Farkle formulas using MathML
Rules of Farkle
- Probability of Farkling with six dice:
-
To Farkle with six dice, you have to not roll any 1's or 5's. (for this
problem, let's choose the dice in order) So, you have to choose
6 dice from the set
2346
.
However, you can't get more than three of any of these elements,
and you can't get three pairs either. So this leaves us with choosing
2, 2, 1, 1 of the set
2346
.
The number of ways to do this is just the number of ways of
first choosing which numbers to choose two of (
4
2
42
6
)
and then ordering these (
6
2
2
180
6
!
2
!
2
!
)
So, the total number of ways to do this is
6
180
1080
,
and the total number of ways to roll 6 dice is
6
6
46656
,
so the total probability is
1080
46656
1080
46656
.0231481
,
or about 2 percent.
Wow, it says in the MathML spec that
As a consequence, raw MathML markup is not primarily intended for direct use by authors. While MathML is human-readable, which helps a lot in debugging it, in all but the simplest cases it is too verbose and error-prone for hand generation.
and they're right. Coding this stuff up by hand is a pretty big pain.
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