Failures of D20

Matt Miller 

Part of what makes the D20 work is the variable DC. Yet, the use of DC increments on 5 (such as for the falling tables) suggests that d20 is excessively granular.

Rob Hicks 

The d20 system, as I saw it, was a way of doing a percentile in 5% increments. It makes it easy from a game design perspective to understand how much of a bonus you are giving across the board.

 Matt Miller 

That is one of the great virtues of d20: A +1 is a +1. But a +1 just isn't a big enough deal. Our minds can't grasp changes in probability that smaller (Our minds max out at about a 10:1 ratio). So get an effect we can intuit as significant, DnD requires math; it requires 'picking up the pennies' of +1 bonuses to get a significant effect. +1 on a d10 works, +1 on a d12 might also.

Rob Hicks

[D20] has too much variance. You need two to four categories of variance. Either "success vs failure," or "success vs failure with critical success and critical failure". The d20 added too much variation on that, which led to a system that was more crunch than flavor.

Matt Miller

You can lower the variance on a d20 by using multiple dice. DnD originally used 2d6, some games use 3d6, FATE uses 4dF. All generate bell-curves that make the outliers possible but uncommon. (As 7 is the most common in Settlers). But for counted variance, the range matters. 2d6 provides 2-12, 3d6 3-18, Fate -4 to +4.  

Matt Miller

Using -4 to +4 provides a range of 9, and that may simply be enough. OD&D abbreviated into -1,0,+1, and 3e made it into -5 to +5. But there is a difference between possible outcomes from the dice, and possible outcomes for attributes. For the former, so large a range may not be necessary. But for the latter, a larger range is required...

Arkham Horror and Bathtubs of D6

Matt Miller 

In Arkham, extra dice is always better. Every die in Arkham adds +1/3. But Arkham does a very nice job of limiting the dice you can add through the use of 'hands'. You only get two, and you you an only use two hands worth of spells/weapons* in a single attack.  In Arkham, things which do add piles of dice (withering, etc) also require a roll to activate, and include an additional cost. 

I recall some game that played with d10s. It made doing the mental math easy...but I think it was based on the ShadowRun style 'bathtubs of D6', where only a 1 counts as a success...which makes it worse than ShadowRun. ShadowRun, a 6d6 makes a success very likely. With a d10 system, you need 10d10. Making it a 1 or a 2 on a D10 doesn't alter it that much: 1/5 chance, vs a 1/6 on a d6--not worth the extra dice required. 

**Recalls to me, before the 'Christmas Tree' twinking out, there was a rule that players could only have one magic item.

Arkham Horror Math

Playing a great deal of Arkham Horror, which has a 1/3 success rate for dice; just came across the math for predicting count of successes, given X dice, an a X success rate. Begs to be used for an RPG.

Subitizing

Matt Miller

Today I happened across a concept for mental math that says people can grasp rather small numbers (<4) almost instantly, and was wondering if there was a way to apply that to gaming. (Subitizing) 

Last week, we played a FATE-based game with regular D6's, and the additional mental time to convert the different symbols to FATE outcomes was notable. FATE uses four dice, with a bell-curve of outcomes, but does it using 3 values, with 2 symbols (blanks as null, so a player just needs to 'subitize'). Rather than explicit counts, FATE dice make it possible to subitize pluses and minuses; a substantial portion of the time, there will be only 1 symbol to subitize as well.

Tom Vogt

I've done some extensive work on dice systems, including presenations. In general, comparison > addition > substraction > multiplication. FATE balances somewhere between as theoretically you need to do addition and substraction, but with the usual low numbers, it is basically instinctive, you don't actually "do the math", exactly due to the effect you describe.