2009年5月13日 星期三

賭博遊戲

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。


11 則留言:

  1. 因為勝卡賠率和敗卡賠率不一樣 ?
     
    [版主回覆05/15/2009 08:26:00]雲兒:請參看The Teacher的解釋。

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  2. 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。
    [版主回覆05/15/2009 08:27:00]南爾:說得好!我從來沒想過這點呢!

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  3. I don't suppose it's THAT simple.  Just take one win and one loss,
     
    $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

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  4. Oh, you already gave the answer.  I must be blind.  Ok, you want the reason why.
    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 ...

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  5. 今天大跌了 ............. 再低會入貨.  
    [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

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  6. Simply by reading on the numbers, it doesn't feel right.
    15 is only 50% increase of 10.
    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

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  7. 十賭九騙呀!
    [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!

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  8. 咁深嘅數我唔識計 ,不過賭係條死路就係1字咁淺 .

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  9. 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 ~

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  10. 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.
     
    慧行爺爺 :  Please see my first reply below, I proved that the order or wins and losses does not affect the outcome.

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  11. 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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