Comments on: probability http://malvasiabianca.org/archives/2007/04/probability/ Fri, 10 Feb 2012 05:54:57 +0000 hourly 1 http://wordpress.org/?v=3.3 By: Mark Gritter http://malvasiabianca.org/archives/2007/04/probability/comment-page-1/#comment-42253 Mark Gritter Mon, 30 Apr 2007 05:02:14 +0000 http://malvasiabianca.org/archives/2007/04/probability/#comment-42253 4 possibilities, xy = HH, HT, TH, TT. What we want is functions g(x) and h(y) such that P(g(x)=y && g(y)=x) is maximized. h(x)=x, g(y)=y give cases coins guesses xy g(y)h(x) HH HH -- correct HT TH -- incorrect TH HT -- incorrect TT TT -- correct So guessing that your partner's coinflip matches yours results in a 50% success rate. So does guessing that your partner has the opposite. It is easy to see that this cannot be improved because even if your partner is perfect, you must guess wrong at least 50% of the time. 4 possibilities, xy = HH, HT, TH, TT.

What we want is functions g(x) and h(y) such that P(g(x)=y && g(y)=x) is maximized.

h(x)=x, g(y)=y give cases
coins guesses
xy g(y)h(x)
HH HH — correct
HT TH — incorrect
TH HT — incorrect
TT TT — correct

So guessing that your partner’s coinflip matches yours results in a 50% success rate. So does guessing that your partner has the opposite.

It is easy to see that this cannot be improved because even if your partner is perfect, you must guess wrong at least 50% of the time.

]]>