Difference between revisions of "Sandbox"

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<center>
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== Another game==
{| border="1" style="text-align:center"
 
|+ Transition Matrix
 
!      !! 0 !! 1 !! 2 !! 3 !! 4
 
|-
 
! 0
 
| 12/36 || 6/36 || 8/36 || 10/36 || 0
 
|-
 
! 1
 
| 3/36 || 27/36 || 0 || 0 || 6/36
 
|-
 
! 2
 
| 4/36 || 0 || 26/36 || 0 || 6/36
 
|-
 
! 3
 
| 5/36 || 0 || 0 || 25/36 || 6/36
 
|-
 
! 4
 
| 0 || 0 || 0 || 0 || 1
 
|-
 
|}
 
</center>
 
<math>= a_0+a_1x+a_2x^2+\cdots</math>
 
  
Let a coin with shows H and T with probabilities 1/2, 1/2 , be tossed repeatedly.  Let B be the sequence HTH.  We want to compute the expected time to get the sequence HTH  ENB. Imagine that a gambler bets 1 dollar on the sequence B occurring to the following rules of fair odds.  At the first toss, if heads appears, he receives 2 dollars (including his bet) and must parley the 2 dollars on the occurrence of Tails on next toss. In case he wins he receives 12 dollars and must partly the whole amount of 12 dollars on the occurance of heads on the next toss. If he wins, he recieves the toal amount of 2 dollars and the game is over.
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In his book xxx Keynes wrote<br><br>
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<blockquote> Professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the price being awarded to the competitor whose choice most nearly corresponds to the average preference of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees </blockquote>
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This game can be easily replicated by asking people to pick a number between 0 and 100, and telling them the winner will be the person who picks the number closest to two-thirds the average number picked. The chart below shows the results from the largest incidence of the game that I have played - in fact the third largest game ever played, and the only one played purely among professional investors.

Revision as of 19:52, 18 August 2009

Another game

In his book xxx Keynes wrote

Professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the price being awarded to the competitor whose choice most nearly corresponds to the average preference of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees

This game can be easily replicated by asking people to pick a number between 0 and 100, and telling them the winner will be the person who picks the number closest to two-thirds the average number picked. The chart below shows the results from the largest incidence of the game that I have played - in fact the third largest game ever played, and the only one played purely among professional investors.