Jufo, your apology is immediately accepted.
There is an error in this page:
The standard deviation is proportional to the square root of the number of games, so the SD of 2000 spins is about 214.6 (units). As a percentage of the amount wagered, it is about 10.7%.
GrandMaster,
Thanks for the input. As I said in an earlier thread to Jufo, I appreciate people pointing out any errors. My goal is an accurate publication.
I'm assuming that you got your 214.6 units by the formula: Square Root of 2000 = 44.7 * published SD of 4.8 = 214.6. 214.6 / 2000 ~= 10.7%.
Given the back-and-forth that Jufo and I have been doing, I was also curious as to what minimum sample size (other than the 2,000 rounds currently used) would be required in order to approximate the breakdown presented in the Help file's example.
(I ran these experiments and crunched these numbers yesterday, before I read your post. Jufo's sim has the reel layout for my Hot Peppers slot, so I did the following experiment using this slot rather than the Crazy 8 Line slot referenced in the Help file. However, please note: the SD for Crazy 8 Line, at 4.8, is almost exactly the same as Hot Peppers at 4.7.)
If you've read through this thread, you're aware that I have a table in my database containing 20 million rounds of Hot Peppers. For no reason in particular, I picked 5,000 rounds as a place to start. So, I did what was needed to get the RTP for the first 5,000 rounds, then the next 5,000 rounds, and like that.
(This was kind of tedious, so I did it for only 50 sets rather than the 100 mentioned in the Help file's example.)
Here is the data: Hot Peppers has a Theoretical RTP of 97.48 and a Standard Deviation (SD) of 4.7.
-3 SD | -2 SD | +/-1 SD | +2 SD | +3 SD |
83.38% | 88.08% | 92.78% to 102.18% | 106.88% | 111.58% |
86.51 | 88.14 | 93.23 | 104.16 | 108.64 |
86.55 | 88.66 | 94.22 | 106.48 | |
87.02 | 90.05 | 94.26 | 106.86 | |
87.69 | 90.29 | 94.38 | | |
87.87 | 90.51 | 94.40 | | |
| 90.62 | 94.51 | | |
| 91.05 | 94.65 | | |
| 91.10 | 94.74 | | |
| 91.11 | 94.75 | | |
| 92.08 | 95.39 | | |
| 92.10 | 95.62 | | |
| 92.22 | 96.33 | | |
| 92.28 | 96.42 | | |
| | 96.57 | | |
| | 97.26 | | |
| | 97.37 | | |
| | 98.08 | | |
| | 98.28 | | |
| | 98.63 | | |
| | 99.21 | | |
| | 99.37 | | |
| | 100.03 | | |
| | 101.18 | | |
| | 101.21 | | |
| | 101.50 | | |
| | 101.86 | | |
| | 101.88 | | |
There was one outlier - it was in the +4 SD range at 112.85.
So, a sample size of 5,000 falls reasonably well into the +/3 SD range using an SD of 4.7.
I am going to use my admittedly very limited understanding of your previous post, and perform a similar calculation.
Square Root of 5000 = 70.7 * published SD of 4.8 = 339.4. 339.4 / 5000 ~= 6.8%.
Backing your formula up would result in a sample size of 10,000 yielding an SD of 4.8. However, although 10,000 rounds gives the more precise result, 5,000 rounds is not exactly out of the ballpark either.
I know that when the issue of Theoretical RTP comes up, often the response is "Oh, you need to play a gazillion games before you'll ever see anything approaching that value.", and like that. I'm being facetious, but I'm sure you get my point. A Player can begin to see the statistics come into play with significantly less rounds than a gazillion.
I am thus left to conclude that where you state "There is an error in this page:", you are referring to the sample size of 2,000. If true, I agree. I'll perform some calculations, and run some verification tests, but this number needs to be changed.
Chris