Jeopardy oddity
(as for tonight, both players did exactly what I said and both won)
The ironic twist is this is a much better position for player two than if he had a lot more money (but not as much as player 1), because if he has, say, $21,000, player 1 has to bet enough to beat him, and will usually bet a dollar more. This creates a situation where player 2, late in Double Jeopardy, would do well to attempt to get his score to half if at all possible. For example, if he gets a Daily Double as the last clue, it would be better to bet enough and get the question wrong on purpose to get to half, rather than try to bet enough to overtake player 1 and risk falling below half. I intend to mention this to Alex the next time I am a contestant.
Your analysis assumes that the only goal is to win, and the amount by which you win is irrelevant. However, if the first place player feels that he has a high enough probability of getting the question right, it might be in his best interest to bet a lot anyway. Exactly how high of a probability he needs depends on the actual dollar value of coming back again.
I could be wrong, but thought only the winner keeps his winnings and the other get fixed consolation prizes, like $2000 and $1000 or something like that.
Quote: WizardI'll be sure to watch it. That is an interesting point about throwing a question. Maybe I'll ask Teddy about it on the radio show this week.
I could be wrong, but thought only the winner keeps his winnings and the other get fixed consolation prizes, like $2000 and $1000 or something like that.
Quote: AxiomOfChoiceInteresting. I don't actually watch the show, but doesn't the winning player get the amount of money that he ends up with? ie, it's not just there to keep score; it's real money if you win!
Your analysis assumes that the only goal is to win, and the amount by which you win is irrelevant. However, if the first place player feels that he has a high enough probability of getting the question right, it might be in his best interest to bet a lot anyway. Exactly how high of a probability he needs depends on the actual dollar value of coming back again.
Wiz: The winner keeps it all, but if there is a tie, they both keep it and both come back. If it was a one show appearance only, Axiom, your strategy might be sound. But by betting nothing and winning it, you are 1. Getting a 100% win. 2. Assuring yourself of at least more day on the show to win an open-ended amount. 3. You are returning tomorrow with one player who you know is not likely to completely dominate you, since you doubled them up in your first meeting (unless they threw a question to test my theory). That eliminates 1 of the chances that a Ken Jennings is waiting in the Green Room to destroy you.
It is classic Jeopardy betting strategy for the first place bettor to risk just enough to win by 1 dollar if the second place bettor bets it all and gets it right. So if they have exactly half, you bet nothing and lock the win.
Otherwise I'm betting nothing and coming back tomorrow.
Quote: cclub79Wiz: The winner keeps it all, but if there is a tie, they both keep it and both come back.
That I knew. But what to the losers get?
Quote:It is classic Jeopardy betting strategy for the first place bettor to risk just enough to win by 1 dollar if the second place bettor bets it all and gets it right. So if they have exactly half, you bet nothing and lock the win.
Let's say the situation going into final Jeopardy is the top player has $10,000 and second place has $5100. Suppose second place had a low percentage of correct answers, but bet big on the Daily Doubles and got them right. Wouldn't playing against this second place player be potentially be higher EV than a stranger? Normally first place would bet $201, but maybe $200 would be better if you thought he was weaker than the median player. Yet, I can never recall seeing this happen.
Quote: WizardThat I knew. But what to the losers get?
2000 and 1000 you are correct.
Quote:
Let's say the situation going into final Jeopardy is the top player has $10,000 and second place has $5100. Suppose second place had a low percentage of correct answers, but bet big on the Daily Doubles and got them right. Wouldn't playing against this second place player be potentially be higher EV than a stranger? Normally first place would bet $201, but maybe $200 would be better if you thought he was weaker than the median player. Yet, I can never recall seeing this happen.
Rarely over the years (maybe 3 or 4 in the 25 years I've been watching) players have tried to be "generous" and bet enough to tie not win by a dollar. Once I remember a player doing it several times, though it is contingent on both first and second getting it right, so it doesn't always work even if it's tried, and when it doesn't work, few people even notice unless they are doing a lot of meaningless math on the side.
1) You're basing a strategy on getting FJ correct, far from a guaranteed prospect.
2) You're not just leaving money on the table, but throwing it away.
