Partying with Bill Gates...and a Coin-Toss Quandary

Nov 04, 2000

RAY: A fellow finds himself at a party at, of all places, Bill Gates' house. And, who should be standing next to him but Bill Gates himself! The fellow says, "Gee, this is a pretty big living room you have. It's jam-packed with people."
Gates says, "How many people do you think are here?"
The fellow says, "I don't know. Maybe about 1100?"
Gates replies, "That's very good. There are about 1100 people here. You're very good with numbers. Are you into games of chance? If we flipped a coin 10 times in a row, do you think there's anyone in this room who could call it correctly each time?"
The fellow says, "I suppose there's a chance, but it's got to be a pretty small chance."
And Gates says, "I think there is a chance. In fact, I'll bet you $10 million to your $1,000 that it can happen in this room, that there's one person who could guess it correctly 10 times in a row."
The guy says, "You're on, Gates."
Should he have taken the bet? What do you think?
TOM: He's right, but he's gonna lose. Because it sounded very good. Maybe he just wanted Bill Gates to feel good. I mean, the guy's probably got an ego as big as Cleveland. Cleveland? As big as Australia, maybe.
RAY: Maybe.
TOM: And if the guy didn't fall for his little trick here, then Bill Gates might have lost a little of his self-esteem.
RAY: Well, anyway, Gates is gonna win his money.
TOM:: Yeah.
RAY: Unfortunately. Because it is going to happen, and it must happen.
TOM: Mmmm?
RAY: Let's say out of those 1,100 people we take, for the sake of convenience, 1,024 of them. It's just a number I picked out of the air.
TOM:: Just a number you picked out of the hat by doubling 512.
RAY: And let's take that 1,024 people and make 512 pairs of people.
TOM:: Yeah. OK.
RAY: OK? And each one of those pairs will do a coin toss. Well, obviously, one is going to . . . one of them is going to win.
TOM:: Mmm-hmm.
RAY: So, we're going to have 512 winners.
TOM:: Yeah.
RAY: OK? And conveniently, we take those 512 and we divide them into 256 pairs now.
TOM:: That's a nice number too.
RAY: Isn't it amazing?
TOM:: Yeah.
RAY: And, of course, we're going to have 256 people flipping coins. We're going to have . . .
TOM:: One hundred twenty-eight winners.
RAY: Son of a gun!
TOM:: Isn't that something?
RAY: And you do that nine times.
TOM:: Yeah.
RAY: And you're down to two people.
TOM:: Mmm-hmm.
RAY: And inevitably, one of them's going to win.
TOM:: Mmm-hmm.
RAY: So, of those people that played, you had two people that wound up doing it correct nine times, and one person who had to do it correct 10 times in a row.
TOM:: Right.
RAY: And Gates wins his money.
TOM:: And that was his bet.
RAY: He wins all the time, man! I'm getting sick of it!
TOM:: He's getting sick of it too.
RAY: Who's our winner?
TOM:: The winner is Mark Kime from Valparaiso, Indiana.

Get the Car Talk Newsletter