近日熱錢流竄，香港股市再度成為賭徒的樂園。可恨栗子妹蟹貨纏身，未能去湊湊熱鬧，真是可憐復可悲。
說起賭，記得在書中讀過這樣的一個賭博遊戲：
桌上有 100 張蓋著的卡，其中 55 張寫了「勝」，餘下的 45 張寫了「敗」。每翻開一張「勝」卡，賭本便會增加 50% (例：$10 --> $15)；若是翻開「敗」卡，賭本便會減少一半 (例：$10 --> $5)。
問：假若閣下有 $10,000 賭本，在翻完所有卡後 (全部翻開，一張不漏)，賭本還有多少？
有人以為「勝」卡比「敗」卡多，在翻完這 100 張卡後，口袋應該會有進賬。這樣想便大錯特錯了！要知道在賭博遊戲中，勝出的永遠只有莊家，賭仔只有賠錢的份兒。栗子妹可以告訴大家，在翻完所有卡後，閣下的賭本只會餘下 $1.38！
至於為甚麼會這樣，大家不妨想想。
因為勝卡賠率和敗卡賠率不一樣 ?
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[版主回覆05/15/2009 08:26:00]雲兒：請參看The Teacher的解釋。
正如一隻股票由2元跌至1元，其股價跌了50%。但要它由1元升回2元，那便要升100%了。
回覆刪除[版主回覆05/15/2009 08:27:00]南爾：說得好！我從來沒想過這點呢！
I don't suppose it's THAT simple. Just take one win and one loss,
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$10-->$15-->$7.50.
Reverse the order and you get the same $7.50. This establishes the fact that the order of wins and losses doesn't change the results. So we could just do the calculation as:
$10k x (1.5) ^55 x (.5)^45 = $1.37616162511746
Oh, you already gave the answer. I must be blind. Ok, you want the reason why.
回覆刪除The macro explanation is: the simplistic but incorrect answer you gave earlier was based on "linear" assumptions, but the rules of +50% and -50% on each trial are exponential. We intuitively think linearly, that's why the actual answer feels odd.
The micro explanation: Take the one win and one loss. I think to make it even afterwards, the win needs to yield a 100% gain in order to offset the 50% loss on the loss. So, a 50% only gain will give you a net of a 25% loss after a win/loss combo, after 45 of such combo, or 90 cards, we have about 2.4 cents left, then we win 10 times in a roll, at 50% gain each, reaching $1.38.
[版主回覆05/15/2009 08:30:00]Thank you so much for the detailed explanation, Teacher . It's good you mentioned the word 'exponential'. Few people will think of it (unless you study Maths). And fraudsters just make use of that to cheat people ...
今天大跌了 ............. 再低會入貨.
回覆刪除[版主回覆05/15/2009 08:31:00]小月：我倒希望它多升一會兒，好等我先沽點貨
Simply by reading on the numbers, it doesn't feel right.
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But losing 5, it's like getting a 100% decrease, which left 5 only.
I don't know how to explain, but it just doesn't feel right.
[版主回覆05/15/2009 08:33:00]Teamaster: 不是呀，減少也是50%，因為百分減少的算式是：
(10-5)/10 x 100% = 50%
不過一般人很少會這樣想的。騙徒就是利用我們的錯覺去行騙。真是要不得
十賭九騙呀！
回覆刪除[版主回覆05/15/2009 08:33:00]井兄：說得再對不過。所以小賭怡情，大賭亂性！
咁深嘅數我唔識計 ，不過賭係條死路就係１字咁淺 ．
回覆刪除栗子妹：在上述賭博遊戲中，那要看翻開的勝卡和敗卡的先後次序和次數，才會決定最終的結果。若然在一般的賭博中，慧行相信輸的機會最多 ~
回覆刪除Chestnut: My new blog is under siege by a bunch of ladies. Since you have a good sense of economics, I could use your support. Thank you in advance.
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慧行爺爺 : Please see my first reply below, I proved that the order or wins and losses does not affect the outcome.
所以，當我的股票跌了90%，要回到家鄉，卻要10倍。你話嘞，咁我有乜可能返到家鄉先?
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