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Re: Gambler dilemma inspired by investing
Posted:
Apr 12, 2012 8:42 AM
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On 2012-04-12, David Bernier <david250@videotron.ca> wrote:
[...]
> For each ticket of type T_k, a unit bet which wins will have
> winnings of 4k^2 , and be a winner with prob. of 1/(2k).
[...]
> With total days = M = (say) 25,000 days, what strategy would you
> advise for a young living person, and why?
Long-term monetary needs are irrelevant, as with these payout
schedules even a ridiculously conservative strategy almost certainly
nets trillions of dollars in less than a week.
E.g. buying 1000 T6s on day one yields about 10^-13 probability of
doing worse than quadrupling your money, and about 10^-29 of actually
making a loss. A median run would return about $11,900.
One the second day, buying 11900 T100s yields about 10^-13 probaiblity
of doing worse than $500,000. The probability of a loss is on the
order of 10^-26. If day one did better or worse, different ticket
types may be bought to maximise expected return given risk levels.
The median yield would be about $2,300,000.
On day 3, almost certainly the best strategy is to buy T1000s, with
expected yield in the billions of dollars for day 4. The risk of loss
is on the order of 10^-500. The same again yields trillions of
dollars on day five with risk so low as to be difficult to calculate.
I suspect different choices of bets and payouts would have better
illustrated various types of trade-off.
--
Tim
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