I absolutely love this article by Tim Urban on how much people stake in Final Jeopardy. How those in the lead optimise their chances of winning, while making sure they still have the most money even if they get the final question wrong.
Quite simple right?
If you have more than twice second place, then bet little enough that second place doubling up still can’t catch you.
The next level can guarantee the leader a win if you get it right and also if both of you get it wrong.
But then there is a level where second place can bet to win if first place is covering their all in bet while making sure 3rd place can’t overtake them.
so far so good...
But then the great bit. Tim THEN looks at the first place strategy to cover this seemingly logical second place assumption.
Game theory at its best.
Ahh – just read it yourselves. Its great.