"Basic strategy" for Final Jeopardy wagering?

[RKane]

So I have a general question for the vikings since this has come up.

Lets say the final scores are
18800
13800
12800

But basically any case where (third's score) > 2 * (first's score - second's score). This will overlap quite a bit with Stratton's Dilemma but I don't think either is a subset of the other.

Anyways, first has the well-defined strategy of $8801. Second (in Stratton's dilemma) has two well-defined strategies of everything (but at least $11801) or nothing (but at most $3800, or at most $999).

But what about third? The archive says at most $2800 to stay above first on a miss by first (also, in this case, at least $1001 in case second wagers zero, since $1001 < $2800).

But I feel like, in that situation, I would bot be able to go below $6001. I know it's not wise per se, but the thought of first getting cute by wagering zero, and me (third) being right and able to win but underbetting, is awful, and I would rather lose any way but this. In fact, in this case I would even be tempted to wager $11000 in case first tried to pull a Colby.

Now, whether I wanted too go $6001 or $11000, if wrong I am below the magic number (here $10000). So I may as well bet it all.

I guess my question is if I bet it all in such a situation (or at least $6001) would that be unjustifiable and raise the ire of the vikings?

Cheers

I think this comes up often, moreso with second place wagering than with third, but there are similarities. Sure if you absolutely positively feel that you wouldn't be able to live with yourself if you got it right and lost due to underbetting, then you should bet it all, every time. It's always possible that first or second fails to cover, or tries to cover and makes a math error, or tries shoretegy, or feels no confidence and bets $0, or just bets $4000 or some other round number. In these cases, sure, it's possible that betting big might win you a game you would otherwise lose. You might get ridiculed here on the forum but if it wins you a game and $20k+ and the chance to play again, I think you'll survive the wagering vikings.

That being said, I guess in deciding on 2nd/3rd place wagers, the battle is between giving yourself what you feel is the best chance to win based on all known information, and between that nagging feeling of not wanting to get it right and still lose a winnable game. The long term history has been that the leader almost always bets to cover. This has always been the one thing you could generally count on, while 2nd/3rd place betting has seemingly always been 100% crapshoot. These days it seems the leader bets to cover less and less. I wonder if someone like cheezguyty could run something to determine how much this is the actual case. I'd be looking for "in what percent of non-lock games does the leader make at least the MSB, season by season?". My hunch is that the last two seasons would have the lowest numbers since the 1980s. If this was proven to be the case, then I'd love to see a long conversation about why this might be.

Yeah you actually draw out a more basic point, what I am talking about applies when you are in second far more than when you are in third. Especially if you have more than 2/3 of first but less than 3/4, so your strategy should not involve covering even a zero wager by first. To me that's the toughest zone; at least if you are between 1/2 and 2/3 you are justified in betting it all and if you are above 3/4 you can at least cover a zero wager (and of course if above 4/5 cover any kind of cutesiness).

[Lefty]

Edited to add: Bob Blake is quoted here saying that he can't remember why he bet so much but possibly it was because he was in search of a record. I still think it was probably an arithmetic mistake (even though he is an actuary by trade). He was going to set the 5-day record even if he wagered zero; in fact he did set the 5-day record, even though he wagered $4000 and did not get the clue. If he had been correct, with his $4000 wager, his final score that day would have been $19,100, not even close to a one-day record.

One of my favorite thread titles on the old Sony board was something like "Bob Blake's mistake (it was bigger than you think)". If I recall correctly, Blake appeared on the board in that thread to express bemusement that people were still talking about it.

Not very long afterward, Blake went down in the first round of the UToC after another bad FJ overbet.

[cheezguyty]

That being said, I guess in deciding on 2nd/3rd place wagers, the battle is between giving yourself what you feel is the best chance to win based on all known information, and between that nagging feeling of not wanting to get it right and still lose a winnable game. The long term history has been that the leader almost always bets to cover. This has always been the one thing you could generally count on, while 2nd/3rd place betting has seemingly always been 100% crapshoot. These days it seems the leader bets to cover less and less. I wonder if someone like cheezguyty could run something to determine how much this is the actual case. I'd be looking for "in what percent of non-lock games does the leader make at least the MSB, season by season?". My hunch is that the last two seasons would have the lowest numbers since the 1980s. If this was proven to be the case, then I'd love to see a long conversation about why this might be.

