Game Theory on The Chase - Keddy Chose Poorly
I really do enjoy the new game show, "The Chase" - we're watching episode 4 right now which features James Holzauer as the Chaser. A simplifed explanation for the show's structure: Three competitors answer trivia questions to bank an initial amount. There is a very short deal-making offer, and then they go head to head with the chaser, if they survive that... chase, they add their total into the team's total. The team then faces the chaser as a group to answer more questions in the final round, if they win, they split the prize pool evenly. There's a bit more to it, but that's the main structure.
This episode is one where I have a major gripe with one of the competitor's metagame strategy.
The middle competitor is a woman named Keddy. She had a fairly weak initial round of accruing money and only barely earned $75,000. Her first teammate had already doubled her money in his earning, and the remaining team member has a very respectable Jeopardy pedigree (having won 8 games of Jeopardy.)
Keddy should have played from a position of weakness and out of selfishness, and prioritized making it to the end round to try and win her share of the prize money off the strength of her two team members. I think her mistake, and granted even if she followed my strategy she still might have gotten knocked out, was in the deal making phase of the game.
When it comes time to face the Chaser directly, he offers you a deal: You can either compete for the earned amount with a 3-question lead in the head to head questions. They offer you a lower amount for a 4-question lead. Or they offer you a higher amount (usually at least 2x your amount) to shorten your lead to 2-question. Keddy should have taken the 4-question lead.
She would have only contributed $25,000 to the overall total but she would have had that extra step of lead and given herself that extra bit of life to be part of the end of the game.
Had she made it to the final round, her team mates had earned $325,000. She would have brought the total to $350,000, and earned herself $116,667 all because she opted for the safe route.