Game design with AnyDice

AnyDice is a useful tool for designing and analysing different dice mechanics.

Tabletop roleplaying games often make use of dice to resolve situations in the fiction. From simple pass/fail skill checks of classical games to exploding dice, re-rolls and dice pools in later games. It’s fun to roll dice, at least when the roll of the dice influence the fiction you are creating through play. Clever dice mechanics do exactly that.

In this post I show you how to use AnyDice to analyse two popular dice mechanics and how I used AnyDice to design the dice mechanic of one of my games.

AnyDice is made by Jasper Flick and is free to use but accepts donations.

Still rolling after all these years.

How to use AnyDice

You input a dice mechanic with a simple syntax and the website answers with a probability.

For instance, if you write ‘output 2d6’ and AnyDice shows you the probabilities for the sum of two six sided dice coming up as the numbers between 2 and 12.

You see that the chance of the two dice coming up with a sum of two is 2,78% or 1/36. You can switch to views that present the results as at least, at most, and mean, deviation.

The input syntax is well documented and the error messages are quite detailed so you will quickly get the hang of it. Let's have a look at two dice mechanics.

Apocalypse World

A popular dice mechanic is the one introduced in Apocalypse World and now used in a long range of games.

You roll two six sided dice and add a modifier. The roll produces one of three outcomes in the fiction. Yes (hit), yes-but (partial hit), no-and (miss). A result of 10 or higher is a success. A result of 7-9 is a partial success. A result of 6 or less is a miss or a serious failure. For instance, if you try to seduce or manipulate someone and miss, you may get to meet the protective guardian of your target real quick.

Typically players care a lot about not getting a miss so let us ask AnyDice what the probabilities are when you have different modifiers to the roll.

Enter 'output 2d6 < 7' and we get:

AnyDice shows that the chance of a miss is 41,67%. Let’s ask AnyDice for the probabilities of a miss for each of the modifiers +1, … +4.

If you can set yourself up in the fiction to roll 2d6+3, the risk of a serious failure is 8.33% or much reduced.

Year Zero

Another popular dice mechanic is the Year Zero engine used by Fria Ligan (e.g. Tales From the Loop). Here players roll a variable number of dice decided by their competence in a skill and count the number of 6’s rolled. Usually, rolling at least one 6 is a success.

Intuition might say that rolling six dice will give you a decent chance for a success, but let’s ask AnyDice:

Rolling six dice will give you around 66% chance of spotting that robot before it grabs you and throws you into the garbage chute. Here we use the notation {0, 0, 0, 0, 0, 1} to express that we really only care about one of the six sides. The other five sides we count as 0. 

Dice pools in Year Zero games typically range from 1 to 10 so let’s ask AnyDice to calculate probabilities for this range.

Chances of rolling at least one six on a roll of N dice for N between 1 and 10. Link to the query.

Rolling 10 dice will give you a decent 83.85% chance of jumping that ravine on your BMX bike.

Year Zero games allow players to press a roll, i.e. to reroll on a failed result by paying a cost in the fiction. One way of calculating this is simply to ask for the success probability when rolling double the number of dice.

Chances of rolling at least one six on a roll of 2N dice for N between 1 and 10. Link to the query.

So our expert biker has around 2.5% risk of tumbling into the abyss and getting some bad bruises to show mom and dad later.

Death of Rapacus

One feature of the Apocalypse World dice mechanic is that once you get a roll with a modifier of +5 or higher, there is no longer any risk of failure. Expert characters in good circumstances will avoid a good deal of the fun that comes with failure. 

A feature of the Year Zero dice mechanic is that is does not provide a grade of success or failure. Rolling many 6’es gives you extra effects in the fiction, but these situations are uncommon. For games where player characters may end up in direct conflict, this mechanic is not ideal for opposed rolls: You just end up with a lot of draws.

So when I decided on a dice mechanic for my game Death of Rapacus, I combined the dice pool from Year Zero with the 2d6 distribution from Apocalypse World.

Death of Rapacus is a game about wizards battling out who among them should be their new leader (think Last Man Standing but with wizards) so very much player versus player.

As two characters duel, other players vote with dice which player character they prefer should win. Players roll the resulting numbers of dice and calculate the sum of the two highest for a result between 2 and 12. Highest wins and deals damage to the loser, on a draw, both sides take damage. Rounds continue until one side yields.

I used AnyDice to validate this mechanic. How likely is it that players get a draw? How likely is it that players roll a 12 with a given number of dice?

Sum of the two highest dice for number of dice between 2 and 10. Link to the query.

Players can gain extra dice through either means but still it is extremely unlikely that both players will roll 10 dice. If they do, there will be about 25% chance of both rolling 12, around 9% chance of both rolling 11 and so it drops. Hence, even in this extreme scenario, a majority of the dice rolls will yield a single winner.

Have fun!

This was an introduction into AnyDice with examples to get you started. More examples here. Have fun exploring! Subscribe for more tips on game design and software development.