Final Jeopardy betting question

blackaces13 · #1 10-05-2004, 07:50 PM

Lets say that you (an average Jeopardy player) made it to Final Jeopardy against Ken Jennings, the current longtime champ, with $16,000 to his $24,000. The other player finished with a negative total so they are not participating in the final round.

What should you wager on the final question?

I think the answer is the same regardless of category or any other factors. Also realize that 2nd place doesn't get to keep their dollar amount, they get something like a weeks vacation which you are assured at worst anyway at this point. So your only concern is trying to win.

Ulysses · #2 10-05-2004, 07:56 PM

.

blackaces13 · #3 10-05-2004, 08:03 PM

Yeah, this is pretty easy I guess. I thought it was interesting when it dawned on me today. For some reason I spent a large portion of my day thinking about optimum betting strategy against Ken Jennings. Go figure.

I also think that 95%+ of Jeopardy players in this spot would NOT bet $0. As smart as they may be I'm sure the proper strategy would elude them.

Ulysses · #4 10-05-2004, 08:28 PM

Somewhat more interesting. You have $15k or $17k, he has $24k.

SnakeRat · #5 10-05-2004, 08:39 PM

What are the rules for a tie?

Doesnt it matter if it is a category you are especially good in? Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

blackaces13 · #6 10-05-2004, 08:42 PM

[ QUOTE ]
Somewhat more interesting. You have $15k or $17k, he has $24k.

[/ QUOTE ]

For 15K you can go ahead and bet anything from $3K on up. Actually, you should just go ahead and bet it all because you'll only win the times you get it right so betting it all gets you more actual money.

17K and you should bet 3k if you believe that you have greater than a 50% chance of getting the question right. Or zero again if you are less than 50% confident in answering correctly.

blackaces13 · #7 10-05-2004, 08:51 PM

[ QUOTE ]
Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

[/ QUOTE ]

Well, this is why I thought it was interesting. It doesn't matter at all. The only way you win is if he gets it wrong and you a) get it right or B)bet nothing. He is obligated to bet $8001, forced is more like it.

So by betting, even if you are 99% likely to get it right, all you do is increase your chance of losing by that slight amount.

I suppose you could make a case that a slight decreased chance in winning would be worth it because of the extra 16K that you earn right then and there when you win. But if you were only 90% sure (which is nearly impossible anyway due to the general vagueness of the categories) then it likely doesn't make sense to risk the 10% costing you the win if Jennings misses (and he does miss) because you not only lose the 16K now, but more importantly your chance to continue winning on subsequent shows. This would be a tremendous opportunity cost considering you went toe to toe with Jennings for that long and were still close.

benfranklin · #8 10-05-2004, 08:59 PM

[ QUOTE ]

Doesnt it matter if it is a category you are especially good in? Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

[/ QUOTE ]

If you have $16K and bet it all, and he has $24K and bets $8001, then if you miss the final question you lose, and if you both get the final question, you lose. The only way to win is for you have to be right and for him to be wrong.

If you bet $0, he still has to bet $8001 in case you bet it all. Now, he still has to be wrong for you to win, but you don't also have to be right on the final question.

If you bet, you have to be right AND he has to be wrong.
If you don't bet, he just has to be wrong.

ohkanada · #9 10-05-2004, 09:23 PM

Simple, nada.

Ken

Senor Choppy · #10 10-06-2004, 11:32 AM

The answer depends on too many other factors.

If you have a 95% chance of getting the final jeopardy question correct but aren't that exceptional overall compared to most players, it would be throwing away money to not risk everything. Of course, if you were as good as Ken Jennings, and knew you could rack up a few million in winnings if you were somehow able to make it past him, then you'd want to maximize your chances of winning this round and not necessarily the most money, so you'd wager $0.