Find how often peeking rolls back a healthy canary

A canary puts a new version of your agent on a small slice of traffic. Your controller compares it with the current version on paired tasks, and it looks at the running score after every pair.

Write false_rollback(pairs, line) that returns the chance that a version no better and no worse than the current one gets rolled back.

Input and output:

• pairs: how many pairs the canary runs for, a whole number from 1 to 5,000,000.
• line: how far behind sets off the rollback, a whole number from 1 to 5,000,000.
• Return a float. The tests accept any value within 0.000001 of the exact one.

Rules:

• The score starts at 0. Each pair moves it up 1 when the new version wins and down 1 when it loses, each with a chance of one half, whatever the other pairs did.
• The rollback happens the first time the score reaches -line, and no more pairs run after it.
• If the score has not reached -line by the end of the last pair, there is no rollback.