Jeopardy!

Factual Questions
21

This is a different case than the one to which Irishman was responding. In that case, the top two players had the same amount of money. They each almost have to bet it all, to at least tie if they get the question right. If either gets the question right, the third place player loses, so he should play assuming they both get the question wrong. And if the top two players get the question wrong, the third place player should assume he will get it wrong also, and so bet nothing (unless he really knows the category well).

It is too clear, and so it is hard to see.

22

In general, the third place player should bet to have at least twice the difference between the first and second place players. He should wager just enough to get there, betting nothing if that works (and barring extenuating circumstances, like being an expert on that particular category).

It is too clear, and so it is hard to see.

23

I’,m afraid I have to do a little correcting on the discussion of strategy and Jeopardy. There have been some errors.

This should now be looked upon as the final word on the Final Jeopardy quiz strategy:

The following is based on the premise discssed in earlier posts. That is, that at the end of two rounds of Jeopardy, the players have the following scores:

A: $6000

B: $5000

C: $1000

While the concepts below will apply here to this example, they may just as well be used with a little deduction to any other scoring situation.

One crucial point of Final Jeopardy that keeps this betting round from being purely a mathematical exerceise is that a player may have specific knowledge of the catagory in Final Jeopardy.

In Final Jeopardy, as we all know, the players are given the category, and then must bet based on their knowledge in that catagory. After the bets are placed, the players receive the “answer” to which they must give the appropriate question. The problem is, how to bet?

  1. Player A. You believe you will not know the correct response. Bet $0 dollars. Let someone else beat your $6000 if they can. Why risk your money if the liklihood is that you will respond incorrectly? This maximizes the amount of money you will win if no one else knows the answer. If B knows the correct response, he/she will probably win or tie you, and there is nothing you can do. If B does not know the correct response, you will claim $6000 and a return trip regardless of what C does.

  2. Player A. You suspect from the category that you will probably know the correct response. A bet of $4000 here is best. Remember, unless you have some particular grudge against B, there is no reason to try to eliminate him/her.It is OK to tie. This also helps you if you respond incorrectly and C does not, as you will tie C. A bet of $4001 on an incorrect response may well lose to C.

  3. Player A. You are almost certain to know the answer. Bet $5999 to achieve near maximum payoff. You carefully leave a buck in the miniscule chance you will not be able to answer the question, and everyone else also bombs.

  4. Player B. You believe you will not know the correct response. Bet $0. This maximizes your win if A overbets and fails. This also assures you at least a tie for second place.

  5. Player B. You suspect you will know the correct response. Bet $1000. Hopefully A will not know the answer.

  6. Player B. You are nearly certain you will be able to give the correct response. Maximize your chance for a winning payoff by betting $4999. If A also gets it right, you still have second place. If A doesn’t get it right then you have a powerful payoff. Again, always leaving a buck for insurance against a surprisingly difficult problem is prudent.

  7. Player C. You believe you will not be able to give the right response. Bet $0. This keeps you alive for a possible decent win if A and B go down in flames.

  8. Player C. You think that perhaps you can give the right response. Bet $1000. You may tie A for second place, or beat an overzealous A. While it is unlikely that you tie B, you could also beat B if he/she fouls up.

  9. Player C. You are certain to know the needed response. Bet $1000. You win if A loses the $4000 or higher bet and B foolishly blows over $3000. You cannot afford to bet only $999 and leave an insurance dollar as A may bet exactly $4000 and lose, a very realistic possibility.

*Though difficult, a careful and alert player might be able to make some inferrences regarding the other two players range of knowledge from their earlier round’s performances. This player may then use this information to predict the liklihood of a player being able to give the correct response to the Final Jeopardy category, especially since the Final Jeopardy riddle will probably have some connection with an earlier category. this information would be helpful in wagering as you decide your expertice and wager on the Final Jeopardy problem.

For instance, say you are Player A, with $6000. The category is “Astronomy”, which in this hypothetical case you know little about. Your specialty is “The Arts”. However, B (with $5000) has shown remarkable skill in responding to all science related categories throughout the show. Now, even though you know little about astronomy and are likely to be wrong, you know with near certainty that B will be right. Therefore, you must break the above rules and bet $4000 in hopes that you get lucky on the Final Jeopardy “Answer.”

*From watching Jeopardy, I am unclear about how long the TV 60 second commercial break is as related to the actual time allowed the contestants to make their wager. I’d love to think that contestants might get up to 15 minutes to make this all-important wager. Then one could use the above rules only as a basis for the beginning of an analysis of how to bet, while then delving into the subtle nuances of the past 20 minutes of game.

  • As part of any strategy, one should of course scout the opposition. Unless you are champion, or you are appearing after a 5 time champion, you should have a decent idea as to some of the strengths and weaknesses of the returning champion. You will also get those little on-air interviews they do after 5 minutes of game. I’d recommend lying about your interests during this time to confuse opponents. Listen, however, to what the other two folks are saying. If they have kids, for instance, and the Final Jeopardy category was “Walt Disney”, they might have an edge of which you could be aware.

