https://x.com/pi_ni_ki/status/1807609334488264867 計算スクリプト

index.js

// 試合を繰り返して昇格する確率を求める
// ・5勝の貯金を積み上げると昇格
// ・3敗の借金を積み上げると降格
// ・借金中に勝利すると今までの借金がチャラになり＋1勝になる
generateCSV();

function generateCSV() {
  const header='1試合の勝率,昇格確率,降格確率,合計';
  let csv = header + '\n';
  for (let p = 0; p <= 100; p ++) {
    const result = calculate(p / 100);
    csv += `${p / 100},${result.promotionProb.toFixed(4)},${result.demotionProb.toFixed(4)},${result.sum.toFixed(4)}\n`;
  }
  console.log(csv);
}

/**
 * @param p 1試合の勝率
 */
function calculate(p = 0.5) {
  let promotionProb = 0;
  let demotionProb = 0;
  for (const pat of patterns()) {
    let prob = 1;
    for (const event of pat) {
      if (event === 'WIN') {
        prob *= p;
      } else if (event === 'LOSE') {
        prob *= 1 - p;
      } else if (event === 'PROMOTE') {
        promotionProb += prob;
      } else if (event === 'DEMOTE') {
        demotionProb += prob;
      }
    }
  }
  return {
    promotionProb,
    demotionProb,
    sum: promotionProb + demotionProb,
  };
}

/**
 * 勝ち負けのパターンを生成する
 */
function* patterns(win = 0, lose = 0) {
  if (win === 5) {
    yield ['PROMOTE'];
    return;
  }
  if (lose === 3) {
    yield ['DEMOTE'];
    return;
  }
  for (const winPat of patterns(win + 1, 0)) {
    yield ['WIN', ...winPat];
  }
  for (const losePat of patterns(win, lose + 1)) {
    yield ['LOSE', ...losePat];
  }
}