49 lines
1.2 KiB
Markdown
49 lines
1.2 KiB
Markdown
---
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id: 5900f4771000cf542c50ff8a
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title: 'Problem 267: Billionaire'
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challengeType: 5
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forumTopicId: 301916
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dashedName: problem-267-billionaire
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---
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# --description--
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You are given a unique investment opportunity.
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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.
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Your return is double your bet for heads and you lose your bet for tails.
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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.
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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?
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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.
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# --hints--
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`billionaire()` should return `0.999992836187`.
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```js
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assert.strictEqual(billionaire(), 0.999992836187);
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```
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# --seed--
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## --seed-contents--
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```js
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function billionaire() {
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return true;
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}
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billionaire();
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```
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# --solutions--
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```js
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// solution required
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```
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