How to cheat a bad mathematician

Source: seneca.fis.ucm.es
Topic: Cheat

Short Desciption:
How to cheat a bad mathematician. 1. Game A:. I pay you one dollar with probability 1/2 + . you pay me one dollar with probability 1/2 ...

 

Content Inside:
How to cheat a bad mathematicianPage 1How to cheat a bad mathematician1Game A: I pay you one dollar with probability 1/2 + you pay me one dollar with probability 1/2.Game B: if my current capital is a multiple of 3:I pay you one dollar with probability 9/10 + you pay me one dollar with probability 1/10; if my current capital is not a multiple of 3:I pay you one dollar with probability 1/4 + you pay me one dollar with probability 3/4.One can prove that both games are fair for = 0 (detailed balance).Then setting > 0 will give in each game advantageto the mathematician (i.e. his average gain grows in time).I make to the mathematician either one of these two offers:Lets play twice game A twice game B and so on.(for sceptical but still bad specially at Markov chains mathematicians)In each run lets toss a coin to choose which game we play.0250500t20246810my gainperiodicrandomgame agame b0250500t64202468my gainperiodicrandomgame agame b = 0 = 0.0051This slide was part of a presentation by Juan MR Parrondo entitled Efficiency of Brownian Motors given inthe Workshop of the EEC HC&M Network on Complexity and Chaos (#ERBCHRXCT940546) at the Institute forScientific Interchange (ISI) Foundation (Torino Italy) July 1996.

 

 

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