  • If there is time before or during the game, chat it up with the opposition regarding their interests, hobbies, college studies, etc. Then use this information. If a category pops up during the game that might tie in with one of their interests, avoid it if you can. Perhaps not all of their favorite category answers will get used in the alloted time. When talking, be sure to drop misinformation about your areas of knowledge. In our above example with Players A, B, and C none of the scores are tied. But should a tie exist in Final Jeopardy, analysis of opponent history and prior Jeopardy action would be even more critical in deciding what to risk.

*An interesting comparison might be made between Daily Double betting, and the betting on the final round. A player who bets heavily or conservatively in a Daily Double round might be expected to bet the same way during Final Jeopardy. Of course, if a player bets heavily in a Daily Double round and loses, this might lead him/her to bet more conservatively in Final Jeopardy. Conversely, if a player bets conservatively in an early Daily Double and is correct, he/she might be encouraged to take it up a notch during Final Jeopardy because of this earlier success. If I was going on jeopardy, I’d investigate this over several weeks.

*Another “tell” on the Final jeopardy round may come from actions of the opposition upon seeing the final category. A wise player would do well to watch for reactions during the announcement and bet accordingly.

*A final question for the Scheming Millions: Question: Is it possible to cheat at Jeopardy? Has anyone ever tried?

24

My apologies for the poor spelling in the last posting. Too much coffee too late at night.

25

In 1965 I appeared on the daytime show which was hosted by Art Fleming. The prize money was more modest, I came in second and we all got to keep the money ($2,000 in my case). The winner retired as an undefeated five-time champion with a total for all five games of no more that $10 or $12,000.
My have times changed.
Renee

26

It sounds like the prize money has gotten worse, then. $2,000 in 1965 was probably worth something like $12,000 today.

27

I’m not complaining about the $2,0000…it was a downpayment on my very first car (a plymouth fury)…but there were quiz shows that were offering higher rewards even then…of course, not as princely as the $64,0000 jackpot or the jackpot on “21” in the mid '50s before the scandals.
ren

28

Good Gravy, BigTop! Nice analysis there. The long-neglected game theory portions of my brain are heating up. Thanks.

Your Quadell

29

Thanks. A couple of corrections on my previous lengthy post:

If B bets $0, he cannot tie for 2nd place. That bet merely assures him/her of at least second place.

If B feels certain to know the correct response, I think it can be argued he/she should bet the entire $5000, because A quite possibly will be wagering $4000, and B wants a tie. I am uncertain now which is the correct bet here. It most probably involves an analysis of the playing style of A. In most Jeopardy games I have seen, the leader seems to try to bid so as to eliminate opponents, not tie them. If A is such a player, that extra dollar may well be better spent for insurance as I originally posited.

If B feels somewhat likely to know the correct response he/she might well choose to bet the entire $5000 as well, just in case A bids $4000 and answers correctly. This of course makes B now vulnerable to C. However, with just the scores to go on, A would seem a bigger danger than C, and the higher bet would be justified. Then again, if A is a “$4001” style better, then the $1000 bet makes most sense.

I think any analysis of this A, B, and C problem shows that B certainly has the most difficult choice to make in betting. I’m pretty sure I’ve thought it all through now for B’s bet, but it’s an interesting problem, to be sure. Anyone else have an idea on this?

30

Thank you Q. for your kind words. I must, however, mention a couple of errors in my analysis.

  1. If B bets $0 he/she cannot tie for second place. The $0 bet assures B at least sole possesion of second place, though he/she may win first place.

  2. If B is certain to know the correct response, he/she may well choose to bet the full $5000 and not save the dollar for an unlikely low-end win. A, if betting correctly, might be betting only $4000, and a tie for first place and $10,000 seems the better risk for B. Unfortunately on Jeopardy, the leader all too often eliminates the second place player instead of allowing that player to tie. If A is such a bettor, than my original analysis of the $4999 bet would be right.

  3. If B only might know the correct response, then one can also argue that a bet of $5000 is better than the one for $1000. If A bets and wins $4000, then B also wins with a correct response. However, if A is the type of bettor to try and eliminate B with a $4001 bet, then my originally posited best bet of $1000 is accurate. It’s tough, but B must make educated guesses as to A’s character in order to decide what to bet!

As this all shows, player B has the most difficult betting decision of all. I think I have thought things through on this matter completely, but it’s a much trickier problem than I originally suspected. Anyone else have a perspective or another opinion on how B should bet?

31

Now why did this double post? I’m sorry about that folks. Please ignore either one or the other of the above posts.

32

Nice analysis, Bio. One factor that I think is important is the association between the category and the actual question. Frequently you can figure out the answer without knowing anything about the category. If it is Opera, I would be in a bet nothing situation, but then the question might mention a famous play or fairy tale on which an opera is based, or even a Bugs Bunny cartoon. In other words, I would not rely too heavily on the category to determine my betting strategy.

Aside, does anyone else do this? For years my wife and I have been attempting to guess the final jeopardy “answer” (the question the contestant would have to write) as soon as we are given the category. If the category is Presidents, my wife always shouts out JFK, while I usually say Garfield. We occasionally get it right, but you would be surprised how often. We gave up keeping score. I would say once per month or so one of us gets the answer correct. Thrilling and worthy of celebration. Try it.

33

Biotop said:

and also

and

::scratches head::
So it’s okay to lie to mislead your opponents, but be a good sport and don’t try to eliminate them in the final round?