Normally, I would just right a script to answer this question, but I have really been pressed for time lately. Could somebody do this for me?
I'm trying to find the probabilities of getting the numbers 1 - 25 when rolling a d6 with 6's "acing". What this means is if you roll a 6, you reroll and add 6 to the number. As an example, if you roll a 1, the total will be one. If you roll a 6, you will roll again and if you get a 5, the total will be 11. The 6 can "ace" any number of times.
Thanks.
1 to 5: each 1/6th
6 : 0
7 to 11: each 1/36th
12: 0
13 to 17: each 1/216th
18: 0
19 to 23: each 1/1296th
24: 0
25 to 29: each 1/7776th
Thus as you can see, no 6, 12, 18 and 24. Since when you roll a 6, you add at least 1.
And overall, the average roll on an individual d6 that aces (ala Savage Worlds) is slightly higher than its standard average. The websites TROLL or ANYDICE are terrific for this kind of thing, as well as looking in Google for "d6 probability exploding dice".
Anydice: http://anydice.com/
Paste this in, click Calculate: output [explode 1d6]
Troll: http://topps.diku.dk/torbenm/troll.msp
Pick Savage Worlds (d6) from the top right pulldown, click Calculate Probabilities
The average roll?
While 1D6 gives 3,5
The described system in the first post gives 5,04
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Thanks X3M. That was easier than I thought (my Statistics skills are rusty).