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class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><iconify-icon class="vp-icon" icon="fa6-solid:lightbulb" sizing="both" width="1em" height="1em"></iconify-icon><span class="vp-sidebar-title">学习笔记</span><span class="vp-arrow end"></span></button><!----></section></li></ul><!----></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!----><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->赌博中的数学：Martingle策略</h1><!----><hr></div><!----><div class="" vp-content><!----><div id="markdown-content"><h1 id="赌博中的数学-martingle策略" tabindex="-1"><a class="header-anchor" href="#赌博中的数学-martingle策略"><span>赌博中的数学：Martingle策略</span></a></h1><p>前段时间在Las Vegas待了一个星期左右，以前虽然也来过赌城，但不像这次这么长时间，趁机好好体验了一把赌徒的生活。</p><figure><img src="/images/2016/07/gamble_01.jpg" alt="" tabindex="0" loading="lazy"><figcaption></figcaption></figure><p>来赌场的华人最爱玩的是一种叫做“百家乐”（Baccarat)的游戏，这个游戏的规则并不复杂，节奏也很快，简单来说，就是类似于最简单的猜大小的游戏，每局产生的结果有三种可能性，要么是“庄”，要么是“闲”，或者是“和”，每个结果的概率和赔率大概分布如下：</p><table class="gridtable" style="width:180px;text-align:center;border-collapse:collapse;margin:auto;"><tbody><tr><th style="width:90px;">结果</th><th style="width:90px;">概率</th><th style="width:90px;">赔率</th></tr><tr><td>庄</td><td>45.86%</td><td>0.95</td></tr><tr><td>闲</td><td>44.62%</td><td>1</td></tr><tr><td>和</td><td>9.52%</td><td>8</td></tr></tbody></table><p>举个例子，假如押10块钱到“庄”上，如果牌局结果是“庄”，那么不仅可以把本金10块拿回来，还可以再获得9.5元，但如果结果是“闲”，那么这10块钱本金就赔进去了。很多赌徒之所以痴迷百家乐，除了节奏明快，百家乐的发牌方式设计的也很独特，先发两张牌，然后再通过一定的规则“补牌”，在补牌的过程中结果可能完全反转，整个过程很“刺激”，另外一个原因来自于百家乐的“路单”。所谓路单就是用来记录赌局已经产生的结果的图案，除了直接记录每一局是“庄”、“闲”还是“和”，百家乐的路单中还有“大路”、“大眼仔”、“小路”、“曱甴路”这些古怪的额外数据，用来记录诸如结果是否“齐整”等信息。<br> 作为一个死理性派，我自然一开始就明白“赌徒谬论”（<a href="https://en.wikipedia.org/wiki/Gambler%27s_fallacy" target="_blank" rel="noopener noreferrer">Gambler’s fallacy</a>）这个道理，所有赌局在概率上都是互相独立的，即便连续开出十几次“庄”，下一次是庄的概率仍然是45.86%，那些花花绿绿的路单纯粹就是给人心理安慰罢了，所以我始终没有去费力气分析什么路单，但我一直在尝试另一个和赌博相关的问题，就是“Martingle策略”（<a href="https://en.wikipedia.org/wiki/Martingale%5F%28betting_system%29" target="_blank" rel="noopener noreferrer">Martingale</a>）。<br> Maringle是一种投资策略，在赌徒中间流传甚广，这种策略可以简单描述为“输钱后加倍下注，直到赢钱”。比如在百家乐游戏中，我一开始押10元到“闲”上，如果押对，那么下次仍然继续押10元，如果押错，相当于我赔掉了10元，那么第二局就押20元，这样如果第二局赢得话，我就可以获得40元，刨除两局投入的30元，仍然盈利10元，如果继续输，那么就加倍到40、80、160…元，这样一旦赢钱，就可以把连续输掉的钱都翻本回来。</p><p align="center"><img src="/images/2016/07/gamble_02.jpg"></p> 理论上讲，如果本金足够，并且赌局没有押注上限的话，这种方法是可以绝对盈利的，事实上也的确如此，Martingle策略最早在18世纪就在法国的赌场上流行，我在拉斯维加斯用这个策略，用5美金做最小赌注押“闲”，一度把1000美元本金翻到3000美元，当时心情激动，认为找到了发财的好方法。不过好景不长，很快我遇到连续的“庄”,几乎在瞬间，我几天辛辛苦苦赢来的钱就全赔了进去，最终兴趣索然，就再也不玩了。 为了真实重现这种状况，我用Mathematic模拟了一下Martingle策略： <p align="center"><img src="/images/2016/07/gambler_03.gif"></p> 其实这就是Martingle策略的真相，在运气比较好的情况下，通过输和赢交替进行，资产会小量的逐渐提升，不过一旦遇到连续输的结果，押注翻倍上升，而获利仍然是最小押注，风险就会急剧升高，最终无一例外出现破产出局的情况，所以使用这种策略的最终要的事情就是“见好就收”，一旦赢到一定程度就赶紧收手，所谓久赌必输就是这个道理。 </div><!----><!----><!----></div><footer class="vp-page-meta"><!----><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><!----><!----><!--]--></main><!--]--><footer class="vp-footer-wrapper" vp-footer><div class="vp-footer">使用 <a href="https://theme-hope.vuejs.press/zh/" target="_blank">VuePress Theme Hope</a> 主题 | <a href="https://beian.miit.gov.cn/" target="_blank">京ICP备16018986号-1</a></div><!----></footer></div><!--]--><!--]--><!--[--><!----><!--[--><!--]--><!--]--><!--]--></div>
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