---
id: 5900f4771000cf542c50ff8a
challengeType: 5
title: '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 = 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.
## Instructions
## Tests
```yml
tests:
- text: euler267() should return 0.999992836187.
testString: assert.strictEqual(euler267(), 0.999992836187, 'euler267() should return 0.999992836187.');
```
## Challenge Seed
```js
function euler267() {
// Good luck!
return true;
}
euler267();
```