Using 3d20 for all d20 rolls

[Theodoxus]

I'm thinking of going with a 3d20 system for rolling anything using a d20 now. The idea being on a "standard" roll, you pick the middle roll; advantage, you pick the high roll and disadvantage, you pick the low. I'm not a statistics guy though, so I don't know if that would make rolls more average or not... My assumption is since they're not added together, each die is a separate instance... yet I can't shake the feeling that rolling a specific number, say, 20, on two of the dice to achieve a crit on a standard roll would be more rare.

Is my assumption correct?

[Anderlith]

I don’t know, but I don’t like it

[Contrast]

Anydice (https://anydice.com/program/191b3) is pretty good for this sort of thing if you don't want to do the math yourself.

[Vaern]

You'd have to do a lot of rebalancing throughout the game to make it viable. Using the median of three rolls on a regular check means that results will tend toward average (10-11) moreso than rolling only a single die per check. As you need to roll two results of 20 on three dice in order for the "middle" roll to be a 20, our chances of getting a natural 20 decrease from one in twenty to one in four hundred, as do your chances of getting a natural 1.
But this doesn't just mean that crits and fumbles are much more rare - you're unlikely to see anything higher than a 13 or lower than a 7 or 8 without advantage or disadvantage in effect. Using three dice will make the game much less random, and all of your rolls will tend towards mediocrity.

[diplomancer]

My gut feeling is that this could be a good idea for ability checks, but definitely not for attack rolls, and probably not for saving throws either. I also would not use it for contested ability checks, like grappling.

[zinycor]

Well... you would highly reduce the chance for criticals and critical failures with this system.

[Keltest]

I feel like this is a solution in search of a problem. If you have (dis)advantage, sure, feel free to roll 2d20 and pick the appropriate one, but otherwise youre just adding in more complication for no benefit.

[Mr Adventurer]

On standard rolls, you would have to roll 2 natural 20s in order to pick one of them, so your chance to crit drops to 1 in 400 instead of 1 in 20.

On disadvantage rolls, you have three times as many chances to roll a 1 (since whichever die rolls it, you are forced to take it).

On advantage rolls, you are three times as likely to roll a 20.

[bid]

yet I can't shake the feeling that rolling a specific number, say, 20, on two of the dice to achieve a crit on a standard roll would be more rare.

Is my assumption correct?
Your 3d20 will result in 20 in very few cases:
- 20 20 20
- 20 20 and any of the 3 dice rolling 1...19
That's 1+19*3 = 58

Compare to 1d20 = "20 on the first dice, anything on the other 2" which is 400 (7 times more).
Compare to disadvantage = "20 on the first and 2nd dice, anything on the 3rd" which is 20 (3 times less).

If you crit on 19-20, you're still at 18*12+8 = 224, still half normal.
If you crit on 18-20, you're still at 17*27+27 = 486, about the same as normal.


BTW, this would boost rogues and any other once-per-turn extra damage.

[bid]

On standard rolls, you would have to roll 2 natural 20s in order to pick one of them, so your chance to crit drops to 1 in 400 instead of 1 in 20.
Barely below 3 in 400, because any of the 3 dice can be non-20.

[Theodoxus]

I've also been using the PF2 +10 over AC = crit. With the mean? Standard deviation? (whatever that is that measures the most likely roll) being 10.5, my players would still roll crits more often than 'just on a 20' - though I might need to lower enemy AC by a point or two...

All in all, I think it goes a long way to solving the swingyness of d20 rolls without using a different mechanic (3d6 or 2d10, etc) for skill checks. I might rule that a "1" isn't an auto miss, since it would come up more often, just as a 20 will more than likely result in a crit just based on the +10 rule... maybe make it a "super crit"? doubled and maximized dice? Maybe only if it's not on an advantage roll...

[zinycor]

I've also been using the PF2 +10 over AC = crit. With the mean? Standard deviation? (whatever that is that measures the most likely roll) being 10.5, my players would still roll crits more often than 'just on a 20' - though I might need to lower enemy AC by a point or two...

