3d6 vs. d4+d6+d8 vs. d5+d6+d7 Bell Curve



If there's one thing for sure about gamers, they love their polyhedron dice. Every gamer I know has purchased more than one set of Poly's. Even people like me, who play mostly GURPS, have more than one set of dice. I even bought a weird set of dice which included a d3, d5, d7, d16, d24, and d30 (pictured to the right). There's just something about those little platonic solids, and even the nonplatonic ones, and once you have those dice you want to use them, which I don't really get a a chance to do with GURPS. Here I give some advice on using Polyhedral dice with GURPS.
The most important roll in GURPS, and the one you will do the most, is rolling 3d6. This is used for all skill checks, attribute checks, disadvantage SelfControl rolls, rolling on the Freight Check table and on the Reaction Table. Thus it is the most obvious place to do a little switcheroo. The easiest switch is to roll 1d4+1d6+1d8 instead of rolling 3d6. Or, if you have the weird set of die you can use 1d5+1d6+1d7. This will change the shape of the bell curve slightly, and increases the chances of rolling the extremes (36, 1518) slightly while decreasing the chances of rolling the central values (813) slightly. However, these changes are all small, less than 1% difference, making it a great place to do a simple change which gives the game a vastly different feel.
Die  Avg. 

d3  2 
d4  2.5 
d5  3 
d6  3.5 
d7  4 
d8  4.5 
d10  5.5 
d12  6.5 
d16  8.5 
d20  10.5 
d24  12.5 
d30  15.5 
For damage rolls there's a few ways you can convert them. Each +1 to damage moves a die up one step from 1d4 to 1d6 to 1d8 to 1d10 to 1d12. So 2d6+1 yields the same average as 1d6+1d8. Similarly, each 1 moves the dice down one step. These can even be combined, turning 2d6 into 1d4+1d8. And like the skill roll, you can always convert 3d6 into 1d4+1d6+1d8. You could then use +1's to convert the dice into something higher, for example 3d6+3 could be 3d8, or even 1d6+1d8+1d10.
A second option is to find the average damage for a specific roll by multiplying the number of dice by 3.5, then adding or subtracting any bonuses or penalties to the roll. For example, 3d6+3 averages to (3×3.5)+3=10.5+3=13.5. From there you just need to figure out the best dice to use for the conversion and can subtract, in this case it's a little over a d24, so you could use 1d24+1 since the average of 1d24 is 12.5, adding +1 to that results in the same 13.5 average. It also happens to be 3×4.5=13.5, which is the average result of a 3d8. 2×6.5=13 is the average of 2d12, which is just below the target number we're looking for. Generally, when converting dice I recommend using at least two dice, so I would would recommend using 2d12 or 3d8 over 1d24+1.
Another option is that you can use or create a standardized conversion table like the one I provide below to help you convert damage dice rolls into a polyhedron roll. I purposely didn't use the weird dice on the table because most gamers are unlikely to have them, but on your own table you could use them.
In general I would also suggest that you do all the conversions away from the gaming table, and if a new damage needs to be figured out ingame just use the standard GURPS rules using d6's until you have a chance to convert it away from the game. It'll make things less confusing.
d6  Poly  d6  Poly  d6  Poly  d6  Poly  

1d2  1d41  3d+2  3d81  6d+2  2d20+2  9d+2  3d20+2  
1d1  1d4  3d+3  3d8  6d+3  4d10+2  9d+3  5d12+2  
1d  1d6  4d2  2d10+1  7d2  5d8  10d2  6d10  
1d+1  1d8  4d1  2d12  7d1  5d8+1  10d1  6d10+1  
1d+2  1d10  4d  2d12+1  7d  5d8+2  10d  6d10+2  
1d+3  1d12  4d+1  2d12+2  7d+1  5d102  10d+1  8d8  
2d2  2d4  4d+2  4d6+2  7d+2  5d101  10d+2  6d122  
2d1  2d4+1  4d+3  4d81  7d+3  5d10  10d+3  6d121  
2d  2d6  5d2  3d101  8d2  4d12  11d2  7d102  
2d+1  2d6+1  5d1  3d10  8d1  4d12+1  11d1  7d101  
2d+2  2d8  5d  3d10+1  8d  4d12+2  11d  7d10  
2d+3  2d8+1  5d+1  3d121  8d+1  6d8+2  11d+1  7d10+1  
3d2  2d81  5d+2  3d12  8d+2  8d6+2  11d+2  7d10+2  
3d1  2d8  5d+3  3d12+1  8d+3  6d102  11d+3  9d8+1  
2d102  6d2  2d202  9d2  3d202  12d2  4d202  
3d  2d8+1  6d1  2d201  9d1  3d201  12d1  4d201  
2d101  6d  2d20  9d  3d20  12d  4d20  
3d+1  2d10  6d+1  2d20+1  9d+1  3d20+1  
3d82 
Copyright © 2018 Eric B. Smith