A Horsey Race

Bryan Bischof bio photo By Bryan Bischof Comment

I’ve been playing with some puzzles lately(slightly egged on by Jeff).

Some recent puzzles

I’ve thought about some of the recent puzzles, even automating some and making some fun visualizations.

Also spent a little time writing some puzzles myself, and some out of left field questions.

However, for the most recent 538 puzzle, they suggested making an animation, so I thought I’d spent a few hours making a d3 vis for fun. Here’s the puzzle.


The setup is relatively straightforward; using the list of probabilities, generate 20 sequences of steps, continuing to sum them until one exceeds 200. Here’s the little function—keep in mind that I don’t know Javascript:

function run_race(race_length){
  horsey_probabilities = [.52,.54,.56,.58,.60,.62,.64,.66,.68,.70,.72,.74,.76,.78,.80,.82,.84,.86,.88,.90].reverse()
  horsey_paths = [[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]]
  winning_position = 0
  while (winning_position < race_length) {
    new_steps = horsey_probabilities.map(function(d){return rand_step(d)})
    horsey_paths.map(function (list, idx) {
      return list.push(new_steps[idx]);});
    winning_position = Math.max.apply(Math, horsey_paths.map(function(d){return d.reduce((a, b) => a + b, 0)}))
//   console.log(winning_position);
  return horsey_paths

The ‘hardest’ part was that I wanted to display the data as a bump chart of who was winning the race at each step. So I had to compute the ‘position’ at each step. Consider the following problem:

Given a square matrix of numbers of integers, a list of rows, convert the integers to the columnar rank of each entry.

For example:




It’s a little strange, but mostly involves changing the direction of the lists, and then computing the ranks; even in Python gave me pause:

a = [5,2,4,3,0]
[z[1] for z in
 sorted([(y[0],j+1) for j,y in
         enumerate(sorted([(i+1,x) for i,x in
                          ], key=lambda x: x[1]))
        ], key=lambda x: x[0])

So you can imagine it was a little awkard in JS, but here ya go:

function matrix_transpose(matrix){
  return matrix[0].map(function(col, i) {
    return matrix.map(function(row) {
        return row[i];

function convert_list_to_ranks(list_of_sums){
  output = list_of_sums.map(function (i,idx){return ([idx+1, i]);})
    .sort(function(a,b) {return b[1] - a[1];})
    .map(function (p,idy){return ([p[0], idy+1])})
    .sort(function(a,b) {return a[0] - b[0];})
    .map(function (x){return x[1]})
  return output

Without further ado, here’s the vis.

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