Author Topic: How are the numbers affected here?  (Read 2098 times)

Offline SneeR

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How are the numbers affected here?
« on: May 03, 2012, 09:36:10 AM »
I am considering a certain kind of rolling system for my game: 3d6 with a twist.

If you roll natural 16, it counts as natural 20.
If you roll natural 17, it counts as natural 30
If you roll 18, it counts as natural 40

If you roll 4, it counts as natural 0.
If you roll 3, it counts as natural -10

I have never been a fan of critical failures, so the layers are rewarded more for rolling high than punished for rolling low, but this will also help the gap between specialists and nonspecialists. It has the added benefit of keeping things nicely in multiples of 10 at the top and bottom for easy adding.

However, how much does this help? How wildly does this affect RNG? I know the effect may not be much because 3d6 is already pretty stable towards the middle, but does this system make things more swingy?
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Offline sirpercival

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Re: How are the numbers affected here?
« Reply #1 on: May 03, 2012, 09:43:28 AM »
Well, the probabilities become:

-10 * 1/216
0 * 3/216
5 * 6/216
6 * 10/216
7 * 15/216
8 * 21/216
9 * 25/216
10 * 27/216
11 * 27/216
12 * 25/216
13 * 21/216
14 * 15/216
15 * 10/216
20 * 6/216
30 * 3/216
40 * 1/216

For a mean of 10.778.  Not much of a change there...
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Offline RobbyPants

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Re: How are the numbers affected here?
« Reply #2 on: May 08, 2012, 09:23:14 AM »
Also, due to the bell curve nature, just over 80% of your results will fall in the range of 7 to 14. 90% fall from 6 to 15.

So, depending on how your DCs are set, if you lie anywhere near either end of the RNG, you'll be sitting at near auto success or auto failure.

For example, if you need a natural 6 to hit, on a d20, that's a 75% chance of success. In this method, it's a bit over 95% (also note that getting fiddly +1s here and there at this point have a negligible impact on success). Likewise, if you need a natural 16 to hit, it's normally a 25% chance of success on a d20, but it's less than 5% here (although getting small +1s to push you toward the center has a much higher impact).

Also, if someone is hanging around just above or below the middle of the RNG (say around 8 or 13), a +2 bonus or -2 penalty has a much bigger impact on success. For example, if you need a natural 8 to succeed, you have an 83% chance of success. A +2 bonus gives you a bit over a 95% chance of success (a net shift in about 12%). A -2 penalty gives you a 62% chance of success. That -2 penalty just hit you by over 20%! So, against NPCs that are likely hanging around the center of the RNG, a debuffer will be brutal, and buffs on the party can be really strong.
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