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?


11 Responses

  1. I don’t “feel” much difference in variability and unpredictability between 4 Fudge dice and d6-d6. However, even though it’s mechanically about the same, I prefer the 2d6+skill vs. average difficulty of 7 of PDQ because (1) it’s faster for me to add everything than to subtract dice then add skill (d6-d6) or add with negative numbers (Fudge dice); and (2) I like the range of variation to be numerically smaller than the mean result value.

    For example, I dislike not only D20 for the insignificance of skill values compared to the importance of the roll result, but many other systems. A game company that is notable for this is R. Talsorian Games; its games Cyberpunk, Mekton, Castle Falkenstein, etc. have all committed this minor sin at some point (for Castle F, it’s with card results rather than dice). Nevertheless, I recognize that this is all a matter of perception if how successful your character’s actions are remains the same.

    Topic switch: one thing I don’t much like about Fudge dice is that in many systems which use them (primarily variants of the Fudge, FATE, and Shadows of Yesterday systems) the maximum and minimum scores you can aspire to are capped at absolute values. The difference between two characters’ skill levels can become a huge handicap. I like system variants that allow you to overcome that at a price, e.g., using FATE Points.

  2. Pretty great analysis, Erik.

    In regards to comparing Starblazer’s mechanic to D&D’s mechanics, I have a few observations:

    In D&D, you may, as you indicated, have a situation where someone’s total attack roll bonus (BAB + dex or str modifier + magic weapon bonus or other boost) is +10. As you mentioned, that pretty much means it’s all about what the die rolls, because the die can contribute up to twice as much as the skill.

    As you said, in starblazers, our skills ranged between 0 and 4. The die roll on top of that was -5 to +5, again just as you mentioned, the die roll is about twice the factor that the skills are. So far, so much like D&D.

    But that’s where things diverge.

    IIRC, in the starblazers game combat was all contested rolls, wasn’t it? I could be remembering wrong, it’s been months.

    If it was all contested rolls in combat, then the variance on our rolls in starblazers then wasn’t just -5 to +5. Against evenly matched opponents, the variation was effectively -10 to +10.

    The equivalent in D&D would be like if you rolled a d20 for your armor class round-by-round, as well as for your to-hit rolls.

    On second thought, it goes beyond even that, because only one side could hit in starblazers. In D&D, you can both hit in a round. If the kobold rolls a lucky 20 and hits the Paladin, the PC still has the chance to counter-attack.

    So the more accurate analogy might be taking just the initiative roll in D&D, and saying whoever got initiative does damage and the other person doesn’t. Then the next round starts.

    As a further wrinkle, in D&D, the numbers don’t reside purely in the middle of the randomness range. In the kobold vs mid-level Paladin scenario, the kobold only hits about 10% of the time, and the paladin hits 70% of the time. Plus, the kobold has to smack the paladin 5 or 10 times to kill him, whereas the paladin drops another kobold with every successful attack roll.

    In our starblazers game, the skills were always within a point of each other, and everyone had the same number of “hitpoints”. Now maybe that speaks more to scenario design than to mechanical randomness, but it was definitely a factor that lead to us feeling the way we did. None of the characters felt like they were actually better at anything than anyone else. Ironically, it may be that the characters were too well balanced.

    Anyhow, that’s all assuming that I’m remembering the contested rolls mechanic correctly. If that wasn’t the case, then I withdraw my arguments.

  3. Thanks Rolfe,
    You remembered some of combat correctly. When you attack you roll an attack roll and they roll a defense roll, so the variance is increased but everyone gets to attack as in DnD.
    What’s interesting is that I decided to try d6-d6 because with Fudge dice one point of skill difference was ridiculously huge. If you run the calculations for using d6-d6 you find that you go from a 50% chance of defeating someone just as good as you, to an 88% chance of defeating someone that you are 1 better than, to a 99% chance of defeating someone that you are 2 better than.
    One skill level may not feel like much, but it makes a big difference.

  4. I think I just figured out why the randomness felt more severe in Starblazers than it does in D&D. (I mean, on top of the “you both roll, so there’s twice the random element” aspect)

    In a game like D&D or Savage Worlds or even Vampire, you have more ways to denote “my character is good at this”. All those fiddly Feats and Edges and Spells and Powers, establish the ways your character shines, and define what makes you good at your niche.