All in all, I think it goes a long way to solving the swingyness of d20 rolls without using a different mechanic (3d6 or 2d10, etc) for skill checks. I might rule that a "1" isn't an auto miss, since it would come up more often, just as a 20 will more than likely result in a crit just based on the +10 rule... maybe make it a "super crit"? doubled and maximized dice? Maybe only if it's not on an advantage roll...

Any other house rules we should know? cause knowing you did this was important to answer your original post.

[Mr Adventurer]

Barely below 3 in 400, because any of the 3 dice can be non-20.

Any two of the three have to be 20, yes, sorry.

[Theodoxus]

There's a ton, but I was curious about the probability math of 3d20. The answers helped bring things in line. A straight d20 roll has been critting a bit more often than I would like, given the lower AC values of 5th Ed, which I grok, when modding things in from different systems.

I've been running an unmodified 5E game for a couple months now with the same players who've been playing the modding campaign. Most of my players and I prefer a more robust system...

[Tanarii]

It increases the chance of a 6-15 by ~1-2%, reduces the chance of a 2 or 19 from 5% to 2%, and makes 1 and 20 almost nonexistent (3/4%).

https://anydice.com/program/ba6

If you use it, you're going to need a new rule for crits.

[Tzun]

Probability to roll at least two 20's when rolling three 20 sided dice = probability to roll a 20 on the {1st and 2nd rolls} + {1st and 3rd rolls} + {2nd and 3rd rolls} + {1st and 2nd and 3rd rolls} = .0025 + .0025 + .0025 + .000125 = .007625 = 0.7625%

Edit: You could say for crits or fumbles only, that only the 1st roll or die has to be a 20 or a 1. This will give the same probability as just rolling 1 die.

[bid]

Probability to roll at least two 20's when rolling three 20 sided dice = probability to roll a 20 on the {1st and 2nd rolls} + {1st and 3rd rolls} + {2nd and 3rd rolls} + {1st and 2nd and 3rd rolls} = .0025 + .0025 + .0025 + .000125 = .007625 = 0.7625%
It's less than that. You counted 20-20-20 4 times.

[Tzun]

It's less than that. You counted 20-20-20 4 times.

Edit: Nevermind, you're right. In the first 3 probabilities, I need to exclude the probability of rolling that third 20 so the prob for the first 3 terms should be 0.002375. So total prob is now 0.00725.

[Chronos]

Absent any other modifications, consistency favors the player. In any given encounter, you expect everyone to make it out all right, with only a small chance of things going badly wrong. Increasing consistency makes the likely outcome more likely, and the unlikely outcome more unlikely.

On the other hand, at the same time that you're making ordinary rolls more consistent, you're making advantage and disadvantage more extreme. So everyone, players and monsters alike, are going to be scrambling like crazy to do whatever they can to gain advantage or impose disadvantage. And whatever you're doing to determine whether someone has (dis)advantage will turn into the real game, not the rolls you make after that point. Which is a problem, because the rules for when to give (dis)advantage mostly boil down to "when you think it's appropriate", which means all your table time will be spent on arguing whether it's appropriate.

[Hytheter]

Even ignoring the mathematical implications, 3d20 just seems annoying to me. Having to throw three d20s for every roll and then looking for the middle one just seems like a huge hassle.

With "AC+10=crit" the maths probably works out decently for standard rolls. Easy things would become easier, and hard things would become harder - if that's desirable to you then this will do it. It may have some other consequences but nothing comes to mind.

But as Chronos said, Advantage and Disadvantage both become somewhat more powerful when you're rolling three dice, which could be problematic.

Overall I just don't see it being worth the trouble.

[Tzun]

I like this idea. With a few extra d20's this should be easy to implement. Get 3 d20's of varying sizes or colors so you can designate one as the 1st die and another as the 2nd die. For every roll, roll all 3 at once.

