const rnd = Math.random;
const play_round = choices => {
    // Place prize behind one door
    const winner = choices[rnd() * 3 | 0];

    const pickIdx = rnd() * 3 | 0;
    const pick = choices[pickIdx];
    choices.splice(pickIdx, 1); // Remove door from future randoms

    const showIdx = rnd() * 2 | 0;
    const show = choices[showIdx];
    choices.splice(showIdx, 1); // Remove door from future randoms

    // if (show == winner) {
    //     // Do nothing if Monty accidentally won
    // } else {
    //     // Also do nothing if Monty showed an empty door
    // }

    // Now that monty has shown a door, player may change their guess to final door
    const pick2 = choices[0];

    // return doors (so next round does not need to re-construct the array). Order doesn't matter!
    choices.push(pick);
    choices.push(show);

    // Check win
    return (pick == winner) | ((pick2 == winner) << 1);
};

const test = _ => {
    const start = performance.now();
    const rounds = 10 ** 7;
    const tolerance = 0.01; // 1 %

    let choices = [...Array(3).keys()];
    let wins_unchanged = 0;
    let wins_changed = 0;
    for (_ of Array(rounds)) {
        const result = play_round(choices);
        wins_unchanged+= result&1;
        wins_changed+= (result >> 1)&1;
    }
    const wins = [wins_unchanged, wins_changed];

    const win_percent = [wins_unchanged / rounds, wins_changed / rounds];
    const diff = Math.abs(win_percent[0] - win_percent[1]);

    const floor2 = (v, precision) => {
        const nudge = 10 ** precision;
        return Math.floor(nudge * v) / nudge
    }
    const precision = 2;
    console.log(`unchanged: ${wins_unchanged} wins; ${floor2(100 * win_percent[0], precision)} %`)
    console.log(`changed: ${wins_changed} wins; ${floor2(100* win_percent[1], precision)} %`)
    console.log(`difference: ${100 * diff} %`)

    if (diff < tolerance) {
        console.log("Within tolerances!!! There is no difference!!!")
    }
    console.log(`time: ${performance.now() - start} ms`)
}

test();