Fate Minus d6 and Counting

I recently ran a game for the Emerald City Gamefeast using Starblazer Adventures. The mechanics are a variation of the FATE mechanics used in Spirit of the Century (SotC). Skills are rated from 0 to 4, to higher for more experienced characters. SotC uses Fudge dice to give a roll from –4 to +4. Starblazer Adventures uses the more readily available six-sided dice (d6). To roll, a player rolls one d6 and adds the result to their skill and another and subtracts the roll. This yields a spread from –5 to +5 on the roll. For reasons laid out in my post on SotC combat, and the fact that all the players would have d6s available, I thought that this option was worth trying.

Overall, the mechanic just felt like it had too much variance, and several players expressed the same sentiment. Obviously, at the edges this is clearly the case. The d6-minus-d6 (d6–d6) mechanic has a 1/ 36 chance of yielding a –5, the same for +5. In contrast, four Fudge dice have a 1/ 81 chance of a –4 or a +4. Also the spread, -5 to +5, is over twice the range of the skills, 0 to 4 (see Figure 1).

However, in thinking about the mechanic I came to wonder if it was more a matter of perception rather than really being so much worse than Fudge dice. Now, Feng Shui uses a d6–d6 die mechanic, and the dice even “explode”, resulting in even more variance than the Starblazer mechanic. Yet Feng Shui never felt too roll-dependent. Of course, Feng Shui skills tended to be in the 12 to 15 range and thus around the spread of the roll rather than less than half of it. However, I’ve played in several d20 games where characters’ best skills were at +11 or +12, about half of the spread of a d20, and people didn’t really complain about too much variance. And that is with a d20, which has a flat distribution and so significantly higher variance than d6–d6.

So the question becomes, what do the numbers really look like in practice? Figure 1 shows the distribution of four Fudge dice versus a d6–d6 roll while Table 1 shows the chance of succeeding on a non-combat roll for given difficulties.

Table 1: Comparison of 4 Fudge dice with d6 minus d6

Skill relative to difficulty	Chance of success
	4 Fudge	d6 – d6
5	100	100
4	100	97
3	99	92
2	94	83
1	81	72
0	62	58
-1	38	42
-2	19	28
-3	6	17
-4	1	8
-5	0	3

While Figure 1 clearly demonstrates more variance in the d6–d6 roll, it doesn’t appear to be that radically different. And from the practical standpoint of succeeding on skill rolls, Table 1 shows that the odds don’t change that much except at the edges. In the heat of a game, it seems unlikely that a player would notice the difference between an 81% chance of success and a 72% chance. At the extreme of low player skill the chance of succeeding is greater with d6–d6, something few players complain about. At the other extreme, if the player has a skill 4 or 5 higher than they need for the task why bother to waste time rolling?

This left me wondering whether the response to the die mechanic was partially psychological. After all, the popular d20 uses a higher variance mechanic. But with d20 the result is always positive, a skill of +10 with the lowest roll, 1, would yield an 11. d20 games also have take 10 and take 20 mechanics that help smooth things out. Of course, FATE has a similar concept, the game master can assign an automatic success if a character’s skill exceeds the target number. However, unlike the always positive d20, with the d6–d6 mechanic even the highest skill can still end with a negative roll, 4 –5= -1.

One way to test if this is really psychological would be to just use a 2d6 and add skill mechanic. The average result for d6–d6 is a 0 while it is 7 for 2d6. However, the distribution around the average roll is identical between them.

The reason FATE uses a distribution around zero is that skill numbers are associated with descriptions of their proficiency, i.e. a +4 skill is a great skill. The idea is to get away from saying, “I roll a 4”, and instead say things like “I make a great leap.” In practice, this pretty much never occurs. So a d6–d6 mechanic can just be replaced with a 2d6 mechanic by increasing the target numbers by 7. What would need a 1 in d6–d6 would require an 8 in 2d6 + skill, and so on. The result would be similar to PDQ, though with a narrower range of skills. This might make the system much more palatable to players, without actually changing anything.

I still think that the d6–d6 has a bit too much variation for my tastes, and intend to try Fudge dice the next time I use the FATE system. However, combat still worries me. The rules from SotC had far and away too little variance in outcomes. Which means that I need to do a statistical comparison between the different combat systems.

An alternative mechanic that I had considered and that Sophie also suggested is to use a d4-d4, rather than d6-d6. This would narrow the range while in theory giving more variance than four Fudge dice. As shown in Figure 2, while it does narrow the range, the probability distribution is in fact almost identical to using four Fudge dice and so highly unlikely to give better combat results than the original mechanic.

So what did people think of the d6-d6 mechanic? Did you find the swings too large as Rolfe did? Would a more conventional 2d6 plus skill roll be more comfortable?