Percentage of non-lock regular-play games in the Archive where the sole leader made at least the minimum shutout bet, season by season:

Code: Select all

 1 - 91.3%
 2 - 77.8%
 3 - 86.4%
 4 - 83.8%
 5 - 84.4%
 6 - 83.3%
 7 - 81.8%
 8 - 93.1%
 9 - 82.4%
10 - 94.7%
11 - 84.2%
12 -100.0%
13 - 88.7%
14 - 87.9%
15 - 82.4%
16 - 86.9%
17 - 83.2%
18 - 74.3%
19 - 86.2%
20 - 77.7%
21 - 87.7%
22 - 86.0%
23 - 88.1%
24 - 86.1%
25 - 88.7%
26 - 86.2%
27 - 91.2%
28 - 90.0%
29 - 81.9%
30 - 79.3%
31 - 80.1%
32 - 89.5%
33 - 83.9%
34 - 81.0%

[jeff6286]

That being said, I guess in deciding on 2nd/3rd place wagers, the battle is between giving yourself what you feel is the best chance to win based on all known information, and between that nagging feeling of not wanting to get it right and still lose a winnable game. The long term history has been that the leader almost always bets to cover. This has always been the one thing you could generally count on, while 2nd/3rd place betting has seemingly always been 100% crapshoot. These days it seems the leader bets to cover less and less. I wonder if someone like cheezguyty could run something to determine how much this is the actual case. I'd be looking for "in what percent of non-lock games does the leader make at least the MSB, season by season?". My hunch is that the last two seasons would have the lowest numbers since the 1980s. If this was proven to be the case, then I'd love to see a long conversation about why this might be.

Percentage of non-lock regular-play games in the Archive where the sole leader made at least the minimum shutout bet, season by season:

Code: Select all

 1 - 91.3%
 2 - 77.8%
 3 - 86.4%
 4 - 83.8%
 5 - 84.4%
 6 - 83.3%
 7 - 81.8%
 8 - 93.1%
 9 - 82.4%
10 - 94.7%
11 - 84.2%
12 -100.0%
13 - 88.7%
14 - 87.9%
15 - 82.4%
16 - 86.9%
17 - 83.2%
18 - 74.3%
19 - 86.2%
20 - 77.7%
21 - 87.7%
22 - 86.0%
23 - 88.1%
24 - 86.1%
25 - 88.7%
26 - 86.2%
27 - 91.2%
28 - 90.0%
29 - 81.9%
30 - 79.3%
31 - 80.1%
32 - 89.5%
33 - 83.9%
34 - 81.0%

Hey I knew you'd be the man for the job! I had failed to consider the incomplete archive data, so hard to really find any conclusions from the 80s stuff, probably season 13 on is when we can get a true picture. I'm intrigued by some of the spikes and wonder if there are any identifiable factors we'll be able to find. Most of 13-20 are pretty similar, though 18 and 20 are well below. It occurs to me that 20, with Ken Jennings, likely featured a lower number of non-lock games than normal, so there might be some more noise in the statistics.

Seasons 21 through 26 are very steady, about what I would have expected, then it went even higher in 27-28, but since then, 5 of the last 6 seasons have been closer to 80% than 90%. Arthur Chu came around in mid-Season 30 so I don't think the finger can be pointed at him for people suddenly starting to abandon the long-established MSB strategy. Maybe people saw Roger Craig's crazy DD bets in the Season 29 TOC and suddenly all rationality in betting went out the window? Any other ideas?

[AndyTheQuizzer]

That being said, I guess in deciding on 2nd/3rd place wagers, the battle is between giving yourself what you feel is the best chance to win based on all known information, and between that nagging feeling of not wanting to get it right and still lose a winnable game. The long term history has been that the leader almost always bets to cover. This has always been the one thing you could generally count on, while 2nd/3rd place betting has seemingly always been 100% crapshoot. These days it seems the leader bets to cover less and less. I wonder if someone like cheezguyty could run something to determine how much this is the actual case. I'd be looking for "in what percent of non-lock games does the leader make at least the MSB, season by season?". My hunch is that the last two seasons would have the lowest numbers since the 1980s. If this was proven to be the case, then I'd love to see a long conversation about why this might be.

Percentage of non-lock regular-play games in the Archive where the sole leader made at least the minimum shutout bet, season by season:

Code: Select all

 1 - 91.3%
 2 - 77.8%
 3 - 86.4%
 4 - 83.8%
 5 - 84.4%
 6 - 83.3%
 7 - 81.8%
 8 - 93.1%
 9 - 82.4%
10 - 94.7%
11 - 84.2%
12 -100.0%
13 - 88.7%
14 - 87.9%
15 - 82.4%
16 - 86.9%
17 - 83.2%
18 - 74.3%
19 - 86.2%
20 - 77.7%
21 - 87.7%
22 - 86.0%
23 - 88.1%
24 - 86.1%
25 - 88.7%
26 - 86.2%
27 - 91.2%
28 - 90.0%
29 - 81.9%
30 - 79.3%
31 - 80.1%
32 - 89.5%
33 - 83.9%
34 - 81.0%

Hey I knew you'd be the man for the job! I had failed to consider the incomplete archive data, so hard to really find any conclusions from the 80s stuff, probably season 13 on is when we can get a true picture. I'm intrigued by some of the spikes and wonder if there are any identifiable factors we'll be able to find. Most of 13-20 are pretty similar, though 18 and 20 are well below. It occurs to me that 20, with Ken Jennings, likely featured a lower number of non-lock games than normal, so there might be some more noise in the statistics.

