Crazy Probability Math stuff

Kwyndig · Post by **Kwyndig** » Sat Mar 26, 2005 9:46 am

Okay, so I'm kinda designing my own role playing game, and I've got an idea for a dice mechanic, but, I don't know how the probabilities will work out. As experience has shown me (most notedly while playing role-under systems like Tri-Stat) that NOT knowing the probabilities of certain die roles is a hazard of game (or character) design and I don't know enough about statistics and probability, so I turn to the Bulldrek crowd for help.

Now, this part might be a little complicated (and is well beyond my limited experience in the field), but here goes. I'm currently looking at a 2d8 roll-over variable target number system with unusually exploding dice (I may ditch this part and just stick with regular exploding dice if my players can't grasp the idea) where, if you roll any number twice, say the dice are 1,1 or 3,3 for example, they 'explode' and you roll again, continuing as long as both dice end up the same number as the first roll. Of course, for all I know I've just described somebody else's die mechanic...

Ancient History · Post by **Ancient History** » Sat Mar 26, 2005 2:09 pm

Well, let's see. 2d8, added together, gives you possible values of 3 to 15, plus the 1-in-8 chance of an "explosion." The difficulty lies in your target numbers...numbers under 15 will be easier to roll, but numbers higher than 15 might well be impossible since you require an "explosion" to get you over the hump. See what I mean?

Szechuan · Post by **Szechuan** » Sat Mar 26, 2005 2:27 pm

1-in-64 chance of explosion.

1/8 * 1/8 = 1/64

[edit: I suck. Check Moon's post.]

DV8 · Post by **DV8** » Sat Mar 26, 2005 4:25 pm

I'm not really useful in helping you build a game mechanic, and to be honest, I'm also not really interested in the game mechanics. However, once you've figured that out, could you perhaps tell us all a little something about the game?

Ancient History · Post by **Ancient History** » Sat Mar 26, 2005 6:05 pm

Szech: Quite right, I was thinking about the fact there were eight possible explosions. Aargh.

Moonwolf · Post by **Moonwolf** » Sat Mar 26, 2005 6:45 pm

No, the chance of any explosion is 1/8. It's 1/64 for a double, but since there are 8 doubles that's 8/64 chance of any double, which is 1/8 again.

TheScamp · Post by **TheScamp** » Sat Mar 26, 2005 7:13 pm

Right. There are 64 total combinations that can be rolled. Of those, 8 will show the same number on die #1 and die #2. Of course, with trying to match a certain target number, the higher end explosions are going to be much more useful than an explosion of 1's.

Coasini · Post by **Coasini** » Sun Mar 27, 2005 5:20 pm

The problem I have with static numbers of dice (like /always/ rolling 2d8) is you run into the problem that comes with d20 -- That is, your skill becomes irrelevant, you rely wholy on the luck of the dice.
Dicepools eliminate this problem by exponentially decreasing your chance of failure as your skill increases.

That's just something to consider.

Kwyndig · Post by **Kwyndig** » Mon Mar 28, 2005 12:21 am

Coasini wrote:The problem I have with static numbers of dice (like /always/ rolling 2d8) is you run into the problem that comes with d20 -- That is, your skill becomes irrelevant, you rely wholy on the luck of the dice.
Dicepools eliminate this problem by exponentially decreasing your chance of failure as your skill increases.

That's just something to consider.

Actually, in high level D&D, the die roll becomes meaningless as the level of bonuses, skills, etc. exceed +20. But I prefer static die systems over dice pools because of the 'buckets of dice' syndrome.

Coasini · Post by **Coasini** » Mon Mar 28, 2005 3:31 pm

So use a smaller number of dice -- 1 to 5, for example.

And yes, in D&D there does come to be a point where the roll becomes meaningless. I never played high level campaigns of that because they made me ill.

Marius · Post by **Marius** » Mon Mar 28, 2005 6:58 pm

I haven't thought through the full probability curve, because I think it's probably a really odd shape. But at the bottom end it's worth noting: the lowest possible Target Number is 4 (3 being the lowest possible roll, which ought to be a failure). You will only fail a TN 4 task 1 in 32 times. TN 5 fails 1 in 16 times, 6 fails 129 times in 1024 (12.6%), 7 fails 162 in 1024 (15.8%), 8 fails at 17.1% (the denominator of this fraction is 6 digits). Looks like with increases in target number, it doesn't get too much harder to complete a task (provided I'm doing math reasonably well, which is doubtful). That probably changes, though, when you get above 9, which is the peak of the normal curve for 2d8, and where you start getting more significant chances of success in explosion.