A Riddle of Sorts: Dr. John or Fat Tony

By Dan on Jun 5, 2008 in nonsense

I found this in a Sunday (London) Times story on Nassim Nicholas Taleb* and have paraphrased it here for your consideration:

You toss a coin 40 times and it comes up heads every time. What is the chance of it coming up heads the 41st time?

State you answer and I’ll tell you if you think like a Dr. John, or if you’re more of the Fat Tony type.

 PACO WINS

The solution (of sorts) from the article:

Dr John gives the answer drummed into the heads of every statistic student: 50/50. Fat Tony shakes his head and says the chances are no more than 1%. “You are either full of crap,” he says, “or a pure sucker to buy that 50% business. The coin gotta be loaded.” The chances of a coin coming up heads 41 times are so small as to be effectively impossible in this universe. It is far, far more likely that somebody is cheating. Fat Tony wins. Dr John is the sucker.

It’s not that Dr. John is wrong, the probability of any random toss is 50/50, it’s just that Taleb believes that economists and investors and the like put too much faith in models and statistical rules while ignoring the possibility of an unexpected event, which given enough time, will invariably occur. In this instance, the unexpected event was foul play on the part of the coin tosser.

 

*I’m not dropping names, just citing a source.

9 Comment(s)

  1. 50-50

    Dave | Jun 5, 2008 | Reply

  2. Is it a two-headed coin?

    nancy | Jun 5, 2008 | Reply

  3. 50-50

    RickMonday | Jun 5, 2008 | Reply

  4. Dave and Rick are Dr. John-like. Nancy is starting to think like Fat Tony, but it is a two-headed coin.

    Dan | Jun 6, 2008 | Reply

  5. Dan, I assume you meant two sided, not two headed.

    Here are my thoughts. The statistician in me says the odds of heads on the 41st toss is 50%. However, if you examine the odds of hitting 41 heads in a row with a truly random throw and fair coin, the probability is 9×10^-13, or infinitesimal. Therefore, it could be said that the odds of hitting heads are 100%, because either the coin is unfair or the toss is not truly random (i.e. the outcome is somehow controlled by the tosser). However, this thought process may be flawed because if the throw is being controlled, the probability of calling the throw is 0% because the thrower predetermines the outcome.

    Paco | Jun 7, 2008 | Reply

  6. Dag, Paco!

    nancy | Jun 8, 2008 | Reply

  7. So I guess your response to my first comment was meant to read “but it is NOT a two-headed coin”.

    nancy | Jun 8, 2008 | Reply

  8. Paco, Nancy,

    I meant a two-sided coin. One head, one tail.

    Sorry.

    Dan | Jun 8, 2008 | Reply

  9. It is the same coin tossed at the beginning of most college football games and the home team wins almost everytime. This coin has been what has caused many collegfe football teams to play defense first.

    Pem Hawkins | Jun 16, 2008 | Reply

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