49 lines
1.1 KiB
Markdown
49 lines
1.1 KiB
Markdown
---
|
|
id: 5900f4771000cf542c50ff8a
|
|
title: 'Problem 267: Billionaire'
|
|
challengeType: 5
|
|
forumTopicId: 301916
|
|
dashedName: 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.
|
|
|
|
# --hints--
|
|
|
|
`euler267()` should return 0.999992836187.
|
|
|
|
```js
|
|
assert.strictEqual(euler267(), 0.999992836187);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler267() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler267();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|