---
id: 5900f4771000cf542c50ff8a
challengeType: 5
title: 'Problem 267: Billionaire'
---

## Description
<section id='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 = 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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler267()</code> should return 0.999992836187.
    testString: assert.strictEqual(euler267(), 0.999992836187);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler267() {
  // Good luck!
  return true;
}

euler267();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>