choice.js

function DummyStore() {
  var instance;
  return instance = 
    { store: {}
    , setItem: function (key, val) {
        instance.store[key] = val;
        return val;
      }
    , getItem: function (key, def) {
        var val = instance.store[key]; 
        return val == null ? def : val;
      }
    , tryItem: function (key, val) {
        var curr = instance.getItem(key, undefined);
        return curr == null ? instance.setItem(key, val) : curr;
      }
    , clear: function () {
        this.store = {};
      }
    };
}

function PyStore(py) {
  py.data = py.data || {};
  var instance;
  return instance = 
    { setItem: function (key, val) {
        py.data[key] = val;
        return val;
      }
    , getItem: function (key, def) {
        var val = py.data[key];
        return val == null ? def : val;
      }
    , tryItem: function (key, val) {
        var curr = instance.getItem(key, undefined);
        return curr == null ? instance.setItem(key, val) : curr;
      }
    , clear: function () {
        py.data = {};
      }
    };
}

function SessionStore(sessionStorage) {
  var instance;
  return instance = 
    { setItem: function (key, val) {
        sessionStorage.setItem(key, val);
        return val;
      }
    , getItem: function (key, def) {
        var val = sessionStorage.getItem(key);
        return val == null ? def : val;
      }
    , tryItem: function (key, val) {
        var curr = instance.getItem(key, undefined);
        return curr == null ? instance.setItem(key, val) : curr;
      }
    , clear: function () {
        sessionStorage.clear();
      }
    };
}

function persist(cb) {
  window.setTimeout(function() {
    // Determine whether to use Anki's Bridge object (Desktop) or sessionStorage (AnkiDroid) to store data across sides.
    store = typeof(py) !== "undefined" 
            ? PyStore(py)
            : typeof(sessionStorage) !== "undefined" 
              ? SessionStore(sessionStorage)
              : DummyStore();

    if (!document.getElementById('answer')) {
      store.clear()
    }

    cb(store);
  }, 0); //Execute after Anki has loaded its Bridge object.
}

function run(store) {
  elements = document.getElementsByClassName('choice');
  while (elements.length > 0) {
    choices = eval(elements[0].innerText);
    rand = store.tryItem('rand' + choices[0],  Math.random());
    choice = choices.slice(1)[Math.floor(rand * (choices.length - 1))];
    if (typeof(choice) === "string") {
      elements[0].insertAdjacentText('afterEnd', choice);
    } else {
      html = '<div class="choice">'+JSON.stringify(choice)+'</div>';
      elements[0].insertAdjacentHTML('afterEnd', html);
    } 
    var parent = elements[0].parentElement;
    parent.removeChild(elements[0]);
    elements = document.getElementsByClassName('choice');
  }
}

persist(run);

Doesn't work with newer editions of Anki. See replacement using Simon Lammer's Pesistence.