Friday, March 27, 2015

Rolling for advantage and disadvantage in GURPS

The Fudge RPG I been working stalled partly because +1 or -1 is just too great a modifier using Fudge Dice. So I been looking at Heroes and Other Worlds by +c.r. brandon, an interesting mechanic that the game add d6s to represent difficult rolls like use of a untrained skill. If you are untrained you roll 4d6 and see if you succeed instead of the normal 3d6. It is an elegant solution to what GURPS does with modifiers like the ones for default skill use.

By now most of you heard that DnD 5e handles modifiers with its system of advantage and disadvantage rolls. For a positive modifier roll 2d20 and take the best roll. For negative modifiers roll 2d20 and take the worse roll. Again elegant.

For the following I am using the calculators at Any Dice.

The problem with adding 4D as a general negative modifier for system using 3d6 is that it radically changes the odd. Far further than what advantage/disadvantage does for DnD 5e. For example rolling a 10 or less on 3d6 is 50%. Change it to a 4d6 roll it becomes 15%. In contrast in 5e's rolling 11 or better on a d20 (50%) changes to  25% odds on a disadvantage and to 75% odds on a advantage.

Yes I realize 3d6 is a bell curve and the d20 uses linear probability. Regardless it is obvious that adding an extra d6 to a 3d6 roll low system is a major hit. And going the other way for a positive modifier (2d6) looks to be too generous. But then I figured out another way.

Why not roll 4d6 and take the three LOWEST when you want to grant a positive modifier and take three HIGHEST when you want a negative modifier?

I plug in the formula into Any Dice and found that the 10 or less odds of 50% now become roughly 73% for a positive modifier, and roughly 27% on a negative modifier.

Increasing the dice to the three lowest or three highest of 5d6 results in 86% for a positive modifier and  14% for a negative modifier.

Critical have 1.85% chance of occurring (roll a 4 or 3). On 4d6 take the highest or lowest 3 Criticals now go to 5.79% odds with a positive modifier, and 0.39% with a negative. With 5d6 it is 11.39% and  0.08%.

I like this, now sure how and when I will use this mechanics but I am adding it to my bag of stuff. If you like advantage and disadvantage in 5e and want to use it in GURPS, I think this is easier to implement than rolling twice. Plus the it has the virtue of working perfectly with all the quirks of a GURPS success roll as in the end you are still only totaling 3 d6s.

It was pointed out to me by +Douglas Cole that adding 1 die and taking the highest or lowest 3 is roughly equivalent to +1 or -1 to the 3d6 roll. This is a result of how the bell curve works with multiple dice.

For some adding d6s instead of modifier may be more elegant as you don't have to remember the rules for calculating the odds of a critical, 3 or 4 is always critical success and 17 and 18 is always a critical failure.


Douglas Cole said...

highest 3 of 4d6 is equivalent to +2, not +1, at least in the shift of the 50% point. Highest 3 of 5d6 is +3.

Douglas Cole said...

I'll post a follow-up linking to your post. It's actually topical for something else I'm doing too.

Robert Conley said...

Enjoyed reading your commentary. Looking forward to seeing what you do with the idea.

Unknown said...

It's definitely interesting how they have the two roll system. We play
. In it PCs have strength tiers (+1 to +5). These then are added if a PC should have a bonus or removed if a penalty. I like having a solid target like that and it helps to feel like a PC is getting better as they level. Thanks for crunching some numbers to see how it compares.