Comments on: A math problem that might help you win one million dollars http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/ Articles on game theory and personal finance Thu, 29 Jul 2010 12:43:59 -0500 hourly 1 http://wordpress.org/?v=3.0 By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/comment-page-1/#comment-4041 Presh Talwalkar Wed, 17 Dec 2008 08:30:17 +0000 http://mindyourdecisions.com/blog/?p=1060#comment-4041 Thanks for the additional explanations guys. I think it is easy to get caught up in the details of explaining it in words...which can be hard since our intuition focuses on expected wins, as Scott points out. Once the focus is about the necessary condition for a streak, namely winning the middle game, the rest follows somewhat trivially... Thanks for the additional explanations guys. I think it is easy to get caught up in the details of explaining it in words…which can be hard since our intuition focuses on expected wins, as Scott points out. Once the focus is about the necessary condition for a streak, namely winning the middle game, the rest follows somewhat trivially…

]]> By: Scott http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/comment-page-1/#comment-3973 Scott Fri, 12 Dec 2008 23:57:37 +0000 http://mindyourdecisions.com/blog/?p=1060#comment-3973 As shown the second match is necessary while neither the first or last are (you can lose either the first or last and still get a streak by winning the other one). This fact alone shows why the second match is more important. The reason why I initially found this counterintuitive had to do with thinking about it the way most people would: winning the most matches. Under this frame of mind you'd want to go against the easier player more. However, for streaks, the middle matches have higher importance so you want the easier matches focused there. As shown the second match is necessary while neither the first or last are (you can lose either the first or last and still get a streak by winning the other one). This fact alone shows why the second match is more important. The reason why I initially found this counterintuitive had to do with thinking about it the way most people would: winning the most matches. Under this frame of mind you’d want to go against the easier player more. However, for streaks, the middle matches have higher importance so you want the easier matches focused there.

]]> By: Rick http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/comment-page-1/#comment-3971 Rick Fri, 12 Dec 2008 19:36:49 +0000 http://mindyourdecisions.com/blog/?p=1060#comment-3971 It's NOT that winning the SECOND set is important, it's that winning TWO sets in a row is important (winning the FIRST set is just as important as winning the second to make a streak). In my view, the explanation is even simpler: In an alternating series, to make two in a row, you have to win from both players once. Would you rather try twice against the better player (C) or try twice against the easier player (F)? If for abstraction sake we turn playing 'Father' into a walkover, it immediately shows why the CFC is the better choice. It’s NOT that winning the SECOND set is important, it’s that winning TWO sets in a row is important (winning the FIRST set is just as important as winning the second to make a streak). In my view, the explanation is even simpler: In an alternating series, to make two in a row, you have to win from both players once. Would you rather try twice against the better player (C) or try twice against the easier player (F)? If for abstraction sake we turn playing ‘Father’ into a walkover, it immediately shows why the CFC is the better choice.

]]> By: michael webster http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/comment-page-1/#comment-3931 michael webster Wed, 10 Dec 2008 08:08:24 +0000 http://mindyourdecisions.com/blog/?p=1060#comment-3931 That was fun. But I think the point is made easier -once you have drawn out the state space, it then becomes "obvious" that to succeed you have to win the second match. Who would you like to play then in the second match? The weaker opponent of course. That was fun. But I think the point is made easier -once you have drawn out the state space, it then becomes “obvious” that to succeed you have to win the second match.

Who would you like to play then in the second match? The weaker opponent of course.

]]> By: Reddy http://mindyourdecisions.com/blog/2008/12/09/a-math-problem-that-might-help-you-win-one-million-dollars/comment-page-1/#comment-3927 Reddy Wed, 10 Dec 2008 03:17:44 +0000 http://mindyourdecisions.com/blog/?p=1060#comment-3927 Amazing article, Presh. Scott: Your analysis was superb. Amazing article, Presh.
Scott: Your analysis was superb.

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