In situations where there is advantage or disadvantage, just look at the 1st and 2nd dice and ignore the 3rd die.

Whenever the 1st die comes out a 20 or a 1, ignore all the other dice and the result is a crit or fumble respectively (if your table uses fumbles that is). For abilities that expand the crit range, such as the main Champion ability, include the 19 and/or 18 in the 1st die as a crit and ignore the rest of the dice.

For all other situations use the method the OP described. This keeps the probabilities for those special situations the same as the standard way of rolling but takes the swingyness out of the regular rolls.

[Man_Over_Game]

It increases the chance of a 6-15 by ~1-2%, reduces the chance of a 2 or 19 from 5% to 2%, and makes 1 and 20 almost nonexistent (3/4%).

https://anydice.com/program/ba6

To add on that, the total chance of rolling within 6-15 is increased by a flat 18.76%. Normally, you'd have a 50% chance of hitting within that range, but now you have a 69% chance.

I've looked at other options for reducing chaos (2d10, 3d6), but they have the repercussion of punishing the underdog. Since DnD's attack system revolves around attempting to hit past the defender's armor threshold, or you do nothing, any variance in AC makes a bigger deal. Using 1d20 means David has a chance to hit, and Goliath has a chance to miss. Those chances go down by making things less chaotic.



A good rule of thumb is to have contests be chaotic (Attack vs. AC), but have solitaire be consistent (using a skill roll on a lock). Your system would be better introduced as an alternative for skills.

[Theodoxus]

A good rule of thumb is to have contests be chaotic (Attack vs. AC), but have solitaire be consistent (using a skill roll on a lock). Your system would be better introduced as an alternative for skills.

An excellent suggestion. I'll start there.

[Tanarii]

A good rule of thumb is to have contests be chaotic (Attack vs. AC), but have solitaire be consistent (using a skill roll on a lock). Your system would be better introduced as an alternative for skills.
Another good rule of thumb is to have combat resolutions be quick and easy, and save slow and complex resolutions for out of combat.

Of course, it also helps if that slowness and complexity is done in a way that ratchets up tension somehow too.

[Wuzza]

I feel like this is a solution in search of a problem. If you have (dis)advantage, sure, feel free to roll 2d20 and pick the appropriate one, but otherwise youre just adding in more complication for no benefit.

That's my feeling. Why do you need this?

If a PC has, say 3 attacks, they'll generally be rolling 9 die, instead of 3. I don't see any benefit.

[darkbuu_1]

How would it affect things if crits were then changed to Any two dice match?

So a 17, 10, 10 would be a crit chance, assuming 10 hits. This would mean people could roll missing crits but maybe a missed crit becomes a normal hit?

This is probably becoming too slow and confusing.

[kazaryu]

I've also been using the PF2 +10 over AC = crit. With the mean? Standard deviation? (whatever that is that measures the most likely roll) being 10.5, my players would still roll crits more often than 'just on a 20' - though I might need to lower enemy AC by a point or two...

All in all, I think it goes a long way to solving the swingyness of d20 rolls without using a different mechanic (3d6 or 2d10, etc) for skill checks. I might rule that a "1" isn't an auto miss, since it would come up more often, just as a 20 will more than likely result in a crit just based on the +10 rule... maybe make it a "super crit"? doubled and maximized dice? Maybe only if it's not on an advantage roll...

on just a traight d20 roll there is not 'most likely' result. 10.5 is jsut the average result. in theory if you averaged all of your d20 rolls together they'd come out to 10.5. but 'most likely' number doesn't come into play until you add multiple dice.

and how you adjudicate those dice also matters. so like, for a damage roll using multiple dice (where you just add the dice together) your most likely result is the average. however if you're rolling advantage/disadvantage (i.e. rolling multiple dice and keeping the 'highest' or 'lowest') then the most likely result shifts towards whatever is closest to your criteria. so like for rolling with advantage you're have the best odds of rolling a nat 20 (just under 10%) and the odds drop from there (down to .25% at nat 1)