Using the Lottery to Break a Tie

[jakka]

Two brothers, Mike and Kilby, living in two Canadian cities, place a wager on a hockey game. Not the NHL, they're not playing. But the game ends in a tie. This is a disappointment, because they need to break this tie.

Because they can't get together to flip a coin, Mike, the older brother, suggests that they somehow use the published results of the next Lotto 649 to settle their wager. Now the Lotto 649 is Canada's national lottery. They draw 6 numbers at random from 1 to 49. They also draw a 7th bonus number. When published in the newspapers, the six numbers are listed from low to high, then the bonus number is given.

Kilby says this is not so easy to do. So here's the challenge. How can they agree to use the next 649 results, such that they each have a 50% chance of winning?