An alternative to Simmetry and d20

[JMendes]

Hey, :)

In this thread, we tossed around a few ideas for different fortune mechanics that would obey a certain set of specs. Walt (wfreitag) came up with an interesting table, with rerolls, that exhibited certain interesting behaviors. A friend and I got together and explored this table, and came up with the following possible replacement for the d20:

Code Select Expand

1-19 20-23 24-28 29-34 35-41 42-50 51-59 60-66 67-72 73-77 78-81 82-100
5-r    6     7     8     9     10    11    12    13    14    15   16+r

1-18 19-33 34-45 46-55 56-63 64-70 71-75 76-100
±0     ±1    ±2    ±3    ±4    ±5    ±6   ±(7+r)

In case anyone is wondering, here's how it works: start with the first table and roll d%. If you get an r result, go to the second table and roll d% again, then add or subtract the result to the previous base. If you get an r result again, roll again on the second table and keep adding or subtracting the result until you don't get an r result.

If you are interested, these tables were built with a 0.82 decay rate.

This table has pretty much the same advantages over d20 that Simmetry has, with a slightly worse handling time and a slightly better search time. It has the big advantage over Simmetry that it can generate degree of success in much the same manner as the d20 can.

As soon as I have one, I'll post a table with an odd number of results to this thread.

Comments are welcome, as usual, but this is really a take-it-and-use-it-if-you-like-it-and-want-it post. :)

Cheers.

J.

[marknau]

Philosophically, would you prefer a method that has a lower handling time, even if it means that it is a less-refined approximation of a perfectly symetrical curve with constant decay?

In other words, are you happy with this or are you still looking for a better answer?

-M

[marknau]

In other words, are you happy with this or are you still looking for a better answer?

For example:
Roll 3d6 and add them
Every 1 is a negative reroll. Every 6 is a positive reroll. These cancel each other out.
On the rerolls, a 4,5,or 6 means adjust the original result by 1 in the appropriate direction and reroll again.

This gets rid of the chart, but isn't a perfect logarithmic decay. Is that worth it?

The results over 100,000 rolls was:
-12:    1
-11:    0
-10:    2
-9:    1
-8:    1
-7:   11
-6:    8
-5:   22
-4:   50
-3:   79
-2:  147
-1:  232
 0:  388
 1:  620
 2:  977
 3: 1544
 4: 2395
 5: 3530
 6: 4842
 7: 6438
 8: 7723
 9:10331
10:10760
11:10824
12:10157
13: 7738
14: 6396
15: 4752
16: 3447
17: 2408
18: 1618
19:  997
20:  634
21:  389
22:  215
23:  138
24:   75
25:   49
26:   27
27:   13
28:    9
29:    7
30:    0
31:    1
32:    2
33:    1
34:    1

[JMendes]

Hey, all, :)

Aghh... I haye to be 'reviving' a thread from the 'second page'... I guess the rate of new threads has been up. :)

Anyway, I did promise I'd post an odd-numbered table as soon as I had one, and it just made more sense to post it here than in a new thread. Hope it's forgiven. :)

Anyway, here's the table:

Code Select Expand

1-14 15-17 18-22 23-28 29-35 36-44 45-56 57-65 66-72 73-78 79-83 84-86 87-100
-6-r   -5    -4    -3    -2    -1    0     +1    +2    +3    +4    +5   +6+r

1-21 22-38 39-51 52-61 62-69 70-76 77-81 82-85 86-88 89-100
±0     ±1    ±2    ±3    ±4     ±5    ±6    ±7    ±8  ±(9+r)
The mechanics are the same as in the first post in the thread.

You'll note that this table was built with a slightly steeper decay rate of 0.79. If anyone is mathematically inclined and wants to hear about it, I'll be glad to explain why.

As before, comments are welcome, but this is only a take-it-and-use-it-if-you-like-it-and-want-it post. :)

Lastly, marknau, I appologize for not having replied to your suggestion, though it was not ignored. I'd like to take this opportunity to thank you for taking the time.

Cheers.

J.