Runs thousands of trials to evaluate whether putting the seat down or up or not changing it is best

graph.txt

https://shared.benc.io/screencaps/2018/09/Oropendula/24704094-46c0-4af6-afdb-56f7747625bc.png
That graph shows the default code's (seen above) results. Lower on the graph means better. This graph indicates that the best approach is to leave the seat where you had it except in the niche case where there is less than 2% biological males using that toilet. My guess is that would only apply to biological males who have undergone a gender change and now use the women's restroom.

main.js

const TOTAL_PEOPLE = 20000;
const FREQUENCY = { 1: 6.5, 2: 1 }; // number 1 vs number 2

const doTrials = (percentMale = PERCENT_MALE, setTo = 'same') => {
  let isUp = false; // false = down
  const strategy = results => {
    // penalizing any changes made after you've "gone"
    if (setTo !== 'same' && setTo !== isUp) {
      results.needChange++;
    } else {
      results.noChange++;
    }
    isUp = setTo === 'same' ? isUp : setTo;
  };

  const results = { needChange: 0, noChange: 0 };
  for (let i = 0; i < TOTAL_PEOPLE; i++) {
    const isMale = Math.random() < percentMale;
    let neededState;

    if (isMale) {
      neededState =
        Math.random() < FREQUENCY[1] / (FREQUENCY[2] + FREQUENCY[1]);
    } else {
      // female
      neededState = false;
    }

    if (isUp !== neededState) {
      // if a change is needed
      results.needChange++;
      isUp = !isUp;
    } else {
      results.noChange++;
    }

    strategy(results);
  }

  return results.needChange / (results.needChange + results.noChange); //
};

(() => {
  let percentMale = 1; // starting percentage
  const results = [];
  while (percentMale > 0) {
    const strategyRecords = {
      percentMale,
      down: 0,
      same: 0,
      up: 0,
    };

    const NUM_TRIES = 6;
    for (let i = 0; i < NUM_TRIES; i++) {
      strategyRecords.same += doTrials(percentMale); // leaving it wherever you left it
      strategyRecords.up += doTrials(percentMale, true); // always leaving it up
      strategyRecords.down += doTrials(percentMale, false); // always leaving it down
    }

    strategyRecords.same /= NUM_TRIES;
    strategyRecords.up /= NUM_TRIES;
    strategyRecords.down /= NUM_TRIES;

    results.push(strategyRecords);
    percentMale -= 0.005;
  }
  results.forEach(trial =>
    console.log(
      `${trial.percentMale}, ${trial.same}, ${trial.up}, ${trial.down}`,
    ),
  );
})();