# Most faithful way to convert a d20 base roll to a d6 base roll?

I'm semi-converting an old adventure from DnD 3.X to d6 Fantasy, but I'm having trouble getting a roll conversion that I am happy with. The adventure calls for an extended test of d20 +X rolls until the party reaches a certain total.

What would be the most faithful ( i.e. with a similar amount dice rolling, randomness and probability ) way to reproduce this in a d6 game?

• FYI AnyDice (anydice.com) is a great tool for experimenting with nontrivial dice mechanics and observing their distributions. Jan 7, 2020 at 2:57

The usual way of doing a conversion between systems is to not try to reproduce the mechanics, but to look at what the mechanics are trying to accomplish or model and then figure out the "native" way in the new system for how that would be done.

Since you're using D6 Fantasy, you're presumably using D6 Fantasy's combat system instead of trying to emulate d20's BAB system and armour classes – in the same way, make up a rule that "feels D6-ish" to handle this adventure mechanic. That's all the original authors did, after all.

But even given that, it's not hard to convert the mechanic fairly faithfully because you're not trying to convert a single roll, you're trying to convert a series of rolls and the probabilities involved there make the conversion easy.

Consider that an accumulated total is actually going to be a bit of a bell curve regardless of how you roll the individual checks, because the average of a d20 roll is 10.5 and after a few rolls in the series, the total will be likely close to 10.5 times the number of rolls, because the addition of multiple rolls smooths out probabilities. Because of that, you can use 3d6 to generate 3–18 (average 10.5) and your accumulating average will end up being very similar after enough summed rolls.

• Just be aware that the variance of a d20 vs 3d6 is different. (i.e. d20 +2 is a boost of a flat 10% vs 3d6+2 where the +2 increases your changes by +25% if you need a 12+ but only +4% if you need an 18). This radically changes the concept of a +X to the rolls.
– Nat
Aug 27, 2013 at 1:09
• @Nat Yes, but the D6 system's rolling method and bonus scale will take care of that. Just don't use d20 bonuses on the D6 system rolls! Besides, even that may not be a problem, since they're accumulating the results. Aug 27, 2013 at 1:22

Looking at D6 Probabilities with the Wild Die,

If you're going to be purely technical about it, it's trivial to figure out the odds of success on a skill check in D&D assuming a set of characters with skills:

$$\frac{1-\left(\text{difficulty-bonus}-1\right)}{20}$$

Therefore, assuming DC 10, and a bonus of 4, the above returns .75. For a strict translation, therefore, figure out the odds of success for every roll you desire, and simply compare to the chart at the bottom of this page, as a function of how many d6 you anticipate your players will roll.

I, however, would recommend against a literal translation, and instead adapt the mechanics from mouseguard for how challenges work, insofar as every roll matters and failures advance the plot but provide complications. The mouseguard system has already been hacked by the Chatty DM In: Mouseburning it. He notes:

• A task's outcome must be uncertain.
• The task must have significant stakes.
• Don't waste time on tasks and types of activity that have already been resolved (See: let it ride, scene economy).
• Only one Lead, but many helpers (and all share in the stakes)
• Everyone puts their cards on the table, and explains the difficulty and stakes.
• Failure must be interesting and awesome.
• It's a good answer (esp. that formula, ta kindly), but not a strictly helpful one. I've already adapted the other 'mechanics' of the encounter, but wanted to make sure that I hadn't messed up my probabilities - the encounter is (in my version) timed. Additionally, I never did find the adventure. If I ever do, I'll make sure to come back and post it for you! Aug 25, 2013 at 19:27
• Just wondering why 1 - (DC - bonus - 1)? In your example scenario above this is -4, which totals to -0.2. If the 1 - is outside the divider you get your intended result, so I'm inclined to think this is a typo? Aug 23, 2017 at 5:53
• Why "1 - (D - 1)" at all? This is equal to "2 - D" without having to do multiple steps.
– Nij
Jan 20, 2020 at 6:41
• From what I can tell, it should have been 20 - (Difficulty - Bonus - 1) This would make the DC 10, Bonus 4 equal 20-(10-4-1)/20 = 20-(5)/20 = 15/20 = 0.75 Jan 29, 2020 at 6:43

The short answer is you cannot really convert from a d20-based ruleset to a d6-system-based ruleset because the probability distributions are fundamentally different: d20 is flat while d6-system is bell-shaped. A +2 bonus in DnD always increases your chances of success in 10%, while in d6 Fantasy it could be more or less than 10% depending on how many dice you are rolling and the difficulty of the roll. Even if you try to adjust the probability of a naked roll to be the same, all the different bonuses that can be applied in every situation (magic, cover, etc) will modify your probabilities to make them different from what they would have been in DnD.