Seasons 21 through 26 are very steady, about what I would have expected, then it went even higher in 27-28, but since then, 5 of the last 6 seasons have been closer to 80% than 90%. Arthur Chu came around in mid-Season 30 so I don't think the finger can be pointed at him for people suddenly starting to abandon the long-established MSB strategy. Maybe people saw Roger Craig's crazy DD bets in the Season 29 TOC and suddenly all rationality in betting went out the window? Any other ideas?

One question: what constitutes the "minimum shutout bet": a bet for the tie, or a bet for $XX,001? If the latter, then that explains the dip in S20 (Tom Walsh) and S30 (Arthur Chu).

[cheezguyty]

That being said, I guess in deciding on 2nd/3rd place wagers, the battle is between giving yourself what you feel is the best chance to win based on all known information, and between that nagging feeling of not wanting to get it right and still lose a winnable game. The long term history has been that the leader almost always bets to cover. This has always been the one thing you could generally count on, while 2nd/3rd place betting has seemingly always been 100% crapshoot. These days it seems the leader bets to cover less and less. I wonder if someone like cheezguyty could run something to determine how much this is the actual case. I'd be looking for "in what percent of non-lock games does the leader make at least the MSB, season by season?". My hunch is that the last two seasons would have the lowest numbers since the 1980s. If this was proven to be the case, then I'd love to see a long conversation about why this might be.

Percentage of non-lock regular-play games in the Archive where the sole leader made at least the minimum shutout bet, season by season:

Code: Select all

 1 - 91.3%
[...]
34 - 81.0%

Hey I knew you'd be the man for the job! I had failed to consider the incomplete archive data, so hard to really find any conclusions from the 80s stuff, probably season 13 on is when we can get a true picture. I'm intrigued by some of the spikes and wonder if there are any identifiable factors we'll be able to find. Most of 13-20 are pretty similar, though 18 and 20 are well below. It occurs to me that 20, with Ken Jennings, likely featured a lower number of non-lock games than normal, so there might be some more noise in the statistics.

Seasons 21 through 26 are very steady, about what I would have expected, then it went even higher in 27-28, but since then, 5 of the last 6 seasons have been closer to 80% than 90%. Arthur Chu came around in mid-Season 30 so I don't think the finger can be pointed at him for people suddenly starting to abandon the long-established MSB strategy. Maybe people saw Roger Craig's crazy DD bets in the Season 29 TOC and suddenly all rationality in betting went out the window? Any other ideas?

One question: what constitutes the "minimum shutout bet": a bet for the tie, or a bet for $XX,001? If the latter, then that explains the dip in S20 (Tom Walsh) and S30 (Arthur Chu).

It was the latter. Here are the percentages for the leader betting at least enough to tie:

Code: Select all

 1 - 95.7%
 2 - 94.4%
 3 - 96.6%
 4 - 87.8%
 5 - 92.2%
 6 - 95.2%
 7 -100.0%
 8 - 93.1%
 9 - 88.2%
10 - 94.7%
11 - 89.5%
12 -100.0%
13 - 90.3%
14 - 92.4%
15 - 93.9%
16 - 93.4%
17 - 93.1%
18 - 86.1%
19 - 90.2%
20 - 90.1%
21 - 89.2%
22 - 86.8%
23 - 90.2%
24 - 89.9%
25 - 90.8%
26 - 90.6%
27 - 93.9%
28 - 92.9%
29 - 87.7%
30 - 88.4%
31 - 86.3%
32 - 89.5%
33 - 86.3%
34 - 83.5%

[jeff6286]

Well that flattens out the data considerably. I would have had no idea that people "betting for the tie" was so prevalent, pre-Arthur Chu, outside of Tom Walsh as the notable example.

[triviawayne]

So I have a general question for the vikings since this has come up.

Lets say the final scores are
18800
13800
12800

But basically any case where (third's score) > 2 * (first's score - second's score). This will overlap quite a bit with Stratton's Dilemma but I don't think either is a subset of the other.