A better idea with a DD and you're in 2nd with more than half is to bet up to a tie with the leader on a correct response. If you're still tied going into Final, you still have to respond correctly to win, but so does your opponent. A contrary opinion is to bet the minimum and wait for FJ.
I believe it is far better to win the game outright instead of a tie, especially if the champion is part of that tie. (I don't want the player with more experience playing against me again.)
And yes, only the champ keeps the money, 2nd place gets $2,000, and 3rd gets $1,000. For a tie for 1st, all players involved keep the money and are credited with a win.
'Brian
The reasons are that you both get to keep the money, you both come back, and, crucially, you then lock in one player you have demonstrated you can out-play and out-buzz for the next game.
If I ever get on the show, that will be my strategy.
Quote: sodawaterMultiple-time champion Bob Harris recommends (in his book) that if you're not in a situation where you cannot be caught, you should ALWAYS bet such that if the second-place contestant doubles his money, you will be tied.
The reasons are that you both get to keep the money, you both come back, and, crucially, you then lock in one player you have demonstrated you can out-play and out-buzz for the next game.
If I ever get on the show, that will be my strategy.
Did not read this post. Apologies. Says the same as mine more or less other than I'd be willing to lose up to a couple of thousand deliberately in order to tie.
Quote: WizardThat I knew. But what to the losers get?
Let's say the situation going into final Jeopardy is the top player has $10,000 and second place has $5100. Suppose second place had a low percentage of correct answers, but bet big on the Daily Doubles and got them right. Wouldn't playing against this second place player be potentially be higher EV than a stranger? Normally first place would bet $201, but maybe $200 would be better if you thought he was weaker than the median player. Yet, I can never recall seeing this happen.
Wizard: Say you are on Jeopardy. You're the leader going into the final question, with $25k. Second place has $10k. The topic for the final question is "The Mathematics of Gambling". How much are you betting?
In your place, I'm betting it all. You will not get a better gamble than this in your lifetime. Sure, you are reducing your probability of winning from 100% to 100% - epsilon, but that epsilon chance of moving forward is not worth the 99.99% x $20k you are giving up if you bet only $5k.
Besides, if you somehow lose, you are the "crazy gambler" and you will be able to get on other gameshows with no problems (which also has high EV)
Quote: AxiomOfChoiceWizard: Say you are on Jeopardy. You're the leader going into the final question, with $25k. Second place has $10k. The topic for the final question is "The Mathematics of Gambling". How much are you betting?
In your place, I'm betting it all. You will not get a better gamble than this in your lifetime. Sure, you are reducing your probability of winning from 100% to 100% - epsilon, but that epsilon chance of moving forward is not worth the 99.99% x $20k you are giving up if you bet only $5k.
Besides, if you somehow lose, you are the "crazy gambler" and you will be able to get on other gameshows with no problems (which also has high EV)
The problem is, This is Jeopardy! (pun intended). I suppose there could be a .001% chance that it's a category worth risking it for. But I know every US Congressman and Senator, Presidents, and everything about Politics, but even if it was "US Congress", I wouldn't risk it, because they like to make it a trick rather than flat out knowledge in Final Jeopardy. Sometimes it's one of the simplest questions of the day, sometimes it's near impossible. It's a special type of question that is very dangerous to risk on if you don't have to.
Also, almost every game show requires you not have been on any other game show for X years prior. I think Jeopardy is 5 years, and you can never be on it again if you've been on it since it's been hosted by Trebek (unless invited back for ToC). But Jeopardy doesn't have the audience that would make you any type of "Crazy Gambler" that would get you attention to be on another show. you would just be labeled "Stupid Contestant" by the people on the Jeopardy message boards and fade off into history with your $1000 from Alleve.
Quote: AxiomOfChoiceWizard: Say you are on Jeopardy. You're the leader going into the final question, with $25k. Second place has $10k. The topic for the final question is "The Mathematics of Gambling". How much are you betting?
Either $5001 or or $5000, depending on how good I thought the other guy was. Probably $5000 because I outscored him significantly and can probably beat him again.
Why not all? Sometimes I get answers wrong on kid's Jeopardy because I overthink it. For example, I'm still mad at myself over my low score on a Brady Bunch quiz I posted here a while back. I blew quite a few questions because I over-analyzed, when the obvious answer was right in front of me. Plus, I would never live it down if I bet everything and got it wrong.
