Two things demonstrate to me that Jeopardy contestants don't understand rudimentary game theory.

Case 1: In many cases you have a score where one person is way ahead, and the other two trail by an amount so that it's a "run-away", meaning that even if the second place contestant bet the maximum amount in final Jeopardy, it's not possible for him to catch up. Example:

Contestant 1 | Contestant 2 | Contestant 3 |

$12000 | $5000 | $3000 |

Suppose there only a few clues left with no Daily Doubles available. What is the best strategy for Contestant 3? If there aren't enough clues in that category for him to get to $6000, **Contestant 3 should stop buzzing in**. Contestant 1 would be foolish to bet a single dollar in Final Jeopardy if he has twice his nearest competitor. Contestant 2, on the other hand, can easily earn enough to get to $6000. Therefore**.** By continuing to buzz in, Contestant 3 does nothing but take potential money away from Contestant 2, and increase the likelihood of a run-away. This hurts himself, not just Contestant 2, because in the event that both Contestant 1 and 2 miss the question, Contestant 3 can then win.

Case 2: In any of the two-day contests, such as the finals of the Tournament of Champions, wagering a huge amount in Final Jeopardy of the first game is extremely imprudent. Instead, **they should treat that final like any other Daily Double**. Although the score is reset at the beginning of the next day, the dollar figure that matters is the total of both days. It's therefore insane to bet all your money, unless you would normally bet all your money on a Daily Double (hint: whenever somebody bets a large amount on a Daily Double there are gasps in the audience).