D&D General Substituting 3Z7 for D20

[Baldurs_Underdark]

I think that D&D 5E is not built for this. The effect of a critical hit (double damage dice) is often (*) quite minor on the outcome of an encounter. As a player I would not like it if I almost never score a critical hit anymore. You would need to massively increase the effect of those super-rare triple-7s.

The predictability of the game goes up a lot (@EzekielRaiden has posted an excellent explanation in post #13). That predictability would result in players wondering why they even roll because it's a near-guarantee to score a success, or players just giving up because rolling is pointless. The next step away from the d20, and into more predictability, is to give players a fixed score: You always have a 10. Add your modifiers to see if you are able to succeed.

(*) Rogue assassins with a Death Strike may be an exception.

 

[David Neuschulz]

It's probably not going to create a problem, per se. You can still play the game just fine, but the dice rolls will be more predictable and less "swingy." It will effectively remove critical hits and critical failures by making them so incredibly rare, too. But maybe that's what you're going for?

Well, this is diverging from my original question a bit, but I think the double-or-triple 1's and 7's for crits/fumbles, being that the probabilities get close to those of D20, I'd like to try that. As for the diminishing returns on +x, my gut feeling is that I wouldn't mind and that my players wouldn't mind.

 

[Haplo781]

For a uniform distribution like d20, +1 is always equivalent to 1/N, where N is the number of sides on the die. So long as failure remains an option, +1 is always an increase of 0.05 (5%) to the probability of success.

For the distribution you're discussing, it would be as follows, assuming that you are using "meet or beat" rules.

DC 9: 68.38%
DC 10: 59.38%
DC 11: 50% (exactly)
DC 12: 40.63%
DC 13: 31.54%
DC 14: 23.44%
DC 15: 16.41%
....
DC 19: 1.95%
DC 20: 0.78%

So, a +1 is the same as reducing the DC by 1. That means, at the center of the bell curve, +1 is equivalent to about 9.5%, roughly double the benefit of +1 in a uniform distribution. At DC 15, +1 is equivalent to almost exactly 7%, and at DC 20, +1 is equivalent to just over 1%.

At the edges of the bell curve, modifiers become nearly worthless unless they're huge. At the center of the bell curve, modifiers have a massive swing--the difference between DC9 and DC 12 is huge. It's equivalent to going from "you succeed twice as often as you fail," which feels like "normal" difficulty to most players, over to "you fail twice as often as you succeed," which is going to feel like absolute garbage for most players. A -2 or -3 penalty when near the center of the curve is terribly punishing; a +2 or +3 when near the center of the curve means nearly guaranteed success.

Perhaps these are desirable effects for you; but you may wish to consider the impact on player psychology, as noted.

The solution here is to replace flat modifiers with extra dice. You can either just add (or subtract, but then you need visually distinct dice) to the roll, or do a pseudo advantage where you roll X and keep Y highest (or lowest).

It's still gonna give diminishing returns, but it scales better.

 

[EzekielRaiden]

It's still gonna give diminishing returns, but it scales better

But it's also significantly harder for the player to understand the amount of benefit they're gaining, and adds a meaningful burden to the process of play--especially if, as you say, penalties are handled with distinctive dice.

You can do it. I'm not saying you can't. But you pay a pretty hefty cost for doing so. There's a reason games rarely use bell-curve distributions. Dungeon World is one of the only ones I know, and there it's more pyramid-"curve" than bell-curve proper--and uses ranges of success anyway.

 

[Haplo781]

But it's also significantly harder for the player to understand the amount of benefit they're gaining, and adds a meaningful burden to the process of play--especially if, as you say, penalties are handled with distinctive dice.

You can do it. I'm not saying you can't. But you pay a pretty hefty cost for doing so. There's a reason games rarely use bell-curve distributions. Dungeon World is one of the only ones I know, and there it's more pyramid-"curve" than bell-curve proper--and uses ranges of success anyway.

Sure - I prefer the "keep X highest/lowest" version since it doesn't require different dice and doesn't break the curve, but it still has its disadvantages vs. single-die resolution.

 

[Blue]

I’d have a success with one 7 mean something extra, two 7’s something great, and three 7’s would be ungodly.

Chance of exactly one 7 is roughly 31.5% of the time. Two sevens is 3.5%. Three sevens is about 0.3% of the time.

So two sevens comes up less than a crit - say if you did a crit+50% bonus it's balanced. Three sevens might come up every few months of play. On the other hand a single seven comes up so frequently that ti would probably slow down play to do something for it.

 

[Blue]

Wouldn't 3z7 make it less swingy and more predictable? Maybe I misunderstand what swingy means.

You're right that people may be using the term "swingy" differently.

Context: D&D 5e with bounded accuracy has most DCs in the middle range. So we focus on that are of the bell curve, not on the ends.

Each 1 point difference in the middle is significantly more than the 5% difference that a +/-1 on a d20 would make. So a character having a +1 over another character is getting a bigger boost. Characters that fall below, say an "off-lockpick" froma high DEX character and the urchin background will find that them being 2 points less than expected will make a much bigger difference than the 10% on a d20.

Static DCs (say AC, saves, various ability checks) will find that each +/-1 the characters have will make a lot more impact on the chance to succeed (or fail) than with a d20. Chances of success to do something like say swim or climb a wall will vary a lot more between characters.

 

[NotAYakk]

3d8-3 has a variance of 63/12*3 and an average of 10.5.
1d20 has a variance of 399/12 and an average of 10.5.

So the variance is half as big as for 1d20. As we experience Standard Deviation not Variance directly, the SD(3d8) is 0.68x SD(1d20).

So to a really decent approximation, the effect is similar to multipling modifiers to d20 rolls by 1.5 and similar to DCs away from 11.

Ie, proficiency went from +3 to +9, attributes from +0 to +7, magic items from +0 to +5, etc, plate had 21 AC, shields 3 AC, studded 13.

The critical mechanics you describe can be summed up as "almost never"; triple 8 is 1 in 512, which is about as often as you get a critical on d20 with disadvantage. To get criticals near 1d20 you need to make them 25x more common.

Two 8s (or 7s) is close; ie, if you roll 2 dice with a max roll, the roll becomes a critical success. As others have noted, this is 3.5% instead of 5%, so make crits (max damage roll) plus (one roll of damage).

Advantage/disadvantage mechanics are typically done with dice pools by just adding 1 additional die, then taking the highest/lowest 3 dice. This won't be as strong as advantage/disadvantage on d20 but won't be that far off.

 

[NotAYakk]

Oh! And lucky 777 should be max damage on both base dice and critical dice! (it won't happen often)

 

[David Neuschulz]

So to a really decent approximation, the effect is similar to multipling modifiers to d20 rolls by 1.5 and similar to DCs away from 11.

Ie, proficiency went from +3 to +9, attributes from +0 to +7, magic items from +0 to +5, etc, plate had 21 AC, shields 3 AC, studded 13.

Thanks for this! It is very helpful.