Tri token reroll stats

[Icefyre]

OK, I screwed up my calc on how to drop the last d6 numbers, but 12345 showed me the errors of my ways:

Do it again:

chances of 1 18: 8.1% 1/12 tokens
chances of 2 18: 0.52% 1/190 tokens
chances of 3 18: 0.025% 1/3917 tokens

For octagonals:
Not going to recalc the percentages, but I would still theorize it's 4X better for 3 18's.

[Daisy]

[quote="13":2h5d2r36]you can postulate all you want, but in the end you just have to shut up and reroll and no amount of algorithm-arguing will make it easier. btw those ma/wa stats suck, he rolls str second and doesnt even have %, plus 12 con..
keep goin, and gl [/quote:2h5d2r36]

A few points:

str second and dosen't even have a % Ermmmm I think I said 18/80
plus 12 con Errmmmmmm I think I said 14
he rolls Ermmmmmmm I was a woman last time I looked

I'm still proud of my stats ... keep rolling yourself no one else is going to do it for you

Lots of love,

Daisy

[12345]

He was referring to your AAA BBB CCC conversation you have posted.

Also, what method did Icefyre use to calculate the percentages? I know I've rolled a fair number of 2x18s in 100 rolls.

[Icefyre]

Using the probability of 1.62% to roll an 18 for 4d6 dropping 1d6,
you have 5 chances on a roll to get an 18.

For 2 and 3 18's, using conditional probability, (i.e., you already have 1 18) then you have 4 chances to get another 18, and 3 to get a third, with the same 1.62%, multiplied by the previous probability for the first and second 18's.

So. P2 = P1 * 4*1.62%, and P3 = P2 * 3*1.62%.

It's pretty straightforward. The harder part is determining the number of possible outcomes.

Fine: I recalculated Oct's as well. Unfornately, it's not as improved as first erroneously predicted. Number of states is only 1069 vs the std 1296. So, it's only twice as good or so.

For 1 18: 9.8% (1/10)
For 2 18: 0.77% (1/130)
For 3 18: 0.0045 (1/2198)

[12345]

Ok... this was bothering me, so I decided to figure it out:

Odds of rolling each stat:
03 - 1:1296 (0.08%)
04 - 4:1296 (0.31%)
05 - 10:1296 (0.77%)
06 - 21:1296 (1.62%)
07 - 38:1296 (2.93%)
08 - 62:1296 (4.78%)
09 - 91:1296 (7.02%)
10 - 122:1296 (9.41%)
11- 148:1296 (11.42%)
12 - 167:1296 (12.89%)
13 - 172:1296 (13.27%)
14 - 160:1296 (12.35%)
15 - 131:1296 (10.11%)
16 - 94:1296 (7.25%)
17 - 54:1296 (4.17%)
18 - 21:1296 (1.62%)

I'm leaning more and more toward the idea that rolls get a +1 to them.

[12345]

This is what I suspect the actual odds are:

04 - 1:1296 (0.08%)
05 - 4:1296 (0.31%)
06 - 10:1296 (0.77%)
07 - 21:1296 (1.62%)
08 - 38:1296 (2.93%)
09 - 62:1296 (4.78%)
10 - 91:1296 (7.02%)
11 - 122:1296 (9.41%)
12- 148:1296 (11.42%)
13 - 167:1296 (12.89%)
14 - 172:1296 (13.27%)
15 - 160:1296 (12.35%)
16 - 131:1296 (10.11%)
17 - 94:1296 (7.25%)
18 - 75:1296 (5.79%)

Using these numbers, only 136:1296 (10.5%) of the stats rolled would be 9 or less. Over 5 stats, this gives about a 50% chance of the set being rerolled for an oct token... which is just about what I worked it out to be when we were playing with octs a few months ago. So, I have good confidence that this is close to actual.

[Icefyre]

I got this same distribution. Except, it's 136 results are less than 9, if you add in the 91 cases for a 9, you get a total of 227/1296 or 17.5% that are rerolled. [1+4+10+21+38+62+91 = 227].

If that's true, then it's 87% chance (5*17.5) that any roll will need to be rolled again because of a low stat on an oct.

[Icefyre]

I meant, I got the same distribution in your first post...what happened to a 3 value in your second post? Your stat didn't include dropping the low die roll, it started with a 4. So, I would add in the other 91 cases you had listed at a 10.

[12345]

Simple, I added +1 to each result, so the 3s became the 4s and so on up to 18, which is the total of 17 and 18 together. I did this for 2 reasons:

1) Many months ago, I was trying to decide if octs were worth it, so I collected all my tri/hex rolls and those of other players. In the end, I determined that only about half had a stat of 9 or less and would be rerolled. Oddly, the 10.5 percent works into this rather nicely.

