AnyDice Classic Archive 17
Take highest of different dice
There's a lot AnyDice can't do, and one of those things is taking the highest of two different dice. It can only compare dice of the same type. Of course AnyDice 2 can do it, but that won't help you right now.
So, how does the distribution of "(d4,d6)h" looks like? For 1 through 4, it looks the same as 2d4h. That does ignore the fact that the d6 could also roll 5 or 6, so you'll have to add those to the graph. Because it doesn't matter what the d4 rolled in those two cases, there are four ways to roll each. Finally, there are 6 * 4 = 24 ways you can roll the dice.
Putting it together, you get a graph that ramps up in a straight line, until it falls back to a flat line.
We can generalize this. Suppose you take the highest of dX and dY, and that X is smaller than Y. Now the following holds:
- There are X * Y ways to roll the dice.
- A 1 can be rolled in 1 way.
- A 2 can be rolled in 3 ways (provided X is at least 2).
- A 3 can be rolled in 5 ways (provided X is at least 3).
- An N can be rolled in 2 * N - 1 ways, provided that N is at most X.
- All values greater than X can be rolled in X ways.
But what if you want exploding dice, or to take the higest of three different dice, or the highest of two sets of dice? Unfortunately, that'll complicate matters a lot. The best approach to find such distributions is to combine them into one cartesian product in AnyDice, exporting that and using a spreadsheet program to extract the data you want.
