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).