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id	title	challengeType	forumTopicId	dashedName
5900f4551000cf542c50ff67	Problem 232: The Race	5	301876	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.

assert.strictEqual(euler232(), 0.83648556);

--seed--

--seed-contents--

function euler232() {

  return true;
}

euler232();

--solutions--

// solution required

1.1 KiB Raw Blame History