var seq = '0000001000011000101000111001001011001101001111010101110110111111'; var index = 0; setInterval(function(){ captureKeyFunc({code : seq[index%seq.length] === '1' ? 'ArrowLeft':'ArrowRight', preventDefault: function () {}}); index++; }, 10);

setInterval(function(){ captureKeyFunc({code : Math.round(Math.random()) === 1 ? 'ArrowLeft':'ArrowRight', preventDefault: function () {}}); }, 10);

    RRRRRRLRRRLRLRLLRRRRLLRRLRRLRLLLRRRLLLRLRRLLRLRL
    RRRRRRLRRRLRLRLLRLLRRRRLLRRLLLLRRLRRLRLLLLLRLLLRRRLLLRLRRLLRLRL
    RRRRRRLRRRLRLRLLRLLRRRRLLRRLLLLRRLRRLRLLLLLLRLLLRRRLLLRLRRLLRLRL
    RRRRRRLRRRLRLRLLRLLRRRRLLRRLLLLRRLRRLRLLLLLLRLLLRRRLLLRLRRLLRLRL
    RRRRRRLRRRLRLRLLRLLRRRRLLRRLLLLRRLRRLRLLLLLLRLLLRRRLLLRLRRLLRLRL
    ...

What's at stake here is the same thing that threatens to eventually cause another civil war in the US, but that is a question for another time. :) It is a broad class of theorems which state that if you have a function f: X -> X and you repeat it over and over it naturally finds an input x such that f(x) = x. This repetition has naturally found a set of moves which resets the Markov matrix back to what it was. If you randomized the prediction on ties then I am not sure what I would do exactly... I would have to steer the Markov matrix into a cycle but assuming that it stores the absolute counts for every single prediction, any oscillations I'm using would want to naturally decay to zero... I might be able to exploit it if you were to only look at, say, my last 1000 moves' history to make your predictions, and maybe I can still induce an oscillation that does better than random chance, but I am not sure that I can.

Is there an error in my patch ?

  diff --git a/not-so-random.html b/not-so-random.html
  index 48c04da..c650b5b 100644
  --- a/not-so-random.html
  +++ b/not-so-random.html
  @@ -169,8 +169,12 @@
         randomHelpFunc = function(evt) {
            evt.preventDefault();
            //document.onkeydown = null;
  -         for (let i = 0; i<10; i++) {
  -            lastKey = Math.round(Math.random());
  +
  +         // db(2, 6)
  +         var inputString = "0000001000011000101000111001001011001101001111010101110110111111";
  +
  +         for (let i = 0; i< inputString.length; i++) {
  +            lastKey = inputString[i] == "0" ? 0 : 1;
               testPrediction();
               updateAll();
               predictNext()

However with $1 vs $1.05 returns, you'll steadily make money.

There was an attack I read about for garage door openers or numeric entry doors where they didn't have an enter button. So entering they entered the De Bruijn sequence and had the answer in a small fraction of the time compared to trying each combo once and hitting "Enter".

http://samy.pl/opensesame/

A de Bruijn sequence DB(2, k) is spelled by an Eulerian path in the corresponding de Bruijn graph, whose vertices are {0, 1}^k and where any arc (x, y) has the following property: x[2..k] == y[1..k-1].

Obviously, there are as many Eulerian paths as there are de Bruijn sequences.

Each such de Bruijn sequence has a different capability at getting a good score at the game "https://www.expunctis.com/2019/03/07/Not-so-random.html".

  diff --git a/not-so-random.html b/not-so-random.html
  index 48c04da..168a287 100644
  --- a/not-so-random.html
  +++ b/not-so-random.html
  @@ -169,8 +169,12 @@
         randomHelpFunc = function(evt) {
            evt.preventDefault();
            //document.onkeydown = null;
  -         for (let i = 0; i<10; i++) {
  -            lastKey = Math.round(Math.random());
  +
  +         // db(2, 6)
  +         var inputString = "0000001000011000101000111001001011001101001111010101110110111111";
  +
  +         for (let i = 0; i< inputString.length; i++) {
  +            lastKey = inputString[i] == "0" ? 1 : 0;
               testPrediction();
               updateAll();
               predictNext()

Mapped the other way, 0=left and 1=right, the guesser gets it right ~43%.