[RNG] Progressive difficulty

[Mario F.]

I'm planning to build a table of random special combat effects. Each group of 6 effects is more difficult to achieve than the previous group.

For now I came up with a simple system in which a 1d6 is rolled. Every time a 6 is rolled, I deduce 1 and sum up the result. I stop rolling when no 6 turns up. However, I need your help coming up with the correct formula to calculate the odds for any given number so I can correctly build the table.

Example 1:
1d6 = 5
End result = 5

Example 2:
1d6 = 6
1d6 = 3
End Result: (6 - 1) + 3 = 8

Example 3:
1d6 = 6
1d6 = 6
1d6 = 2
End Result: (6 - 1) + (6 - 1) + 2 = 12

[NeonBlack]

Wouldn't it take you about 5 minutes just to do a simulation?

[Mario F.]

Yes it would. But that wouldn't tell me the formula, now would it?

[NeonBlack]

Okay, I got bored. It looks like the formula is something like

p(n)=(1/6)**floor((n+4)/5)

[Mario F.]

Thanks Neon. I will try this later tomorrow. I'm busted now.
One question though. Should I latter apply a d20, does the formula become (1/20)**floor((n+18)/19) ?

[tabstop]

Thanks Neon. I will try this later tomorrow. I'm busted now.
One question though. Should I latter apply a d20, does the formula become (1/20)**floor((n+18)/19) ?

Assuming you only keep rolling at a 20, yes.

[Mario F.]

Dammit! This produces a very wide gap between groups of similar probabilities. I need this gap to lessen somewhat.

Here's the results for numbers between 1 and 12 on a d6:

1 = 16.67%
2 = 16.67%
3 = 16.67%
4 = 16.67%
5 = 16.67%
6 = 2.78%
7 = 2.78%
8 = 2.78%
9 = 2.78%
10 = 2.78%
11 = 0,46%
12 = 0,46%

Any ideas how I can manipulate the formula to lessen the gap?

[NeonBlack]

You could try doing something with two dice. Or give an extra roll to a six OR a five. What type of distribution are you trying to achieve?

[Mario F.]

Only was able to get back to this tonight.

What type of distribution are you trying to achieve?

Nothing defined just yet. However I gave this a better look and indeed the current results are satisfying for my purposes. So this is pretty much solved.

Thanks once again.