I know we've been paying too much attention to this one Jeopardy! episode but I wanted to write one more post about how it's unlikely to happen again. The three-way tie was an anomaly in large part because one player didn't play the game to win. Going into Final Jeopardy!, here's how the totals stood…
- Scott: $13,400
- James: $8,000
- Anders: $8,000
So how much do you wager if you're one of those contestants? If you're James or Anders, you'd presume the following: That you can't win unless you're right and Scott is wrong. In theory, you could win the game with the wrong answer if Scott was also wrong and he wagered so much that his total dropped to below where you wound up, but you have to operate from the assumption that he's not dumb enough to do that.
James and Anders made the right wagers. Neither one could afford the risk that the other would bet more than he did. You'd also assume that the odds are that it's unlikely you will get the answer right and the other two will both get it wrong. That's possible but it's much more likely that it either stumps everyone or no one. So you'd wager as each of them did: The full eight thousand.
Now, let's say you're Scott. You'd assume from the above that at least one of the other two players — and probably both — is wagering $8,000. A person who does that will beat you unless you're also right and you wind up ahead of them. Therefore, the correct bet for you is at least $2,601. That way, one or both of them could wind up with $16,000 and you'd have $16,001. You'd also win if all three of you were wrong. The only way you could lose is if you're wrong and one or both of the others is right…but that's going to be true no matter what you bet. So at least $2,601 is the proper bet here. The trouble is that Scott didn't bet that way. I'm assuming the Game Theory expert opined that this wouldn't happen again because future players will recognize that Scott blew his chance to win and they won't make that mistake.
But is it really much of a mistake? If Scott had bet $2,601, he'd take home $16,001 and come back on Monday to play against two new opponents. Since he bet $2,600, he takes home $16,000 and comes back on Monday to play against the same two opponents again. Not much difference from his standpoint. Scott didn't really lose anything except being able to say he won.