Comments on: Getting rich by counting: the coins in a row puzzle http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/ Articles on game theory and personal finance Thu, 09 Feb 2012 18:20:00 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Presh Talwalkar http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/comment-page-1/#comment-12899 Presh Talwalkar Mon, 05 Dec 2011 19:57:56 +0000 http://mindyourdecisions.com/blog/?p=1443#comment-12899 <b>Adi</b>Add up your array and uou'll find out the odd terms and even terms have the same sum of 37, so Alice can always guarantee a tie. She will not be picking only 1's because both the 25th and 26th coins are 1's which changes the parity: it will mean Bob will have to pick the 1's the rest of the game. AdiAdd up your array and uou’ll find out the odd terms and even terms have the same sum of 37, so Alice can always guarantee a tie. She will not be picking only 1′s because both the 25th and 26th coins are 1′s which changes the parity: it will mean Bob will have to pick the 1′s the rest of the game.

]]> By: Adi http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/comment-page-1/#comment-12885 Adi Mon, 05 Dec 2011 14:55:48 +0000 http://mindyourdecisions.com/blog/?p=1443#comment-12885 I am a bit confused. If bob makes an arrangement: 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1. Where the number represents the denomination of the coin. If Alice is allowed to start first then Alice is always forced to pick a smaller denomination coin while Bob always picks up a 2 which will sum up to be greater than that of Alice. I am a bit confused.
If bob makes an arrangement:
1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1.
Where the number represents the denomination of the coin.
If Alice is allowed to start first then Alice is always forced to pick a smaller denomination coin while Bob always picks up a 2 which will sum up to be greater than that of Alice.

]]> By: house-zat http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/comment-page-1/#comment-7238 house-zat Thu, 26 Aug 2010 21:45:33 +0000 http://mindyourdecisions.com/blog/?p=1443#comment-7238 I would be very interested in knowing another proof of the above result. Also does anyone know as to how to get an optimal strategy for this problem? I would be very interested in knowing another proof of the above result.

Also does anyone know as to how to get an optimal strategy for this problem?

]]> By: SauPa http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/comment-page-1/#comment-6474 SauPa Wed, 14 Apr 2010 17:18:22 +0000 http://mindyourdecisions.com/blog/?p=1443#comment-6474 My Prof. set out this very e.g. for the class. I scoured the internet and presented the same solution. My prof. called the odds and evens solution as CHEAP. and said that an elegant solution requires higher math that my class can handle. So can a strategy be developed that does not depend on ODDS / EVENs logic? My Prof. set out this very e.g. for the class. I scoured the internet and presented the same solution.
My prof. called the odds and evens solution as CHEAP. and said that an elegant solution requires higher math that my class can handle.

So can a strategy be developed that does not depend on ODDS / EVENs logic?

]]> By: William http://mindyourdecisions.com/blog/2009/05/11/getting-rich-by-counting-the-coins-in-a-row-puzzle/comment-page-1/#comment-5825 William Wed, 25 Nov 2009 20:38:51 +0000 http://mindyourdecisions.com/blog/?p=1443#comment-5825 As for maximizing, consider this: Say Alice counts the coins and determines that the odds are worth more. However, partway through the game, after collecting most of the large-value odd coins, Alice recounts and sees that now the even coins are worth more. She should then switch to collecting those. But, how often should she switch? Is it better to recount after each turn or is there a better long-term strategy? Also, is there anything that Bob can do to deter Alice from collecting even more? As for maximizing, consider this:

Say Alice counts the coins and determines that the odds are worth more. However, partway through the game, after collecting most of the large-value odd coins, Alice recounts and sees that now the even coins are worth more. She should then switch to collecting those.

But, how often should she switch? Is it better to recount after each turn or is there a better long-term strategy? Also, is there anything that Bob can do to deter Alice from collecting even more?

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