2) During that same time, I was rolling a fair number of 18s. They were usually followed immediately by garbage, and I don't think I was pulling in quite 1 in 4.. but the frequency wasn't horrid. This also follows on that line. I'd have to check out my reroll file to get the exact percentage though.

What I don't like about it is that it figures using these numbers and your equation that a 3x18 happens about 1 in 90 rolls.. and I rolled over 200 and never got one. Then again, I know folks that rolled like 10 times and got stats better than I've ever dreamed of. Go figure... law of averages and the universe hates me.

Another thing, while I've RARELY heard of someone rolling a 4, I think the only 3 I've seen was wearing eq. This also fits with that.

It's a guess. It could very well be wrong, but so could everything else that's been posted. It fits better with my experience than the others, so at the moment, it's my favorite theory. If you have reason to believe it's wrong, I'd love to hear it

[Weasel]

yeah ummm.. the 3x18 occurring 1 in 90 rolls just doesn't ring true for me at all- although classo may have a big effect on this.

With all my chars combined, I would've rolled around 1,000 tokens, maybe a bit more rather than less, and guess how many 3x18's I got?

None. Zip. Nada.

They are all WA primes with old classos, except for 1 char, which strangely enough rolled a 2x18 nat relatively quickly (Cl Ma Wa Th).

I have two theories regarding rolling. One is that each stat cycles high to low, but the frequency of the cycles differ from stat to stat, and the range of each cycle also varies depending on classo. The other theory is that rerolls are in part dependent on the time of day when you roll the token (unsure if it's mud time or real time though), but would need a lot of data to make this more than just a theory.

[12345]

Well, going over my old rolls, I don't think I'm far off. I was rolling an 18 about every 4 rolls, and had a fair number of 2x18. Probably why I couldn't roll an 3x18... all my spare 18s went to 2x18s instead.

[Daisy]

If its any help on the question of what are the odds of 0/1/2/3/4/5 18s when rerolling its fairly simple to write a program to replicate the reroll on Sloth and have a look at the results, if you do this enough times you should get something statistically fairly accurate, the time for such a process to run is much quicker if you discard the actual results and only note a counter on the number of 18s found, therefore it is possible to use a much bigger sample.

I've written a VBA script that does just this, and on 100 million rolls I got the following:

no 18s 92,198,879 (92.2%)
one 18 7,552,235 (7.6%)
two 18s 245,545 (0.2%)
three 18s 3,293 (0.003%)
four 18s 48 (0.00005%)
five 18s 0 (0%)

If you want the script (its fairly simple and took me 10 mins to write and about 5 mins to run) feel free to email me or request it here.

Now the thing that strikes me most about this is that over 100million rolls you'd expect it to reflect the sloth experience quite well, in my view it dosen't, I've seen 2 18s much more often than 1 in 500 rolls. I think the model I proposed near the beginning of this thread, which this script is based on, therefore should be seen as suspect and as such most of the odds calculated in this thread by my myself and others are probably just as suspect.


Let me know what you think.

Lots of Love,

Daisy

[Leaf]

Anyone ever noticed if ur get Awsome stats, it's never like 18 18 15 12 10?
It's usually like 18 18 17 16 14 or something really close. Or if u get crap
rolls its like reaaaaaaal crappy 17 15 13 11 9?

I never had a roll that was like 18 18 and then 14 12 10... Or maybe it's
just me throwing more shit in the fan

[Grue]

I did what Daisy did using Excel and got the same results, BTW.

As for really close awesome rolls, I've actually had both. I rolled an 18/x 18 16 18 17 on on char, but also rolled an 18/x 9 17 18 18 on another, with that one crappy stat (I did keep that roll BTW). Then I have had the kind of intermediate 18/x 18 13 18 15 type roll.

But guys remember Illich before you go for the mega stat! 750 rolls and he still hasn't rolled a triple 18.

[Daisy]

Is there any way of asking a Mud admin / developer to clear up once and for all time exactly what the formular is for stat rolling?

This may seem a purely academic excercise to some, but it can help inform decisions about whether to stick with okayish stats or carry on rolling and perhaps never get as good again.

Out of interest my alt as a W/M rolled:
18/89 18 11 16 14 Total 77

I'm fairly confident I could roll better given time, but is it worth the effort it would take? Its supremely playable as it is esp as Dex is so easy to raise by +2.

Lots of Love,

Daisy