Advantaged, Raw 1d20, and GURPS 3d6 (roll high)

I posted a bit on the merits of the Advantaged/Disadvantaged die roll mechanic that drew some nice commentary on Google+. Part of that was wondering out loud what 3d6, the GURPS basic resolution mechanism, would look like under the type of charts (% success vs. target number) that I used to generate the results.

Good idea, and why not?


One caveat: to make the results sensible, I changed 3d6 from roll low to roll high, so to keep the same flavor. As long as you’re not layering on modfiiers, and the target numbers are in the 1-20 range, this should be decent enough for illustrative purposes.

Edit: I went back using AnyDice.com and got exact figures, thanks to the inherent friendliness of the interface. So the caveat about simulations no longer applies.

Chart Me

First, while I have a nice, intuitive notion of the probability of success for GURPS rolls, putting them up against each other is still eye opening.

The 3d6 curve looks just like the Advantaged curve for low target numbers. Up to 5-7, 3d6 and the roll twice, pick the best look pretty much indistinguishable.

After that, though, it goes down hill fast. For target numbers up through 8 you have an advantage over 1d20, but at 9 you’re basically even, and after that, at 10 and higher, you’re getting very unlikely to succeed where the 1d20 and 1d20 (Advantaged) rolls are still quite favorable. The largest difference between the advantaged and 3d6 in terms of an effective bonus on a 1d20 roll happens at target 13-14 . . . but the fact is the benefits of being Advantaged (1d20) vs 3d6 start at a target difficulty of only 5, and basically get bigger as you go higher.

And of course, you can’t roll 19-20 on 3d6, so there’s that.

Table

The “bonus” – or in the 3d6 case, sometimes a penalty – is simply the delta between the Advantaged or 3d6 roll percent chance of success and the raw 1d20 curve, divided by 5%.

 The bonuses for 3d6 are slightly smaller, only up to +4, while the penalties cover the same range that being Advantaged cover in bonus – that is, up to a -5 bonus while Advantaged covers a local +5.  

Having fixed a few of the errors in the original post, things work out better. The average bonus on the advantaged roll is +3 (exactly 3.33), even though the actual average roll is 13.8.

Parting Shot


Hey, we just proved that 3d6 roll high is harsh at high difficulty numbers. Woo hoo!

More seriously, for most of the range from 13-18 you’re at a -3 or -4 equivalent penalty relative to the raw 1d20 (and still more vs advantaged 1d20). At low targets, it’s reversed, with a +3 or +4, but that’s the regime in which you more or less expect to make the roll anyway.

All in all, it’s why being a few points higher in skill in GURPS is such a big deal; it’s the equivalent (given a +1 bonus for every +2 attribute) in many cases to the difference between a 10 and an 18 DnD flavored stat!