1.2 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4771000cf542c50ff8a | Problem 267: Billionaire | 5 | 301916 | problem-267-billionaire |
--description--
You are given a unique investment opportunity.
Starting with £1 of capital, you can choose a fixed proportion, f, of your capital to bet on a fair coin toss repeatedly for 1000 tosses.
Your return is double your bet for heads and you lose your bet for tails.
For example, if f = \frac{1}{4}, for the first toss you bet £0.25, and if heads comes up you win £0.5 and so then have £1.5. You then bet £0.375 and if the second toss is tails, you have £1.125.
Choosing f to maximize your chances of having at least £1,000,000,000 after 1,000 flips, what is the chance that you become a billionaire?
All computations are assumed to be exact (no rounding), but give your answer rounded to 12 digits behind the decimal point in the form 0.abcdefghijkl.
--hints--
billionaire() should return 0.999992836187.
assert.strictEqual(billionaire(), 0.999992836187);
--seed--
--seed-contents--
function billionaire() {
return true;
}
billionaire();
--solutions--
// solution required