In that way it's a lot like poker (or a blackjack tournament final hand).
Maybe this should be a separate thread, but could it be argued that the Vatican is not a country? For example, the United Nations recognizes it as a state but not a nation, much like Palestine.
I would have gotten this right but I may have misspelled Lesotho. San Marino, I've never heard of.Quote: WizardVery good question tonight, by the way. For the benefit of those who missed it, the question was name two of the three countries completely surrounded by a single other country.
Maybe this should be a separate thread, but could it be argued that the Vatican is not a country? For example, the United Nations recognizes it as a state but not a nation, much like Palestine.
I'm sure I would have missed it. I always forget which one of Lesotho or Swaziland is the one that is surrounded by South Africa. I'm not as strong on African geography as my college buddy who won $128,000 on Jeopardy! I would have gotten San Marino, and probably forgotten about Vatican City.Quote: WizardVery good question tonight, by the way. For the benefit of those who missed it, the question was name two of the three countries completely surrounded by a single other country.
You could argue that, but for the purposes of questions like that they like to include everything, to give the players the benefit of the doubt, and to forestall disagreements later.Quote:Maybe this should be a separate thread, but could it be argued that the Vatican is not a country? For example, the United Nations recognizes it as a state but not a nation, much like Palestine.
Quote: teddysI'm sure I would have missed it. I always forget which one of Lesotho or Swaziland is the one that is surrounded by South Africa. I'm not as strong on African geography as my college buddy who won $128,000 on Jeopardy! I would have gotten San Marino, and probably forgotten about Vatican City.
You could argue that, but for the purposes of questions like that they like to include everything, to give the players the benefit of the doubt, and to forestall disagreements later.
Probably also why they asked for "2 of 3" instead of "all 3". If you insist that the Vatican is not a country you can still get it.
Quote: cclub792000 and 1000 you are correct.
What does the winner get if he/she wins with less than $2,000?
Quote: Mission146What does the winner get if he/she wins with less than $2,000?
he gets what he won and to play the next game which is worth at least $1000
Quote: WizardEither $5001 or or $5000, depending on how good I thought the other guy was. Probably $5000 because I outscored him significantly and can probably beat him again.
Why not all? Sometimes I get answers wrong on kid's Jeopardy because I overthink it. For example, I'm still mad at myself over my low score on a Brady Bunch quiz I posted here a while back. I blew quite a few questions because I over-analyzed, when the obvious answer was right in front of me. Plus, I would never live it down if I bet everything and got it wrong.
This surprises me. Using reasonable approximations for the probability of you getting it right and the value of coming back, I am pretty sure that your EV is significantly higher by betting it all. I could see trying to lock it in if $25k was a life-changing amount, but, based on other threads, I am assuming that this is not the case for you.
Quote: cclub79
The ironic twist is this is a much better position for player two than if he had a lot more money (but not as much as player 1), because if he has, say, $21,000, player 1 has to bet enough to beat him, and will usually bet a dollar more. This creates a situation where player 2, late in Double Jeopardy, would do well to attempt to get his score to half if at all possible. For example, if he gets a Daily Double as the last clue, it would be better to bet enough and get the question wrong on purpose to get to half, rather than try to bet enough to overtake player 1 and risk falling below half. I intend to mention this to Alex the next time I am a contestant.
In your example, if the second-place player has more than half the leader, and then gets the daily-double on the last clue, it would be a much better strategy to risk enough on the daily double to get in the lead than to blow the question to get exactly half -- since most daily doubles are answered correctly.
In the case you cited, I would bet enough to be exactly tied for the lead.
The only time I can think of when it would be good to throw a question is the exceedingly rare case where the leading player buzzes is on the last clue, gets it wrong, and then the second player buzzes in. If the board looked like:
Leader: $16,000
Second: $10,000
Third: $7,999
After the leader missed the last question ($2,000 clue), then the second-place contestant should buzz in and get it wrong on purpose FOR SURE.
