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My best friend and I are doing a thing for a d&d game that involves potentially destroying the universe. This event will occur rarely, but we want to make it show up randomly (because it’s a thought experiment, not something that’s actually going to show up in a game one of us runs).

This event will be represented by a special d20, which is actually an expression rather than a die of its own (it’s using the Dice Maiden discord bot).

We’d like to make an expression of dice (eg: [1d20*4]/[5-1d5]) that has a small chance (less than 5%) of destroying the universe (read: dividing by 0), which otherwise acts as close to a normal d20 as possible (in the range of values and in the distribution of those values, at least).

This means: the range of values, most of the time, should be all integers between 1-20 inclusive. Each integer should occur with equal probability. If the die errors, it is because the result of the roll involved dividing by 0, and this should occur no more than 5% of the time (approximately). What is a valid Dice Maiden Discord bot command that would give 5% or less chance of failing due to a divide-by-0 error, while otherwise acting like a normal d20?

The closest thing we have so far is (d20)/(d20-1), which gives the right range of values and has probability of destroying the universe 5%, but that clusters around 0 and 1 rather than having a result that is distributed evenly (average result is 10.5/9.5 = 1.10, rather than 10.5 like a d20 should have).

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    \$\begingroup\$ I'm not sure I'm understanding this right. You want a 5% of destroying the earth, and all other results don't destroy the earth? \$\endgroup\$ May 13 at 15:13
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    \$\begingroup\$ Is there a reason you cannot do 1d20 / 1d{0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} \$\endgroup\$
    – Medix2
    May 13 at 15:17
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    \$\begingroup\$ Ah, maybe you should specify more clearly that the implementation needs to work using the Dice Maiden Discord Bot. I'll have to look into the Bot to see how it works \$\endgroup\$
    – Medix2
    May 13 at 15:22
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    \$\begingroup\$ I do not understand if the range should be like a d20 or not, since you write otherwise acts as close to a normal d20 as possible (in the range of values and in the distribution of those values, at least) but d20/(d20-1) can not have the same range value of a d20 \$\endgroup\$
    – Eddymage
    May 13 at 15:25
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    \$\begingroup\$ So, what exactly would this die be used for? What is its purpose? What role is it filling that requires it exist? \$\endgroup\$ May 13 at 19:09
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Roll two d20's.

One is the normal d20.

The other is the cataclysm die.

To implement in Dice Maiden, use

!roll 1d20/(1d20 t2)

The first d20 is our regular roll. The second d20 in the denominator does the magic. (1d20 t2) rolls 1d20 and counts the number of dice which have a result greater than or equal to 2. t2 could be translated as "take dice which roll at least 2 as successes (and return the number of successes)", or "test dice for if they are at least 2, treating them as 1 if true or 0 if false". In normal use it would mostly be used for dice pool mechanics.

If the second d20 is anything other than a natural 1, the expression (1d20 t2) will evaluate to 1. The overall result will be 1d20/1 which is, of course, a regular d20 roll. If the second d20 is a natural 1, the denominator will be zero and cause a divide by zero error.

You can adjust the probability of a cataclysm to any arbitrary value by adjusting the die rolled in the denominator and the threshold for it to be a success. For example, a 42% chance of cataclysm can be given by (1d100 t43).

You can also change the "normal" roll to anything you like by changing the numerator.

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!roll 1d21-1

This gives the numbers 1-20 a uniform distribution, each having a 4.76% chance of coming up, and a 4.76% chance of rolling a 0 that destroys the universe. (Or just don’t bother with the “-1” and call a 21 a cataclysm). In Dice Maiden, this is as easy as :

 !roll 1d21-1

And Dice Maiden will output:

 thomasmarkov Roll: [15] Result: 14 Request: [1d21-1]

And the AnyDice graph:

enter image description here

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    \$\begingroup\$ For posterity: this was a correct answer to the original question (which included a zero result as an error), but upon further clarification the questioner is seeking specifically a result that crashes via a divide by zero error without modifying the normal d20 probability distribution otherwise. So please don't downvote this answer or comment that it's incorrect :) \$\endgroup\$
    – ESCE
    May 15 at 3:59

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