Two particular instances occur over and over:
1) A contestant has his opponents more than doubled in money going into Final Jeopardy and thus cannot lose (unless he pulls a Clavin). He then bets everything he can minus one dollar to ensure victory. In real life would this guy (think typical Jeopardy contestant) really bet 4,5,6 thousand dollars on his ability to answer one question? There is a logical disconnect between game money and real money but game money is real money. In fact, this game plan only makes sense if the contestant is uniquely competent in the Final Jeopardy category, it happens far more frequently.
2) A contestant is ahead going into Final Jeopardy but has not doubled up her opponent. She then bets enough to beat her opponent by $1 (assuming her opponent bets everything he has). This strategy is designed to send home a known quantity (the opponent said contestant has already beaten) to be replaced on the following day by an unknown quantity (a different contestant). This strategy is also nonsensical. If a contestant has beaten her opponent through single and double Jeopardy she should welcome the opportunity to play him the following day.
Today's Jeopardy episode featured another interesting scenario peppered with misguided strategy. The returning champion (Contestant A) was awarded with both Daily Doubles in Double Jeopardy. Both times he bet unnecessarily large sums of money in an attempt to separate himself from his opponents. When Final Jeopardy rolled around he had about $15,500 and his two opponents had something like $12,400 (Contestant B) and $12,200 (Contestant C). The Final Jeopardy topic was Royalty Wives (or something like that), a seemingly difficult category. Now, Contestants B and C should certainly have realized that if Contestant A was going down it was not going to be as a result of under betting Final Jeopardy, if he was going to lose he was going to get the question wrong. Therefore Contestants B and C know that he's going to bet $9,301 or more (in fact he bet $9,400) and should factor it into their decisions. In the case of Contestant B the information regarding Contestant A isn't particularly informative. Contestant B still needs to protect her slim lead over Contestant C and thus must wager nearly all of her money (she wagered all of it), but this information to Contestant C is very instructive. Contestant C must realize that the only chance she has of victory is for A and B to get the question wrong, as such she must limit her wager to within the loss A would incur under the circumstances of a wrong answer (she must not end up with less than 15,500 - 9,301 - and technically she probably shouldn't bet anything).
It's strange that people who are smart enough to make it on Jeopardy are so miraculously stupid strategically.
On Friday I depart for a friend's bachelor party in New Orleans that happily and intentionally coincides with Jazz Fest. I will be taking copious notes and blogging about what is sure to be a monumentally dangerous trip. Keep an eye out for my best Hunter S. Thompson impression.