Math for rolling up stats

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Asaris
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Joined: 2011-07-15 15:02
Math for rolling up stats

I've been trying to figure out how I want my players to roll up stats, and I'd like some help. I feel like (1) 3d6 is too likely to give them crappy stats, (2) 5 sets of 3d6 can take a while, and (3) 4d6 drop lowest makes stats too high. (I'm actually unsure what the expected results of (2) are compared to (3)). What I'd like is a method that reduces the odd of low ability scores about the same extent as method 3, but without increasing the odds of high scores over method 1. Is this just mathematically impossible, or is there an easy way to do it? Or should I just use method 2?

Tywyll
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Well, how do you feel about dice rollers? The ACKS site has a thing where you enter your email address and it auto generates five sets. Bam! Instant results (though it loses the tactile sensation of dice rolling).

I think the bell curve on 4d6 drop lowest is moved over by a couple of points. So the avg is something like 12.5 I think. I could be wrong.

Thomas Weigel
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Joined: 2012-06-20 11:57

Some of the basic probabilities.

TL;DR version:

Number (1) in your post has an average of 10.5.
Number (2) is an average of 12.87.
Number (3) is an average of 12.5.

To make 4d6/drop lowest mathematically equivalent to option (2), allow the players to add a +1 to two abilities or add +2 to one ability, to a maximum of 18 in both cases.

Asaris wrote:
What I'd like is a method that reduces the odd of low ability scores about the same extent as method 3, but without increasing the odds of high scores over method 1. Is this just mathematically impossible, or is there an easy way to do it?

Roll 3d6 in order. For each ability that is 9 or lower, add 1d4-1.

This method will never, ever result in a higher chance of a +1, +2, or +3, but will significantly reduce the likelihood of a -3 (from 0.5% to 0.1%), -2 (6.5% to 2.5%), or -1 (51.4% to 26%). Of course, all of the excess pours into a score of 9-12.

Beragon
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Joined: 2012-02-26 22:57

What do you consider crappy stats? If you think method 2 is too long, then I would suggest something along the lines of the following as a house rule:
roll 3d6 (in order or arrange to taste). Total the modifiers derived from your scores... if this total is -1 or worse, you may re-roll your scores.

Alternatively, you could say "if this total is 0 or worse..."

Example:
8 (-1)
11 (0)
11 (0)
14 (+1)
6 (-1)
12 (0)
The total of the modifiers is -1, so the player could re-roll.

Asaris
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Thanks for the input. I think I'm going to stick with 3d6 in order, reroll if the total modifier is -1 or less. It's a one-shot (hopefully to whet their appetites for a future campaign), so it should be easier for them to deal with low scores.