This article is from WeChat public account:Wait But Why(ID:wbwtimurban), author: Urban, compiling Tim: Panda Xie Jun, edit: Vivid & Las, from the cover of the original
Jeopardy! It is a veteran Q&A variety show in the United States. Participants are rewarded by answering questions. The player with the highest score can not only continue to participate in the next game as a defender, but also receive a bonus equal to the points.
The variety show is divided into three sections, Jeopardy, Double Jeopardy, and Final Jeopardy. In the Jeopardy and Double Jeopardy sessions, the three contestants have several opportunities to answer the questions based on the clues given by the questions, and correct the points corresponding to the clues. In the final Final Jeopardy session, contestants can choose the points they want to bet on their own. If they answer correctly, they can get the reward for the bet points. If they are wrong, they will deduct the points.
Tim Urban This essay discusses James Holzhauer, who had won 32 games in a row, and eventually lost the controversial Final Jeopardy bet on the game.
Like many readers, I am recently fascinated by James Holzhauer’s winning streak on Jeopardy. James is a bit weird, his expression is sometimes like this:
or this:
Despite this, he is very flattering and impressive. As the game continued, I found myself getting more and more like a powder sports star. When he was behind the Double Jeopardy, I leaned forward and sat down on the edge of the seat, screaming for him, and when he got it right, I would breathe a sigh of relief. In the Final Jeopardy session, whenever a critical moment is needed to answer the question in a winning streak, I will scream like a madman for him to finally answer.
Unfortunately, on the show on June 3, he broke my heart – it was a pain that was unbearable from breaking the record of the highest total prize money in the history of the show.
James is really very good at Jeopardy. Before his entry, the highest single-game winning percentage of the show in the past 55 years was $77,000. James not only won 32 games (after only 77 games in history, the most consecutive winning streak), and his winning percentage per game was higher than Previous $77,000 record. He is currently ranked in the top 16 in the “one of the highest single-day Jeopardy points ever”.
It’s really interesting to see someone so much better than everyone else in something. This is the same reason I like to watch professional sports events – seeing James attending Jeopardy is like watching Curry score a three-pointer. the only differenceYes, once Curry has a bad game, he will be suspended for life, and he can no longer see him playing. This rule makes watching James more interesting.
After James’s defending failure, there was a lot of discussion about his Final Jeopardy bet amount, and this is the topic I want to discuss in this article. My thoughts are:
Note: For readers who are not familiar with the rules of the show: Final Jeopardy is the last link in the show, with only one question. Only after learning the general subject category, each entrant can place a bet on any problem within the cumulative total amount. If you are correct, you will get extra points for the equivalent bet; if you make a mistake, you will lose the bet points.
After Final Jeopardy, the entrant with the first place will receive the final bonus equal to the amount of the final points and continue to play as the defender the next day. The second place can only get $2000, the third place only has $1000, and then it is eliminated.
No.1 Scenario A
If you are a contestant, the simplest Final Jeopardy scene: When you enter this round, the first point is more than twice the second point. We call this a scenario A:
If you are the first in Scene A, you only need to calculate twice the second point. This is the bottom line you should not cross under any circumstances.
Assuming you have more than 50% chance to answer the question, your best strategy is to bet as high as possible without crossing the “bottom line”, so that once you get the right answer, you can win the most. So in the above case, you should bet $1999. In this case, in the worst case (you answered the wrong question, the second one answered), you can still guarantee a victory of $1 .
If you are the second place in Scene A, you have lost the qualification to get the first, no one will care how you play, I wish you a good time.
Because James is so good at Jeopardy, he almost entered the scene A as the first person, and his points usually (far Far) is twice as high as the second. In these episodes, Final Jeopardy is a very easy and unsuspecting story, except to see how high James’ total income was.
No.2:Scenario B
Scenario B is a bit more complicated. In this scenario, the second place score is more than half of the first place, but less than two-thirds of the first place. Like this:
If you are the first in Scene B, you will want to make sure you win in the correct answer. At this point you have to consider the worst possibility: the second place will be all points and correct. topic. Twice the second point, it becomes “the ceiling line that I must cross when I answer the question.” In the scenario above, the “ceiling line” is $12000, so your bet cannot be less than $2001.
You also want to make sure that you can still win if you and the second one are wrong. The worst situation at this time became: the second place was wrong, but for some strange reason, a penny did not bet. At this time, the original score of the second place before the start of the link became the “bottom line that should not be crossed anyway.” In the scenario above, your maximum bet amount is $3999.
Assuming you don’t hate the subject category of the question, there are more than half of the odds. The most rational bet amount is $3999.
Assuming the first place to play the best and follow the aboveThe range bet, the second place in the scene B is also quite simple. According to the above bet strategy, as long as the first place is correct, the outcome will be a foregone conclusion. The second place is wrong, and the outcome is also obvious.
As the second place, the only chance to succeed in the counterattack is that the first answer is wrong and the second one is correct – because only in this case, the second bet makes sense. and hope to get the highest total score in this case, so the second place strategy is to put all the points.
Until here, I think everyone will not have much controversy about these rules. The final scene C is really complicated.
No.3:Scenario C
In Scene C, the second place score is more than two-thirds of the first place.
