Really inefficiently hacks http://www.loper-os.org/bad-at-entropy/manmach.html.

gistfile1.js

/* 
Generates a perfect solution to http://www.loper-os.org/bad-at-entropy/manmach.html.
Naive algorithm: Maintain array of correct solution so far. Repeat '1' adding each to the solution until the machine scores. When it scores, save the solution, reset, and re-enter the solution up until right before it fails. Toggle between '1' and '0' and continue repeating until the machine scores. Do this until the solution array is size n.

First 1000 digits:
1111100001111000010011101111000001010011010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111010001110100011101000111
*/

var n = 60;  // number of digits to generate

var solution = new Array();
var machScore = document.getElementById('machscore');
var bit = 1;
var count;

Reset();
for (count = 0; count < n; count++) {
	Move(bit);
	if (machScore.textContent !== '0') {
		Reset();
		var arrayLength = solution.length;
		for (var arrayCount = 0; arrayCount < arrayLength; arrayCount++) {
			Move(solution[arrayCount]);
		}
		bit = bit ? 0 : 1;  // toggle bit
		count--;
	} else {
		solution.push(bit);
	}
}

var solutionString = "";
var arrayLength = solution.length;
for (var arrayCount = 0; arrayCount < arrayLength; arrayCount++) {
	solutionString += solution[arrayCount];
}

console.log(solutionString);