    Under certain circumstances, you get an extra attack, or bonus damage, or prophetic visions, or the ability to move through threatened spaces, or the ability to detect magical traps that other characters can’t even roll for, or healing magic, or, heck maybe you’ve got laser beams shooting out your eyes. Whatever the specifics, chances are you’ve got something you can do, that no one else at the table can. Because your specialness and specialty are represented in multiple ways, no single failed die roll has nearly as much sting.

    In the Starblazers game, all you have is the die rolls. Your character concept may be “Miracle-working Ship’s Engineer”, but the person sitting next to you who’s concept is “Spunky Space Amazon” is probably just one or two points behind you in the Repair skill. When you biff your roll to fix the engines, and they fix the warp drive instead of you, you’re left feeling like your character concept didn’t matter.

    I _think_ the opinion I’m landing on here is that the more you abstract out the advantages of a characters’ focus, the more mathematically significant and dependable they should be.

    That’s not to say that 4 fudge dice would have made it any better. I thought it would, but as you pointed out, the odds weren’t much different. Probably either die scheme would feel just as random and arbitrary.

  5. Rolfe,
    I can see that. Though the same kind of thing takes place in many games, as you mention in your discussion of the ‘me too’ syndrome on your blog.
    FATE is supposed to differentiate between “amazing mechanic” and “spunky space amazon” in terms of the ability to spend fate points as well as skill. If the Amazon has only skill 1 and needs to get a 3, that requires a decent roll, and if they fail, they fail. The Mechanic may have a 3 skill, they can still fail to roll a 3 or better, but they have a better chance, and more importantly they can spend a fate point via “amazing mechanic”. This allows a reroll or simply adding 2 to the roll. So if the Mechanic rolled a total of a 1 they could just spend a fate point and guarantee success.
    Also, Starblazer Adventures has feats, lots and lots of feats. I decided not to use them as it was complicated enough as it was. I also didn’t want people to spend 2 hours making their characters as they read through hundreds of different feats.
    You bring up some interesting points about niche protection. I’ll need to give it some thought before running the system again.

  6. FATE is supposed to differentiate between “amazing mechanic” and “spunky space amazon” in terms of the ability to spend fate points as well as skill.

    Either I’m remembering incorrectly now…
    or I just didn’t grok it at the time…
    or the problem was because my wife and I showed up half an hour late to the first session, and so we didn’t get the full explanation…
    or it was swept up in the “some of your aspects are defined by the other PCs” house-rule…
    or maybe I had it down pat for the first session, and then forgot it during/before parts 2 and 3…

    …whatever the cause or circumstance, I didn’t remember that the fate chips were tied to your aspects.

    In fact, I totally thought that you could spend a fate chip for anything. I’m fairly confident I was using them like bennies in Savage Worlds. So, my apologies for most likely using fate chips inappropriately during your game. I promise, I didn’t mean to cheat.

    That misunderstanding is, I suspect, a significant factor that lead to my feeling that skills and focus were meaningless. I got the impression that anyone could spend them on any roll, which meant they’d let an unskilled character wallop a supposed master, if the “weaker” character had been more conservative with their fate chips in previous scenes.

  7. I like the analysis. As far as d6-d6 rolls in FATE games – I think that ICONS does it right. In ICONS there is only one side rolling, so you don’t have the variance of contested rolls that you have in Starblazers and other FATE games.

    I would support d4-d4 in Starblazers – especially if character apex skills are only +3 or +4. I’d also consider only having players roll, like in ICONS, and using d6-d6 or 4dF.

  8. […] 0, or +1, and adds the results generating a number between -4 and +4 highly skewed towards 0 (see FATE Minus d6 and Counting). The roll is added to their attack skill. The attack roll is then compared to the defender’s […]

  9. […] —– 1. Goblinoid Games http://www.goblinoidgames.com/ 2. Grey Ghost Games http://www.fudgerpg.com/ 3. Very Good Fudge http://www.panix.com/~sos/rpg/vgfudge.html 4. Fate Minus d6 and Counting https://gamefest.wordpress.com/2009/11/24/fate-minus-d6-and-counting/ […]

  10. […] If you are the sort of Gamer who detests multiple special use dice you could forgo the Fudge dice altogether and use two differently colored D6’s subtracting one from the other, or two D4’s in the same way, though this gives different results. […]

  11. […] If you are the sort of Gamer who detests multiple special use dice you could forgo the Fudge dice altogether and use two differently colored D6’s subtracting one from the other, or two D4’s in the same way, though this gives different results. […]

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