Anyways, first has the well-defined strategy of $8801. Second (in Stratton's dilemma) has two well-defined strategies of everything (but at least $11801) or nothing (but at most $3800, or at most $999).

But what about third? The archive says at most $2800 to stay above first on a miss by first (also, in this case, at least $1001 in case second wagers zero, since $1001 < $2800).

But I feel like, in that situation, I would bot be able to go below $6001. I know it's not wise per se, but the thought of first getting cute by wagering zero, and me (third) being right and able to win but underbetting, is awful, and I would rather lose any way but this. In fact, in this case I would even be tempted to wager $11000 in case first tried to pull a Colby.

Now, whether I wanted too go $6001 or $11000, if wrong I am below the magic number (here $10000). So I may as well bet it all.

I guess my question is if I bet it all in such a situation (or at least $6001) would that be unjustifiable and raise the ire of the vikings?

Cheers

1st place @ 18800 should bet it all since the minimum bet to ensure a lock would have this person fall below 3rd place's current score of 12800.

2nd place @ 13800 needs to defend against 3rd place, and again, may as well bet it all because 3rd place needs to bet nothing, and any defensive bet will put them below 3rd place's current score.

3rd place @ 12800 should bet 2800 as 1st & 2nd place must get an incorrect answer for 3rd place to win anyway, and thier best minimum bets would make 9999 the top score of their opponents in the case both get the answer wrong.

Of course this does not take into consideration that players bet incorrectly all the time, nor does it consider the category and strengths and weaknesses of the three players, which is why absolute math in betting on Jeopardy doesn't tend to work absolutely.

[Golf]

1st place @ 18800 should bet it all since the minimum bet to ensure a lock would have this person fall below 3rd place's current score of 12800.

2nd place @ 13800 needs to defend against 3rd place, and again, may as well bet it all because 3rd place needs to bet nothing, and any defensive bet will put them below 3rd place's current score.

3rd place @ 12800 should bet 2800 as 1st & 2nd place must get an incorrect answer for 3rd place to win anyway, and thier best minimum bets would make 9999 the top score of their opponents in the case both get the answer wrong.

Of course this does not take into consideration that players bet incorrectly all the time, nor does it consider the category and strengths and weaknesses of the three players, which is why absolute math in betting on Jeopardy doesn't tend to work absolutely.

Am I missing some joke here?

[triviawayne]

1st place @ 18800 should bet it all since the minimum bet to ensure a lock would have this person fall below 3rd place's current score of 12800.

2nd place @ 13800 needs to defend against 3rd place, and again, may as well bet it all because 3rd place needs to bet nothing, and any defensive bet will put them below 3rd place's current score.

3rd place @ 12800 should bet 2800 as 1st & 2nd place must get an incorrect answer for 3rd place to win anyway, and thier best minimum bets would make 9999 the top score of their opponents in the case both get the answer wrong.

Of course this does not take into consideration that players bet incorrectly all the time, nor does it consider the category and strengths and weaknesses of the three players, which is why absolute math in betting on Jeopardy doesn't tend to work absolutely.

Am I missing some joke here?

nope, just reality

[seaborgium]

If first and second may as well bet everything, third place may as well bet everything but $1. Any reason you can offer for that not to be done can probably be lightly altered to reasons why first and second shouldn't bet everything.

[Bamaman]

I see no reason to bet more than the MSB from the lead. I understand the logic behind a leader in a crush betting to where they are $1 ahead of second if they are wrong, since second has to get it right to win anyway. But what if second just decides to play for second place makes a small bet of a few hundred dollars? That happens all the time. Assuming someone else is going to bet logically is risky.

[triviawayne]

If first and second may as well bet everything, third place may as well bet everything but $1. Any reason you can offer for that not to be done can probably be lightly altered to reasons why first and second shouldn't bet everything.

because there's no guarantee that they will, you missed the part about how players bet incorrectly all the time anyway, and how a player should take into consideration strengths and weaknesses in categories, so there never is a perfect correct answer as to what to bet just looking at the numbers.

[seaborgium]

If first and second may as well bet everything, third place may as well bet everything but $1. Any reason you can offer for that not to be done can probably be lightly altered to reasons why first and second shouldn't bet everything.

because there's no guarantee that they will, you missed the part about how players bet incorrectly all the time anyway, and how a player should take into consideration strengths and weaknesses in categories, so there never is a perfect correct answer as to what to bet just looking at the numbers.

"There's no guarantee that they will" figures prominently into why first and second shouldn't bet it all, surprise surprise.