Quote: Mission146In that event, it is theoretically possible that the winner could win and then come in third the following day and be worse off than if he/she had simply come in second place on the first day. That seems odd. You would think the winner would be guaranteed at least $2,000 total.
Yes, but,
1) It would be rare for a player to win with less than $2,000, and
2) The EV of getting to play the next game would dwarf the difference between the (Game 1 winnings + Game 2 third-place prize) and the Game 1 second-place prize. Every player would choose to play again rather than get the extra money between 0 and $999 in your scenario.
Quote: sodawaterYes, but,
1) It would be rare for a player to win with less than $2,000, and
2) The EV of getting to play the next game would dwarf the difference between the (Game 1 winnings + Game 2 third-place prize) and the Game 1 second-place prize. Every player would choose to play again rather than get the extra money between 0 and $999 in your scenario.
I agree with all of that, I just thought that it was unusual.
Quote: AxiomOfChoiceThis surprises me. Using reasonable approximations for the probability of you getting it right and the value of coming back, I am pretty sure that your EV is significantly higher by betting it all. I could see trying to lock it in if $25k was a life-changing amount, but, based on other threads, I am assuming that this is not the case for you.
I'm sure you're right. I just don't trust myself to not get caught in a trick question.
Quote: DRichDid you know that Alex Trebek was the host of a game show called "Wizard of Odds"? I didn't until just now.
Yup. When I make it on Jeopardy that will make for a good topic in the "meet the players" portion.
Quote: WizardWhy not all? .... I would never live it down if I bet everything and got it wrong.
That sounds strange coming from you, especially considering you sig line. Don't get me wrong, I feel exactly the same way about it, even if the clue happened to be about golf or something where I felt extremely confident.
The comment just seems to go against everything you endorse here.
Quote: TheNightflyThat sounds strange coming from you, especially considering you sig line. Don't get me wrong, I feel exactly the same way about it, even if the clue happened to be about golf or something where I felt extremely confident.
The comment just seems to go against everything you endorse here.
it's not a good bet for wizard if the negative utility x chance of losing is greater than the positive utility x chance of winning for him. which he says it is.
Quote: sodawaterIn your example, if the second-place player has more than half the leader, and then gets the daily-double on the last clue, it would be a much better strategy to risk enough on the daily double to get in the lead than to blow the question to get exactly half -- since most daily doubles are answered correctly..
I took this into consideration. But here was the thing. In your example, even if I was moderately confident in the category, I would have to get 2 questions right to return tomorrow (The Daily Double and the Final Jeopardy question), or bank on Player 1 to get FJ wrong. If I got the Daily Double wrong, I would have eliminated myself by having less than half. If I throw the question PRIOR to even seeing it by betting enough to half the score, I've eliminated the question from being a deciding factor and have made it so I will live our die based on just one question, the Final one.
Caveat, I might choose your strategy if I did really like the Daily Double category AND it was an early one in the column (800/1200), because they do get harder as you go down, even for Daily Doubles. If it was a 2000 DD, I'd almost definitely throw it. Plus it's likely that it would be a 2000, because contestants often go down the columns in order. (Which is another whole thread, since I had never seen a DD in the first slot in 25 years until last week (I think), so I don't know why anyone would have voluntarily chosen the first clue in a category at any point in the game. This had been a strategy (not choosing the first clue) by a decent percentage of contestants through the years, and I always applauded them. You might think it's bad to choose the DD early in the round, but I'd be assured that the EV of you getting the DD early is better than your opponent getting it at any time)
Back then, it was rather common for the person with four wins and in first place by Final Jeopardy, to bet enough to beat the person in second place by one dollar. I never understood that. In a tie, they still score five wins and get the cash and the car. All they did by beating the person in second palce was deny that person a win (I know one possible reasonable argument for that anyway).
In fact, I recall once whern the five-time winner was a Catholic priest who played to tie. Alex remarked the priest had told him that, if he found himself in that spot, he'd make a Final Jeopardy bet to tie. Alex approve and admired the gesture. I thought it was simple, efortless common kindness.
In other words, just because you have exactly half of what the person in first aplce has, don't think the first palce won't try to beat you anyway; yes, even if he risks losing.
