[gurps] declining probability

[Captain Joy]

On Monday, June 18, 2007, at 07:37  PM, Max, Dunedin, NZ wrote:

> Hi, age roles, and stuff use declinging probability, ie your stat 
> starts at x, and after a failure, it becomes x-1, and next x-2, until 
> finally it equals x-x, at which stage you are dead, unconciouse, or 
> whatever.
>
> I was woudering if somebody has a table for the progression of how 
> long (many rolls) this takes, as I'm not to hot with staticits and the 
> bell curve.
>
> for example you have a 10, and after two rolls, I believe you (are 
> staticically lickly to ) have a 9, etc.
>
> does anybody have a table...
>
> 11 --> 3
> 10 --> 2
> 9  --> 1.8
>
> (NB:. above were made up numbers as I don' know the real ones)
>
> So then I could just look at the stat's current value at any point, 
> look at the roll interval, and know that (on average) they will hit 
> zero in so many rolls.

Here is what I came up with:

	Avg # or rolls to till you hit 0 given a starting no. to beat
3	3.0046511628
4	4.0235190873
5	5.0720627766
6	6.174103593
7	7.3674737587
8	8.7174737587
9	10.317473759
10	12.317473759
11	14.984140425
12	18.841283283
13	25.012711854
14	35.812711854
15	57.412711854
16	111.41271185
17	327.41271185
18	infinite

For those of you that want to check my math, the above is based on this 
table:

Avg # or rolls to till a loss
3	1.0046511628
4	1.0188679245
5	1.0485436893
6	1.1020408163
7	1.1933701657
8	1.35
9	1.6
10	2
11	2.6666666667
12	3.8571428571
13	6.1714285714
14	10.8
15	21.6
16	54
17	216
18	n/a

To get the first table I used the second table.
To find the value for 3 in the first table, take the value for 3 in the 
second table and add 2 (to represent going from 2 -> 1, then 1 -> 0)
To find the value for 4 in the first table, take the value for 4 in the 
second table and add the value for 3 in the first table.
To find the value for 5 in the first table, take the value for 5 in the 
second table and add the value for 4 in the first table.
etc.

The values for the second table are based on this table:

#	% chance to roll this # or less on three 6-sided dide
3	0.00462962963
4	0.01851851852
5	0.0462962963
6	0.09259259259
7	0.16203703704
8	0.25925925926
9	0.375
10	0.5
11	0.625
12	0.74074074074
13	0.83796296296
14	0.90740740741
15	0.9537037037
16	0.98148148148
17	0.99537037037
18	1

The above table is just statistics.  To get the second table, take 1 / 
(1-value in the above table).
--
captainjoy at mac.com
"It's life, Captain, but not life as we know it." --Commander Spock