Conventional Wisdom for Final Jeopardy!

In the Final Jeopardy! round, contestants are allowed to wager zero. If you’re in the lead, you bet to win, so you bet whatever it takes to beat the second-place person by one dollar. If you’re in second place, you have the most math to do. Assuming the first-place contestant bets to win, the second-place person should bet an amount enough to defeat the third-place contestant by one dollar.

That is, if the third-place contestant goes all-in and has a correct answer. This gives the person in second place a chance to win if the first-place contestant messes up. Game theory is complicated, but can be used to gain an edge.