# Re: Lotteries

From: Dani Eder (danielravennest@yahoo.com)
Date: Wed Jan 19 2005 - 16:41:56 MST

Lotteries can make sense to play if you consider
work time vs lesiure time rather than dollar
return. This is because of the non-linear return
in lesiure from a large lump sum prize.

As an example, assume a \$1 ticket gives you a
one in a million chance of winning \$600,000, and
there are no other prizes (this is a typical payout
ratio of real lotteries). Further assume you earn
\$18/hr, so a ticket costs you 0.055 hours of work
to purchase. Further assume you are 25 years old
and expect to work another 40 years at 2000 hr/yr.

Invested sensibly, \$600,000 will produce \$36,000
per year in income (6% return) forever. Ignoring
the income stream your heirs might receive, it would
produce 80,000 hr of lesiure with a probability of
1/1000000, for an expectation of 0.08 hr of lesiure.

Since the expected return is greater than the cost
of the ticket, it makes sense to play in this case.

If you include the stream of free time your heirs
would receive, any sufficiently large lottery
prize has a positive expectation vs it's cost in
time to buy the ticket.

Of course, investing the \$1 for 39 years at 6%
yields \$9.70, which buys you 0.53 hr of expected
lesiure in your 64th year, so sound investing is
a better choice than playing the lottery in most
cases, but a lottery in and of itself can make
sense if you value time rather than dollars.

Daniel

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