A forward from another group that may interest the mathematically minded,
since there has been some talk of risk/reward. BTW I personally have my
doubts it is inductive proof.
>>The discussion on risk made me think of the following
proof on risk aversion I learned a few years
Imagine you are offered the following game: You will
coin. If it's tails, the game is over, and you
get nothing. If
it's heads, you win two dollars and
keep going. You flip again, and if
it's tails, the
game's over and you leave with your $2. If
heads, you win $4 (total, not in addition to your
and keep going. Again, if it's
tails, you leave with your $4, and if
it's heads you
win $8 and keep going. This continues until
finally get a tail.
You cannot lose money from this game, only win
However, imagine that the person running it charges
you a set fee in
order to play. How much would you be
willing to pay to play this.
Quick, throw out a
number before reading farther.
out how much you should pay, you should
figure out the expected value of the
game. There's a
1/2 probability you'll get nothing. (If the
toss is tails.) There's a 1/4 probability you'll get
$2. (Heads then tails.) There's a 1/8
probability you'll get
(Heads-heads-tails) And so on. So the expected
of playing the game is:
(1/2)*0 + (1/4)*2 + (1/8)*4 + (1/16)*8 +
0 + (2/4) + (4/8) + (8/16) +
(16/32) + ...
Which of course equals:
0 + 1/2 + 1/2 + 1/2 + 1/2 +
Which doesn't converge. The expected value of the
Head scratcher time. How many of you said they'd
an infinite amount of money to play this game? I
don't see too
many hands raised. Which makes sense.
Would you really bet everything
you own, leaving
yourself penniless and naked on the street, to play
game where there's a 50% chance you'll be left with
where there's only a 1 in a thousand
chance you'll get more than a thousand
My suspicion is that very few people said they'd pay
than $10 to play, and almost nobody offered more
than $100. Even now,
that you've seen the math and
know the expected value is infinite, I doubt
more than $100 to play.
People are risk averse,