---
id: 5900f4551000cf542c50ff67
title: 'Problem 232: The Race'
challengeType: 5
forumTopicId: 301876
dashedName: problem-232-the-race
---

# --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 .

# --hints--

`euler232()` should return 0.83648556.

```js
assert.strictEqual(euler232(), 0.83648556);
```

# --seed--

## --seed-contents--

```js
function euler232() {

  return true;
}

euler232();
```

# --solutions--

```js
// solution required
```