The High Roller Society

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OK, from the last to the first ...

for 5d4      75% - 25% is 294 - 1419    50% is 709     and we have rolled 1264 times already.

for 3d10   75% - 25% is 288 - 1386    50% is 693      and we rolled 2623 times, so this is Outside the middle range  4th Quarter

for 3d8     75% - 25% is 147 - 709      50% is 355      and we rolled 133 times which is Outside the middle range  1st Quarter

for 2d20     75% - 25% is 115 - 554      50% is 277      and we rolled 813 times which is Outside the middle range  4th Quarter

for 4d4       75% - 25% is 74 - 354       50% is 177       and we rolled 387 times which is Outside the middle range  4th Quarter

for 3d6       75% - 25% is 62 - 299      50% is 149       and we rolled 265 times which is Outside the middle range  4th Quarter

for 2d12      75% - 25% is 41 - 199     50% is 99       and we rolled 73 times which is Inside the middle range  2nd Quarter

for 2d10      75% - 25% is 29 - 138      50% is 69      and we rolled 130 times which is Inside the middle range  3rd Quarter

for 3d4       75% - 25% is 18 - 88        50% is 44      and we rolled 87 times which is Inside the middle range  3rd Quarter

for 2d8       75% - 25% is 18 - 88       50% is 44       and we rolled 22 times which is Inside the middle range  2nd Quarter

for 2d6       75% - 25% is 10 - 49      50% is 25       and we rolled 31 times which is Inside the middle range  3rd Quarter

for 1d20     75% - 25% is 6 - 27        50% is 14       and we rolled 6 times which is Inside the middle range  1st/2nd Quarter

for 2d4       75% - 25% is 4 - 21        50% is 11       and we rolled 15 times which is Inside the middle range  3rd Quarter

for 1d12     75% - 25% is 3 - 16        50% is 8        and we rolled 3 times which is Inside the middle range  1st/2nd Quarter

for 1d10     75% - 25% is 3 - 13       50% is 7       and we rolled 10 times which is Inside the middle range  3rd Quarter

for 1d8       75% - 25% is 2 - 10       50% is 5       and we rolled 6 times which is Inside the middle range  3rd Quarter

So as you can see as we got to the higher numbers we are habitually outside the middle 50% range from 25% to 75%.  If everything is truly random we should be inside the middle range just as often as we are outside the middle range.  But our data indicates at low numbers we are almost always inside and at the higher numbers we appear to be always outside the middle range.  so my suspicion is that something about the algorithm resists getting the top die number multiple times in a row.

** The number of times we rolled is going to be skewed a little high because I am just counting posts, not valid posts.  So if someone is supposed to roll 5d4 and instead they roll 3d10, that will count as a roll but they never had a chance of hitting the TN because the roll was invalid.  But the number of invalid posts isn't high, so I'm not going back and checking every roll.

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Not checking every single post? Slacker. :P

Thanks for the analysis. It's interesting.

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Nice analysis @MusicScout.

To me it looks like all is good. Should it not be 50% inside and 50% outside? We've been more often inside that's true. Once we hit below the interquartile range and 3 times above, but 2 times was just exactly at the lowest end, which makes it almost equal. 

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Cyreon,

At a glance things might look OK, but ...

It is the trend.

We were consistently inside the 50% range until we hit 3d6, and we only just made it with 3d4.  Now we are consistently outside the range.  My suspicion is now that we are in higher dice counts, we may see ourselves outside more and more.  As an indication of fairness, we should be inside as many times as outside.  Exactly half-and-half?  No.  But "close", whatever you consider that to be.  But we will have time to see how it plays out.

If I were to compute the spread using thirds or fourths, instead of halves, I think we'd see it more starkly.

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But do you suggest that this bias towards non max numbers happens only between posts or also within one roll? The latter would be easy to test with a couple of 100d6 rolls or so.

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Cyreon,

I think it is within a roll.  I don't think it happens over a series of rolls.  If you want to test for 5-4s on d4s, I think it will happen less often than it should.  But if you rolled 5d4 ten times, I think you will get a reasonable number of 4s, or any other value.

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I see, so you're saying that the algorithm avoids chains of maximum rolls of single die. Which is a problem for us as we are looking for those exact chains. You may be well right, but I don't know why something like that would be implemented in the dice roller tool, though, as it would require additional effort and I don't have it clear what purpose it would serve. Also, we would need significantly larger sample sizes to judge reliably the tails of the distributions and whether or not they fit our expectations, we always stop after we hit the maximum for the first time. 

What would be an appropriate test? Rolling a thousand 3d6? With a chance of 1/216 for the extremes, we should get 4 to 5 threes and 36s. Perhaps I can start that as a hobby project on the dice roller thread. I'm curious if there really is anything weird going on. 

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I don't think the algorithm was intentionally written to clip strings of top rolls.  I think it is just a consequence of the way the algorithm is written.

To test it, I think we should roll a big number of single rolls.  For example, if we rolled 100 d12s, we could compute how many strings of 3, 4 or 5 twelves in a row there should be in 100 rolls.  I'll have to sit down and do a computation like that sometime, and then we can talk about whether it is worth a practical test.

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The best streak of 12s is two 12s in a row which occurred twice. Notably, not a single streak with 1s. Best streak overall is three 6s, which happened once and with no other number having a streak of three. 

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Goin' on a trip, so I'll have to get back with you on the 100-d12s.  I should have plenty of down time so I might have a full analysis of the probability of 12s.  I don't know how hard this will be to compute, but it isn't the hardest probability.

In the mean time, you folks might hit 5d4, so let me know which post.

Cheers!

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Cheerio and safe travels.

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Safe journey and a good rest (referring to down time :))

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