---
id: 5900f4551000cf542c50ff67
challengeType: 5
title: 'Problem 232: The Race'
---

## Description
<section id='description'>
Two players share an unbiased coin and take it in turns to play "The Race". On Player 1's turn, he tosses the coin once: if it comes up Heads, he scores one point; if it comes up Tails, he scores nothing. On Player 2's turn, she chooses a positive integer T and tosses the coin T times: if it comes up all Heads, she scores 2T-1 points; otherwise, she scores nothing. Player 1 goes first. The winner is the first to 100 or more points.

On each turn Player 2 selects the number, T, of coin tosses that maximises the probability of her winning.

What is the probability that Player 2 wins?

Give your answer rounded to eight decimal places in the form 0.abcdefgh .
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler232()</code> should return 0.83648556.
    testString: assert.strictEqual(euler232(), 0.83648556, '<code>euler232()</code> should return 0.83648556.');

```

</section>

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

<div id='js-seed'>

```js
function euler232() {
  // Good luck!
  return true;
}

euler232();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