[triviawayne]

If first and second may as well bet everything, third place may as well bet everything but $1. Any reason you can offer for that not to be done can probably be lightly altered to reasons why first and second shouldn't bet everything.

because there's no guarantee that they will, you missed the part about how players bet incorrectly all the time anyway, and how a player should take into consideration strengths and weaknesses in categories, so there never is a perfect correct answer as to what to bet just looking at the numbers.

"There's no guarantee that they will" figures prominently into why first and second shouldn't bet it all, surprise surprise.

By that logic, nobody should ever bet anything, but that won’t happen

[seaborgium]

If first and second may as well bet everything, third place may as well bet everything but $1. Any reason you can offer for that not to be done can probably be lightly altered to reasons why first and second shouldn't bet everything.

because there's no guarantee that they will, you missed the part about how players bet incorrectly all the time anyway, and how a player should take into consideration strengths and weaknesses in categories, so there never is a perfect correct answer as to what to bet just looking at the numbers.

"There's no guarantee that they will" figures prominently into why first and second shouldn't bet it all, surprise surprise.

By that logic, nobody should ever bet anything, but that won’t happen

Makes more sense than "might as well bet everything if betting to cover puts you behind third when you're wrong"

[Golf]

1st place @ 18800 should bet it all since the minimum bet to ensure a lock would have this person fall below 3rd place's current score of 12800.

2nd place @ 13800 needs to defend against 3rd place, and again, may as well bet it all because 3rd place needs to bet nothing, and any defensive bet will put them below 3rd place's current score.

3rd place @ 12800 should bet 2800 as 1st & 2nd place must get an incorrect answer for 3rd place to win anyway, and thier best minimum bets would make 9999 the top score of their opponents in the case both get the answer wrong.

Of course this does not take into consideration that players bet incorrectly all the time, nor does it consider the category and strengths and weaknesses of the three players, which is why absolute math in betting on Jeopardy doesn't tend to work absolutely.

Am I missing some joke here?

nope, just reality

You make the wager that gives you the best chance at winning the game. In this case the leader should wager $8801 (assuming no category issues) and not a penny more because on a miss every dollar saved means a slightly better chance of winning.

[triviawayne]

1st place @ 18800 should bet it all since the minimum bet to ensure a lock would have this person fall below 3rd place's current score of 12800.

2nd place @ 13800 needs to defend against 3rd place, and again, may as well bet it all because 3rd place needs to bet nothing, and any defensive bet will put them below 3rd place's current score.

3rd place @ 12800 should bet 2800 as 1st & 2nd place must get an incorrect answer for 3rd place to win anyway, and thier best minimum bets would make 9999 the top score of their opponents in the case both get the answer wrong.

Of course this does not take into consideration that players bet incorrectly all the time, nor does it consider the category and strengths and weaknesses of the three players, which is why absolute math in betting on Jeopardy doesn't tend to work absolutely.

Am I missing some joke here?

nope, just reality

You make the wager that gives you the best chance at winning the game. In this case the leader should wager $8801 (assuming no category issues) and not a penny more because on a miss every dollar saved means a slightly better chance of winning.

So other than player 3's loss of $2800 in a triple stumper, the betting doesn't change the outcome of who wins the game; player 1 and 2 should bet everything to maximize their winnings and player 3 should bet $2800 unless this person doesn't like the category.

Basic Jeopardy Wagering.png (31.27 KiB) Viewed 5674 times

[RKane]

That's ridiculous. Third should be $12799 by your logic, because then they maximize their winnings (which was your motivation for 1st and 2nd betting it all) if they are right on the sole get, and still win on the TS.

But then...oh wait...1st or 2nd could wager only $18798 or $13798 respectively, and then THEY win on the TS.

But then...oh WAIT...another player could hold back $3!!

It's almost like the strategies that exist do so for a reason.

Now, again, I am not an expert (if I was in 3rd in that situation, I don't know if I'd be able to bet below $6001 unless I really hated the category), but, for a player in first, the strategy is completley unambiguously to bet no more than the minimum safe bet, in any case. The fact that games great strategists like Roger Craig and Alex Jacob and Arthur Chu employed this strategy (in Chu's case betting to tie, but that still proves my point to not bet MORE than the MSB) and the game's winningest player Ken Jennings did as well, should tell you what you need to know.

[RKane]

Side question for the wagering vikings regarding DD wagering:

What are your thoughts on employing the Fritz Holznagel strategy and wagering random, non-whole, numbers (in his case, palindromes specifically) in order to throw off and disorient the competition? This seems to me like a good move, analogous to the Forrest Bounce. I feel like if I were on the show, I would definitely do this...not necessarily biting Fritz's palindromes specifically, but wagering $8134 instead of $8000 and things like that.