As for betting big on Final Jeopardy when you're so far ahead no one can beat you, that's called a Cliff Claiborne[sp?], after the character in "Cheers!" who does exactly that on Jeopardy (and of course loses a lot of money).
Of course, maximizing your EV often means that you have to take some risk of losing. That's why it's called gambling. Just remember that a wise man once said, it's not whether you win or lose; it's whether you had a good bet. If it's a good bet, I'm making it. If I lose, I lose with my head held high, knowing that I made the right bet. It's no different than how all the "experts" at the blackjack table tell you to take even money on a blackjack when the dealer has an ace showing.
Quote: Nareed
Back then, it was rather common for the person with four wins and in first place by Final Jeopardy, to bet enough to beat the person in second place by one dollar. I never understood that. In a tie, they still score five wins and get the cash and the car. All they did by beating the person in second palce was deny that person a win (I know one possible reasonable argument for that anyway).
It's not quite so morally black and white. By playing for a tie in the last game, you would then deny one player in the contestant pool the chance to go on the show. In the situation you outlined, where you are playing your fifth and final game, I'd argue the moral thing to do IS to bet to win by $1, because then you allow one extra person to achieve his dream of going on the show.
Quote: cclub79I took this into consideration. But here was the thing. In your example, even if I was moderately confident in the category, I would have to get 2 questions right to return tomorrow (The Daily Double and the Final Jeopardy question), or bank on Player 1 to get FJ wrong. If I got the Daily Double wrong, I would have eliminated myself by having less than half. If I throw the question PRIOR to even seeing it by betting enough to half the score, I've eliminated the question from being a deciding factor and have made it so I will live our die based on just one question, the Final one.
Caveat, I might choose your strategy if I did really like the Daily Double category AND it was an early one in the column (800/1200), because they do get harder as you go down, even for Daily Doubles. If it was a 2000 DD, I'd almost definitely throw it. Plus it's likely that it would be a 2000, because contestants often go down the columns in order. (Which is another whole thread, since I had never seen a DD in the first slot in 25 years until last week (I think), so I don't know why anyone would have voluntarily chosen the first clue in a category at any point in the game. This had been a strategy (not choosing the first clue) by a decent percentage of contestants through the years, and I always applauded them. You might think it's bad to choose the DD early in the round, but I'd be assured that the EV of you getting the DD early is better than your opponent getting it at any time)
Yeah, that line of thinking makes sense. But I'd still bet big on the DD because at least that way in FJ I'd have two ways to win instead of one. But you are right, it all comes down to category confidence and clue depth.
And you are absolutely right it is INSANE for a player with control of the board not to hunt for the DD. You should always be hunting for it no matter how early in the game.
Quote: AxiomOfChoiceI remember that episode. I'd still bet it all if I felt confident. I am there to maximize my EV, not help someone else tie.
True. But is one dollar worth that much to you? I can undertand if you're 2.1x or more ahead of the second place, there's no reason to bet money and lose it so that person will tie. But the difference between betting enough to beat second place by one dollar and enough for a tie is so trivial it shouldn't be considered.
Quote:Just remember that a wise man once said, it's not whether you win or lose; it's whether you had a good bet. If it's a good bet, I'm making it.
That doesn't apply in this case.
Quote: NareedTrue. But is one dollar worth that much to you? I can undertand if you're 2.1x or more ahead of the second place, there's no reason to bet money and lose it so that person will tie. But the difference between betting enough to beat second place by one dollar and enough for a tie is so trivial it shouldn't be considered.
My point is that, if I am confident, I am neither trying to tie nor win by $1. I am trying to double my money. I'm not giving away that much EV in order to "play it safe"
Quote: sodawaterIt's not quite so morally black and white. By playing for a tie in the last game, you would then deny one player in the contestant pool the chance to go on the show. In the situation you outlined, where you are playing your fifth and final game, I'd argue the moral thing to do IS to bet to win by $1, because then you allow one extra person to achieve his dream of going on the show.
I agree with this 100%. The greater total good is to let one extra person have a chance to play the game.
Quote: Nareed
In other words, just because you have exactly half of what the person in first aplce has, don't think the first palce won't try to beat you anyway; yes, even if he risks losing.
I don't think in my 25+ years of watching nearly every night I'm home, I've ever seen a player bet anything but $0 in that situation.
