Farewell to the d20

Farewell d20, it’s been a wild ride!

GM: “You see before you a huge colossus of a man, surely he must have been mixed with a giant at birth!”
Player: **Turning to friends** “I got this.”
Player: **To GM** “I leap into the fray drawing my sword and charge at the huge warrior.”
GM: “Roll initiative”
Player: Rolls single d20 “Twenty, ah-ha!”
Player: “I slash the mighty foe with my sword **rolls single d20** FOUR?!?”

The Problem

For some time now, I have been bemoaning the swingy nature of the single d20 roll, by its very nature the result will be just 1 of 20 numbers, the clue is in the title and each number has a 5% chance of ruining or making your day. Seems legit I hear you say, well yes it’s certainly an even spread and all things being equal I guess it can work but for me the problem is that if you add a proficiency bonus and no stat bonus you have a 60% chance of failing at something you are meant to be good at, for example:

Farmer Giles, proficient at farming (+2) average intelligence (+0), ploughing a field (Medium Difficulty), poor old Giles needs 13 on a d20 or a 35% chance, let’s say he’s a Level 5 Farmer (+4) he needs 11 on a d20, he took his stat increase in strength and constitution, he now has a whopping 50/50 chance of ploughing his field. Farmer Brown is a smarter farmer (+1) his numbers are 12 (40%) or 10 (55%) still not ideal for something they should be able to do without too many problems.

Typical Difficulty Classes

Task Difficulty DC
Very easy 5
Easy 10
Medium 15
Hard 20
Very hard 25
Nearly impossible 30

Whilst the above example is a little (alright a lot) contrived, it serves to illustrate my point and my frustrations with a single d20 roll, you might say that the Farmers should have advantage on the roll because, you know, farmers, but that’s not really RAW and frankly is a bodge, if I’m going to change it I’m going all in!

Here’s a graph courtesy of AnyDice.com showing numeric distribution of a single d20 and then the advantage/disadvantage distributions.

Pretty straight forward, 5% chance of any number for the single d20, just under 10% for 1 and decreasing chance of the higher numbers with disadvantage, just over 1% for 1 and increasing with advantage.

The Solution?

Adding more dice into the pool will change the distribution spread, with a single dice you will get a straight line (so long as the dice is true and platonic, don’t get me started on non-platonic dice), add a second dice to the roll and you get a pyramid, adding a third one to the pool gives a bell curve.

The number range I am looking for is 1-20 obviously not entirely possible if rolling multiple dice, the obvious answer is to see if I can live with 2-20 and try rolling two d10s, this will have implications for the critical hit chance and if used, the botch chance, but I’ll get into that later.

Here’s a graph showing the distribution of 1d20 vs 2d10:

With 1% chance of 2 or 20, 2% of 3 or 19, etc, etc, the 2d10 is clearly less swingy, but does it do what I want?
Back to Farmer Giles, he now has an increased % chance of ploughing his field, it’s now either 36/64 or 55/45 in his favour, which is an improvement, even though it’s minimal at the lower level, but is it enough? Let’s look at Farmer Brown depending on level he needs to roll 12+ or 10+ he has 44/56 or 64/36 chances of success/failure doing so under the new scheme.

Clearly the changes for lower modifiers are not as great, but even that simple example shows that as the modifiers increase then the compound chance increases too but with a sharper increase, Giles had a 1% increase at +2 but a 5% increase at +4, whilst Brown reaped 4% and 9%.

Level 1 characters will typically have a +3 stat bonus and a +2 Proficiency bonus, they’re looking for 10+ to accomplish a Medium task meaning they should get the result 64% of the time as opposed to the previous 55% which I think is a nice increase and as they level up to 4th level they probably get a +1 from a Stat increase meaning they are looking for 9+ with a 72% chance, which is nice, I’m happy with that.

Advantage and Disadvantage

With standard 1d20 you add another d20 and take the highest for advantage and the lowest for disadvantage, so doing the same with adding a d10 and taking lowest/highest yields the following graph.

NB: Additional rule for advantage disadvantage would be instead of taking the highest 2 you could take a double if it grants you a critical.

Criticals and Botches

With 1d20 you’re looking at a straight (you guessed it) 5% chance of either happening, seems a little on the high side, I know Hit Points do not equal Life Points and the reduction of Hit Points does not equal taking wounds so the whole Critical hit thing is lessened somewhat, 5% is being used because that’s all that’s available with a single roll, we could just say okay roll again and if you hit it’s a critical the same as Pathfinder but it’s really just reducing the percentage chance of a critical, with 2d10 we have a way to achieve this and it makes the chance of a critical hit 3% which is a nice number, but the method is flexible and adjustable.

Here’s how it works, roll 2d10 if the result is a hit and you have rolled double 8, double 9 or double 10 it’s a critical, if you have missed and have rolled a double 1, double 2 or double 3 it’s a botch (if you want to use botches that is).

Damage Extension Rules

Here’s a thing, combats take too much time and are way too swingy, I don’t really like replacing dice rolling with the average damage system offered by Adventurer’s League and had to come up with an alternate system.

I owe this idea to a discussion I had with a Symbaroum player whose name I have criminally forgotten, we were playing at Dragon Meet in London and I credit the unremembered player with helping me visualise the outcome, thanks dude!

Looking at the weapons table there really are only 6 rolls that are made, 1d3 added, why becomes clear later:

  • 1d3
  • 1d4
  • 1d6
  • 1d8
  • 1d10
  • 1d12
  • 2d6

This makes changing the system, reasonably easy, one of the things I didn’t want to mess with was the max damage roll possible, so from that perspective we can put the cap on all the rolls as their current maxima and look to ways to improve damage output without going wild.

NB: I’m going to leave the d4 alone as the swing is not too wild and if there’s got to be an itty bitty weapon then it works.

Initially I thought of using the next dice down and a modifier e.g. 1d6 becomes 1d4+2, it kind of works but it felt very opposed to the initial work in the 2d10 section above, so how about replacing with there must always be at least 2 dice rolled, let’s see how that works.

1d4 stays the same; 1d6 changes to 2d3; 1d8 changes to 2d4; 1d10 changes to 2d4+2; 1d12 changes to 3d4; 2d6 changes to 1d4+1d6+2;

At first glance it seems to work, removes the 1 result completely, moves all the probabilities towards the average and gives differentiation to the Great Axe (1d12) and the Great Sword(2d6), I quite like the choice now, Great Sword Damage starts at 4, Great Axe at 3, Great Sword average 8, Great Axe Average 7.5, the statistical chance of the Great Axe doing lower damage than the Great Sword is maintained and the chances of a 9,10, 11 or 12 are higher for the Great Sword, I like it.

I think I’ll run this iteration up the flagpole and see if anyone salutes it.  

I’d really like to thank Anydice.com, @thedicemechanic and the player from Dragonmeet 2018 for providing graphs, inspiration and conversation.

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