That said, there is one basic idea that d6-system games and d20-system games have in common: they are task-based (instead of goal-based) and tasks are resolved by rolling higher than a difficulty. That makes the conversion of things like skill challenges easier.

A skill challenge where the characters have to succeed a number of times on different rolls (e.g. 8 out of 10 skill checks) can be done exactly the same in d6-fantasy. You will roll more dice (to climb to that difficult window (DC25) the great rogue will roll 8D instead of d20+14) and the probability distribution will be really different, but the basic feeling or progress-or-failure will be the same. A skill challenge where the characters need to add their rolls towards a total can also be done exactly the same: players roll and then add their totals until they achieve the goal. They will roll many more dice, but people who like d6-system like to roll many dice. ;-)

• You can still convert stuff with a direct success/fail template by assuming that you want equitable success/failure; simply ignoring degrees of success or failure as they exist in either system (IIRC they don't) would be sufficient to create the same result, so long as you're clever and willing to accept some small degrees of inaccuracy and assume certain things about a character. A character who is barely better than average (+3) in d20 will roll an 18 or above about 25% of the time, which is about how often a character with 3 dice in D6 would roll a 13 or higher. Aug 25, 2013 at 3:19
• For a given pair character-task you can, but you cannot set a difficulties for tasks (e.g. climb the tower, open the lock, lift open the portcullis, notice that someone is hiding in the shadows) that will give the same chances of success to all characters in both systems. Aug 26, 2013 at 8:51
• That is true, but it is part of the point of having a GM. Aug 26, 2013 at 14:11

For a roll of 1-18, take 2 d6, roll the first and halve the result (rounding up). That will get you a number from 1-3, all equally likely. Roll the second d6.

You will have 2 numbers, 1-3 and 1-6. Now convert that from a base 6 number to a base 10. I.e a roll of 2 and 5 would convert to 11. 1 and 4 would be a 4. 3 and 3 would be 15.

Another way to look at it is groups of 6. First group is 1-6, second group is 7-12, third group is 13-18. Similar to how a percentile roll is 10 groups of 10.

This will give you 18 distinct equally likely results. You don't have the same overall range as a d20, but it is pretty close.

You can actually convert between 3d6 and 1d20. The statistically 'faithful' way to do that is by utilizing their Standard Deviation.

Instead of rolling 3d6; as was suggested by Gygax in earlier editions; why not do this. Roll 4d6 and count any faces that come up 'six' as a zero. Gives you values 0 to 20 but it still has that funky bell curve that 3d6 has too.

• Welcome to StackRPG. When you get a moment, be sure to take the tour. This answer might not get a lot of good reaction because it doesn't really address how to most faithfully replicate a d20 with d6's (as you admit with your "bell curve" comment). You can edit your answer to hone in on the question. Regards, and see you around the site! Aug 22, 2017 at 21:17

According to Dave Arneson, D&D uses a d20 because he liked the die, rather than for any mathematical reason. I think this means that trying to faithfully duplicate d20 probability with d6s is over-thinking the basic idea of "choose numbers by throwing dice," especially if doing so involves complicated math.

Here is a simpler way to get results from 1 to 20: To convert a d20 die roll to d6 dice expression, you just roll 4d6.

The minimum result is 4 and the maximum is 24, so you can have 20 variations, the same as throwing 1d20. For difficulties, you just add 4 to the number you need to reach.

Example:

If you'd normally roll 1d20+2 against a DC of 12, you instead roll 4d6+2 against a DC of 16.

The 4d6 method seems like a useful replacement because the 4d6 probability curve is more realistic than the flat "curve" of outcomes from a d20 and requires very little mid-session math to implement.

• You get twenty possible values, but they’re not each equally likely, which is why everyone else is being more complicated – their results are more “faithful” as requested by the question. Your system will make average values far more likely than normal, and make natural “1” and “20” rolls massively less likely. Dec 3, 2014 at 15:11
• 4d6 has a bell curve, and a d20 roll doesn't. Compare their probability spreads: 4d6 vs 1d20. Because of this, you're more than twice as likely to roll a 14 as you are to roll a 9 or 19, and will roll numbers toward the end of the range rarely. I'll use an example toward the ends of the range to demonstrate what this means: the odds of 1d20 >= 16 are 25%, but the odds of 4d6 >= 20 is only 5.4%. How do you adjust for the bell curve's effect? Dec 3, 2014 at 15:15