Quote:
As for betting big on Final Jeopardy when you're so far ahead no one can beat you, that's called a Cliff Claiborne[sp?], after the character in "Cheers!" who does exactly that on Jeopardy (and of course loses a lot of money).
Cliff Clavin, and again, it happens so very rarely. Another wrinkle I thought of when driving today. If you bet to tie rather than win by a buck, that could endear you to the contestant you allowed to return, and he could similarly return the favor the following day if the roles are reversed.
Quote: WizardI agree with this 100%. The greater total good is to let one extra person have a chance to play the game.
The total good be damned.
If you tie the game, you delay one potential contestant for a day or a few weeks at most. If you beat second place by $1, you destroy all his winnings.
Is taking thousands of dollars from someone to give to someone else worth not delaying someone else? Even if you get paid ONE DOLLAR to do so?
Quote: NareedThe total good be damned.
If you tie the game, you delay one potential contestant for a day or a few weeks at most. If you beat second place by $1, you destroy all his winnings.
Is taking thousands of dollars from someone to give to someone else worth not delaying someone else? Even if you get paid ONE DOLLAR to do so?
Wrong, actually. Contestants stay in the pool for 18 months. If they don't get picked, they have to re-take the test and start the process over again, with no guarantee of making it back in the pool.
Way more people make it into the pool than make it on the show. I have been in the pool for two 18-month periods and have not yet been called to go on the show.
Quote: sodawaterWrong, actually. Contestants stay in the pool for 18 months. If they don't get picked, they have to re-take the test and start the process over again, with no guarantee of making it back in the pool.
Teddy, who is a two-time champion, has said pretty much the same thing to me. There are only x contestants per season. By giving somebody a free extra game you deny somebody else the chance to be on the show at all.
I view the situation kind of like getting a cab in Vegas for a short ride. Generally cabs have to queue for a long time to wait their turn at any hotel. Each driver is hoping for as long of a ride as possible. So, what if you are the Treasure Island and need to go to the Mirage. It is right next door, just down the street, two easy right turns. The cab driver you get is basically screwed because he waited in a long line for a puny fare. However, you created a greater good for all cab drivers, as every other driver in the line moved up to the front a little faster. Plus, the industry as a whole increased revenue by the value of your ride.
Quote: WizardTeddy, who is a two-time champion, has said pretty much the same thing to me. There are only x contestants per season. By giving somebody a free extra game you deny somebody else the chance to be on the show at all.
By winning, too. So don't ever win at Jeopardy, or you rob someone of their chance to be on the show at all.
Quote: NareedBy winning, too. So don't ever win at Jeopardy, or you rob someone of their chance to be on the show at all.
Surprisingly not. Once you are a contestant, unless there is a tie, you winning or losing does not affect someone else's chance to be on the show. Barring ties, there are exactly 10 new contestants every week. Not winning just lets someone else be the champion, but doesn't change the number of new contestants. *Also, in an odd quirk, if all 3 contestants finish with ZERO, then NONE come back, allowing for a magical 11th new contestant that week (one of the two standbys apparently). This is why bettors often leave themselves with a dollar, just in case the other two go all-in for some reason.
I understand and appreciate your greater point, however.
Quote: cclub79I understand and appreciate your greater point, however.
I'm surprised someone does.
Last man standing
How much would you wager in that situation?
Quote: TheNightflyHere's another Jeopardy oddity. Apparently it's only happened a couple of times.
Last man standing
How much would you wager in that situation?
I'd bet a lot, depending of course on the category. In that particular category I would have bet 20,000.
Quote: TheNightflyHow much would you wager in that situation?
$0, as that is not a strong category for me. I think my odds are well south of 50% with anything to do with words.
Unless your odds are just over 50%, and the money really would affect your quality of life, then the right answer is $0 or everything.
I'm ashamed that I didn't get it either. After I saw the "question" I kicked myself.
I would have gotten it right and been up to $37,960.
Quote: WizardI'm ashamed that I didn't get it either. After I saw the "question" I kicked myself.
I got it. :) And the clue sounded familiar to me as well. I probably watched the original airing, but forgot only one person made it to Final Jeopardy! in that show.
