Re: Weekend Puzzle

Ikaro wrote:

I think we can solve this by treating n is a random variable.

In this case n is a negative binomial random variable, with 1 sucess in
n trials.
The mean of the negative binomial in this case is 2.

So that:
What is the expected value of winnings assuming many games are
played? 2

What entry fee would make it a fair game? 2*(2^(2-1))=4

What would you pay?
1 (I am cheap)

The expected return on any bet is the sum of (the return for outcome n
times the probability of outcome n) over all n. It is therefore infinite
in the case of unlimited payout. If the payout is limited, the expected
value of a game is finite. Even for large limits, the expected value is
surprisingly small. http://en.wikipedia.org/wiki/St._Petersburg_paradox
has this table:

Backer Bankroll Expected value of lottery
Friendly game $64 $3.50
Millionaire $1,050,000 $10.50
Billionaire $1,075,000,000 $15.50
Bill Gates $51,000,000,000 (2005) $18.00
U.S. GDP $11.7 trillion (2004) $22.00
World GDP $40.9 trillion (2004) $23.00
Googolnaire $10^100 $166.50

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
.

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