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Re: Gambler dilemma inspired by investing
Posted:
Apr 13, 2012 1:07 AM
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On 04/12/2012 10:47 PM, Tim Little wrote:
> On 2012-04-12, David Bernier<david250@videotron.ca> wrote:
>> At the outer edge for risk-loving gamblers, I figure that about 1%
>> of gamblers making-off over a lifetime at an average fortune
>> doubling-time of 2.0 to 6.0 years (as base approximation) is roughly
>> the right range (for the doubling time) ...
>
> Do you mean over a (say) 60-year period, you would want the scenario
> set up so that 1% of the most risk-taking gamblers multiply their
> wealth by about 2^15, while the rest wipe out completely? That would
> be something like 20% maximum profit with 5% chance of disaster each
> year.
Possibly: yes to X 2^15 factor in a 60-year, at the
doubling time of 4.0 years for 1% of the most risk-taking
gamblers, the 99% others betting the ranch at every occasion,
so yes if 99% applies to those who max-out on risk.
Those with a happy medium between risk-averseness and
risk-lovers would be expected to do medium-well, but with
less average annual growth than the lucky 1% among the
max-out on risk takers (bet the ranch at every occasion ...).
If it's formulated/structured correctly, I've been thinking that
the medium risk-takers ought to get substantially less
average annual growth-rate than the great risk-takers,
but benefit from having a more prudent wealth distribution
after 60 years. For those who exerience a wealth wipe-out,
it's a multiply by zero issue, with average annual growth
rate of -oo % , if you know what I mean. There could be
a $1000 automatic "pension"-like payout after 60 years.
That way, nobody would have zero after "pension" pay,
at the end of 60 years.
David Bernier
> That's doable. I don't think independent "tickets" with variable
> rates of return are the way to do it, though. Independent tickets
> give the opportunity to minimize risk while maintaining returns.
>
> Perhaps something like: buy any number of tickets of type T_x, where x
> is a nonegative real. Some r in [0, 1] is chosen each year, and
> tickets return 1+x if r>= 2 x^2, 0 otherwise.
>
> The average payoff of a T_x ticket is (1+x)(1-2x^2), with a maximum at
> x ~= 0.194. The doubling time is then 3.9 years, with a 1%
> probability of "survival" over 58 years.
[...]
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