anydice
Let's say the rulebook says this:
Roll one 4-sided die, two 6-sided dice, and one 10-sided die. Add the highest two rolls together.
In a different environment, I might write something like this:
int[] results = {1d4, 1d6, 1d6, 1d10}
results.sort_high_to_low
return {results[1], results[2]}
How can I write that in AnyDice?
So far, this is the best I've come up with, but it doesn't do what I'm expecting:
X: [sort {1d4, 1d6, 1d6, 1d10}]
output 1@X + 2@X
Here's the link to the program, and here it is in its entirety:
DICE:{4,6,8,10,12,20}
loop D over {1..(#DICE-1)}{
loop SECOND over {0..5}{
FIRST: 6-SECOND
FIRSTD: D@DICE
SECONDD: (D+1)@DICE
output [count {4..20} in FIRSTdFIRSTD] + [count {4..20} in SECONDdSECONDD] named "[FIRST]d[FIRSTD] and [SECOND]d[SECONDD]"
}
}
The accepted solution disregards the core purpose of the actual question (how does user choice affect the outcome), so I had to try and figure it out...
I'm new to anydice, so I welcome corrections/suggestions. Here, if the player rolls their desired outcome on 2/3 dice, that becomes their choice, otherwise, output a random choice from the 3....
function: choice of A:n and B:n and C:n target T:n {
if A=T { result: A }
if B=T { result: B }
if C=T { result: C }
result: 1d{A, B, C}
}
function: combo of A:n and B:n and C:n target T {
result: [choice of A+B and B+C and A+C target T]
}
loop T over {1..12} {
output [combo of 1d6 and 1d6 and 1d6 target T] named "2/3d6 [T]"
}
Here, we can see the huge difference that player choice makes
Chance of getting a 7:
2d6: ~17%
(2/3)d6: ~42%
This matches the mathematical answer:
The probability that a pair of the three dice has sum '7' is $$\frac{3 \cdot 6 \cdot 4 + 3 \cdot 6}{6^3} = \frac{90}{216} = \frac{5}{12} ≈ 42/100 $$ Src: https://math.stackexchange.com/questions/3283971/probability-that-2-dice-selected-from-3-rolled-dice-will-have-sum-7
Best Answer
As usual with AnyDice, the solution is "write a function." Here's a simple example:
Of course, this technique can be easily extended to more than three types of dice simply by adding more parameters to the function. The trick here is that passing a die into a function that expects a number or a sequence will "freeze" the die roll, invoking the function for every possible outcome of the roll in parallel, and summing up the results (weighted by their respective probabilities). Thus, inside the function, you can just manipulate the sequences of individual dice as you want.
Note that converting dice into sequences like this is a "brute force" solution, since it ends up invoking the function separately for every possible outcome of every roll. For large amounts of dice, it can run very slowly or even time out.
In particular, if you only want the single highest roll in the pool, the solution I presented in this earlier answer is a lot more efficient: by discarding all but the highest die of each type before calling the function, the number of combinations that AnyDice must iterate over becomes a lot smaller.