Re: [機統] 定額下注的賠光機率

[leondemon (狗狗)]

※ 引述《Desperato (Farewell)》之銘言：
: D. 結論
: 四題的答案近似值分別為
: 1) ~= 0.000785711
: 2) ~= 0.000000945        |
: 3) ~= 0.00152243884034744235876...
: 4) ~= 0.00152243884034744481467...
:                          |

寫了一個 JavaScript 代碼模擬遊戲，下方代碼可以用 node.js 執行，
或是開瀏覽器，在網頁右鍵選擇 inspect 找到 console，貼上代碼來執行
=====================================================================
// 宣告函式，不會執行
const WIN = 'win';
const LOSE = 'lose';
const FINISHED = 'done';
const GAME_OVER = 'game over';

function play([win_chances, lose_chances]) {
  const total = win_chances + lose_chances;
  if (total == 0) {
    return [FINISHED, null];
  }
  const result = Math.floor(Math.random() * total);
  return (result < win_chances) ?
    [WIN, [win_chances - 1, lose_chances]] :
    [LOSE, [win_chances, lose_chances - 1]] ;
}

function game(win_chances, lose_chances, lose_threshold) {
  let chances = [win_chances, lose_chances];
  let result;
  let current_wins = 0;
  let current_loses = 0;
  const play_series = [];
  while (chances) {
    [result, chances] = play(chances);
    // For debug
    // console.log(`Play ${series.length + 1}: ${result}, running next play with [${turns}]`)
    play_series.push(result);
    if (result == WIN)  current_wins++;
    if (result == LOSE) current_loses++;
    if (current_loses - current_wins >= lose_threshold) {
      play_series.push(GAME_OVER);
      chances = null;
      break;
    }
  }
  return play_series;
}

function simulate_multiple_games(game_count, win_count, lose_count, lose_threshold) {
  let finished_counts = 0;
  let game_over_counts = 0;
  for (let i = 0; i < game_count; i++) {
    const play_series = game(win_count, lose_count, lose_threshold);
    const game_result = play_series.slice(-1).pop();
    if (game_result == FINISHED)  finished_counts++;
    if (game_result == GAME_OVER) game_over_counts++;
    // For debug
    // console.log(`Game ${i+1}: ${game_result} with ${play_series.length-1} plays`)
  }
  return { finished_counts, game_over_counts };
}
=====================================================================

要模擬 100萬次，53勝47負的賽局，起始有16份籌碼的比賽，可執行：

simulate_multiple_games(1000000, 53, 47, 16)

我跑了10次，取平均和標準差，得到提早結束比賽 (GAME_OVER) 的發生機會為

 ~= 0.0007760
 ± 0.0000282

另外直接跑了 1 億次模擬 ~= 0.0007851

跟 Desperato 的計算結果差不多

感謝 D 大 :)


補充

要模擬 100萬次，60勝40負的賽局，起始有16份籌碼的比賽

simulate_multiple_games(1000000, 60, 40, 16)

一樣10次的平均和標準差為

~= 0.00000710
± 0.00000285

似乎和 D 大的數據有落差？

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※ 文章網址: https://www.ptt.cc/bbs/Math/M.1546522960.A.D16.html
※ 編輯: leondemon (223.72.90.193), 01/03/2019 21:58:04
推 oblivion87  : 板上神人真的多==
推 Desperato   : 沒錯又算錯了XD 已訂正
→ Desperato   : ~= 0.00000580349 進標準差了 至少數量級正確
→ leondemon   : 感謝！我研究一下公式 :P