 bets/spin
Payout | Probability | Inverse Prob. | Return | Variance |
---|---|---|---|---|
4000 | 0.000001 | 1000000 | 0.004 | 15.9924011449 |
2000 | 1.33333333333333E-006 | 750000 | 0.0026666667 | 5.3282680315 |
1000 | 0.000004 | 250000 | 0.004 | 3.9924038522 |
500 | 0.00001 | 100000 | 0.005 | 2.4905093275 |
300 | 0.000005 | 200000 | 0.0015 | 0.4471546031 |
200 | 0.00003125 | 32000 | 0.00625 | 1.2381535801 |
150 | 9.09090909090909E-005 | 11000 | 0.0136363636 | 2.0196283212 |
100 | 0.0004 | 2500 | 0.04 | 3.9243634012 |
50 | 0.003125 | 320 | 0.15625 | 7.5184546023 |
30 | 0.0022222222 | 450 | 0.0666666667 | 1.8753428013 |
20 | 0.01 | 100 | 0.2 | 3.6290365455 |
10 | 0.02 | 50 | 0.2 | 1.6380609697 |
5 | 0.05 | 20 | 0.25 | 0.8201372728 |
0 | 0.9141092854 | 1.0939611007 | 0 | 0.8249310003 |
Total | 1 | 1 | 0.949969697 | 51.7388454536 |