10 Analysis of roll of dice
In this chapter let’s analyze the roll of pair of dice, and see what odds of betting will make you win. For that let’s define a variable named faces, that holds a range of numbers from 1 to 6.
(def faces (range 1 7))faces(1 2 3 4 5 6)Now let’s generate combinations of die throws. So in the code below x and y are variables that hold the numbers from 1 to 6. The for function generates a list of vectors containing all possible combinations of x and y.
(def combinations
(for [x faces y faces] [x y]))combinations([1 1]
[1 2]
[1 3]
[1 4]
[1 5]
[1 6]
[2 1]
[2 2]
[2 3]
[2 4]
[2 5]
[2 6]
[3 1]
[3 2]
[3 3]
[3 4]
[3 5]
[3 6]
[4 1]
[4 2]
[4 3]
[4 4]
[4 5]
[4 6]
[5 1]
[5 2]
[5 3]
[5 4]
[5 5]
[5 6]
[6 1]
[6 2]
[6 3]
[6 4]
[6 5]
[6 6])Now let’s sum up those combinations:
(map #(apply + %) combinations)(2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10
11
7
8
9
10
11
12)Let’s use frequencies to see which number comes up most often when summed up:
(def frequency-of-sums (frequencies (map #(apply + %) combinations)))frequency-of-sums{7 6, 4 3, 6 5, 3 2, 12 1, 2 1, 11 2, 9 4, 5 4, 10 3, 8 5}Now let’s sort frequency-of-sums by its values:
(sort-by val > frequency-of-sums)([7 6] [6 5] [8 5] [9 4] [5 4] [4 3] [10 3] [3 2] [11 2] [12 1] [2 1])Looks like when a pair of dice is thrown, number 7 comes up most often, followed by 6, 8, and 9. So better bet on number 7 when you throw a pair of dice.
10.1 Plotting
TBD