Inverse dice probability?

[ffilz]

If you want a standard bell curve, you can even use Excel (and presumably other spreadsheet programs) to generate the chart for you. Of course the chart mentioned in the cross referenced thread is actually an open ended chart that theoretically allows any point on the infinite bell curve, but in practicality doesn't because you can't pregenerate an infinite chart, on the other hand, you really don't need the results that have an infintesimal probability.

Of course if you want to provide hard limits at one or both ends of the chart, you can do that.

The reccomendation of using 5% intervals is good, though you need to decide what you want regularly distributed, the points on the chart, or the results. For example, if you want the chart to have an entry every 5% (which also only works if you provide hard limits at both ends), then your results will not be evenly spaced (so you might find that the available results say are 10, 30, 35, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 60, 65, 70, 90). You'll also find that you either have an odd number of results and thus have a center result, or your have an even number of results with a pair of results that straddle the 50% boundary. In the chart I presented, there is not the same chance of getting a +1 as a -1 because of this. Of course you see this in regular dice distributions also. 2d6 has an odd number of results with a center result, while 3d6 has an even number of results with a pair that straddles the center.

I'd be happy to try and answer questions on how to produce the results you want from such a chart.

Frank

[geminidomino]

If you want a standard bell curve, you can even use Excel (and presumably other spreadsheet programs) to generate the chart for you.

Yeah, I've got OpenOffice Calc running with this as I type this. :)

The reccomendation of using 5% intervals is good, though you need to decide what you want regularly distributed, the points on the chart, or the results. For example, if you want the chart to have an entry every 5% (which also only works if you provide hard limits at both ends), then your results will not be evenly spaced (so you might find that the available results say are 10, 30, 35, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 60, 65, 70, 90).

The points. The type of limited result set you mentioned are EXACTLY what  I want. I want there to be much more of a chance of rolling up an "Average Joe" (with abilities in the 40-60 range) than a Superman with 4 out of 6 scores in the 90s.  

I'd be happy to try and answer questions on how to produce the results you want from such a chart.
Frank

Well, I used the appropriate functions to come up with both a probability and cumulative probability tables, as well as a table of standard deviations for reference(I wrote the spreadsheet so that the mean and STDDEV can be adjusted by changing one cell each).

Now I'm just trying to work out how to tie a score to a roll to make it usable. ;) It would be easier with a graph, but as I don't have Excel, I have to make do with the table.

[geminidomino]

Now I'm just trying to work out how to tie a score to a roll to make it usable. ;) It would be easier with a graph, but as I don't have Excel, I have to make do with the table.

Woot! I figured it out! Dummy that I am, I kept spacing the "dice points" (the graph reigion separators) evenly by the scores and wondering why it still came out linear!

I put 1 die point at each 5% boundary (or close to it) and came up with the following table (using a "Realistic graph, STD DEV of 20 and a MEAN of 50):

ROLL -> Score

1 -> 10 (fudged to make 10 a minumum score)
* -> 18 (skipped)
2 -> 25                      
3 -> 30
4 -> 34
5 -> 37
6 -> 40
7 -> 43
8 -> 45
9 -> 48
10 -> 50
11 -> 53
12 -> 56
13 -> 58
14 -> 61
15 -> 64
16 -> 67
17 -> 71
18 -> 76
19 -> 85
20 -> 90


That works out just like I'd hoped. :) Using a chart like that was really a brilliant idea!

[ffilz]

Interesting that your chart isn't exactly symetrical, but that's a cool thing about using a chart, you can fudge the results around for your own purposes. If you relied on a 20d6 model or something like that, you're stuck with the result curve the dice generate.

The one thought I would have on using evenly distributed values in the random column as opposed to evenly distributed values in the result column is whether the game significance of a 48 vs. 50 is sufficient to justify the slight extra complexity vs a chart using 1d100 with a wide range producing 50, and smaller ranges producing 45 and 55, etc. out to 10 and 90 with very small ranges. Remember, you use the table once, but you constantly use the results.

On the other hand, it may be nice to have room for apparent differences between "average" characters without there being real differences. For example, if you were to randomly simulate a race with such a table, you wouldn't want 70% of the people to finish with the same time, ideally you would want each finisher to have a different time, but most of them happen to be about the same. If two PCs happened to finish in the center of the grouping, they will want to know who finished first even though the order they finished is irrelevant to the race as a whole, so you don't want to tell them they both finished somewhere between 16th and 85th place.

Of course what this points out is that when you are developing dice mechanics, you need to keep in mind how you will use the results and applyt meaning to them, not just how you generate the results.

Frank

[geminidomino]

Checks are going to be done with roll-under D&D style. Either you hit or miss. For things like running, swimming, meditating, etc, I'm probably going to used an "extended check" style rule... Kind of like "you roll till you fail a check, then you're done/out/etc..."

For all I know, I'll have to redo the charts and/or scrap the whole idea after I get some playtesting in. :)

[M. J. Young]

10d9 was the first thing that occurred to me (sorry--I've been away a few days, so I'm coming to the party late). Of course, d9's are problematic. You can get at them by ignoring the 0's on d10's or by the rather complicated method of using (1/2 d6)x(1/2 d6) for each of them, neither particularly fast in play.

I'm surprised, actually, that my second thought was not spotted by anyone. I thought Walt was going to nail it, but he was all around it because he was looking to match standard dice. (20d5)-10 will get you 10 to 90. Since (1/2 d10) works for d5 pretty easily, it's not as difficult to roll as all those d9's. On the other hand, this is going to have a very steep curve--5^20 permutations, 1 chance of rolling 10, 5 for 11, 15 for 12, and I think if I set my computer to doing those calculations I'd be waiting quite a while for the results.

--M. J. Young