The traditional strategy is that the first person wants to win in the case of answering the question, so according to the calculation method similar to scene B, the first line of “must be crossed” is $16000, and the minimum bet amount is $6001. .
Knowing the second place that the first entrant will think like this, think about the following four situations:
Assuming the first lowest bet is $6001, once he is correct, the second place will not win. If the first place is answered incorrectly, the second place is correct, the first place’s points will be lower than the second place’s initial points, so that the second place can be counter-attacked regardless of the number of bets.
But if the first and second names are wrong?
In Scene B, the first place is more pleasant, both sides have answered (green plaid and yellow plaid) or both are wrong < Span class="text-remarks" label="remarks">(blue plaid) can win. But in Scene C, it’s not so comfortable – when the first name is guaranteed to win and bet when both players are right, the bet amount also makes him score lower than the second in the case of a wrong answer. The original score of the name.
This gives the second chance in the scene C an extra chance to win – the second one knows that the first place will be at least $6001, the second placeI will fight and try to make my points higher than $3999 when both of them make a mistake, and there is a maximum bet of $4000.
In the above case, the second place also wants to ensure that if you make a mistake, it is still twice as high as the third place, which is $6000. So the ideal bet amount for the second place is $1999, which means that in the case of the first answer, regardless of whether the second and third place are correct, the second place can win. (blue squares).
In Monday’s game, James, who usually entered Final Jeopardy as Scene A or B, was in second place in Scene C. The first opponent was Emma Boettcher. Their scores are as follows:
James’s bet strategy is consistent with what I described above. He speculates that Emma will bet at least $20201 to ensure that it exceeds Emma’s “ceiling line that must be crossed” (James points twice: $46800) Emma can guarantee to win if both of them are right.
According to this speculation, if Emma makes a mistake, her points will fall to $6399 or lower. James’s only counterattack was Emma’s answer, and $6399 became James’ “bottom line.” His maximum bet amount is also limited to $17,000. This bet amount will ensure that James’s points will exceed Emma in the case of Emma’s answer.
But as we have described above, Jay Sexton, the third place entrant, also has a chance. Two times Jay’s points ($22000) became James’ second “bottom line” – so James’s bet amount is ” Perfect for $1399.
Under this bet, Emma made a mistake, James could attack, and Jay couldn’t turn over anyway, and it doesn’t matter if James himself answered correctly. The second place was not the best start, but James created the best counterattack for himself.
No.4: But is this really true?
Tactical thinking at this time has become interesting. James explained his logic in the post-match interview:
This is consistent with the traditional logic I wrote above. This scenario C The second unique tactic, the benefit is to be able to win in the first and second place. The final result did not have much reversal. Emma did put $20201 to prevent James from betting on the ceiling line. James put a $1399 bet on traditional logic. Both of them answered the question correctly, and Emma won.
But is this part of the assumption really correct?
” She will definitely bet at least $20201 for my double bet on the ceiling.”
Let’s think about it. If you are Emma, you know that James is a very effective strategist and I have definitely analyzed the various scenarios of Final Jeopardy. You can guess that James will use the above logic to give a small bet of $1399 to make sure he can counterattack when both of them answer. If James makes a small bet of $1399 based on your guess of your (Emma), you have a chance to put “both people answer Wrong”(blue grid) and “I made a mistake, he answered correctly” (Orange plaid) The winning rights in both cases are grabbed, as long as you (Emma) the bet amount is more than the traditional logic The low is good.
In other words, just as James would assume that Emma “will definitely bet at least $20201 for my double bet on the ceiling,” Emma can further assume that “James will definitely assume that I will bet at least $20201.” . Emma’s assumption means she will pushIt is estimated that James’s bet amount is $1399 – this means that even if James is correct, the final score is only $24799, which is not as high as Emma’s initial score of $26600. So Emma won’t bet if he doesn’t make a bet.
This is Emma’s bureaucracy.
If you are Emma, you know that James is a very smart person. You also know that James thinks that you (Emma) is a very smart person, but if you are not smart enough to think of the opponent in this game, this game will be a good game. Strategy. This is risky. In case James doesn’t have a small bet of $1399, the probability of losing the game is great.
But the traditional ceiling line logic is also risky, and you (Emma) must answer the questions to win. I don’t know if the two risks are high or low, but this bureau strategy is not unreasonable.
This brings us back to James’ decision. Both James and Emma are good at Jeopardy, so we assume that their final Jeopardy’s correct answer rate is 90%, and our quadrant becomes such a probability:
If this assumption is accurate, James has a winning rate of only 10% using traditional strategies.
This win rate is too low, so James is likely to make it out of the mid-game.
James’s mid-game board logic is like this, because Emma might make it out of the game. And if Emma really makes the middle game strategy, James’s winning rate after a big bet will increase dramatically.
The following are four details:
James gave up the traditional strategy and adopted the mid-game innings. He just gave up the winning percentage of both he and Emma, and the situation itself was only 1% likely. And he got a lot of things, using the mid-game strategy of a big bet, if Emma adopts the mid-game strategy, his winning percentage can reach 90%.
Although Emma is still more likely to adopt traditional strategies, how likely is this? It should be remembered that in addition to its own advantages, Emma’s own confidence in the subject category of the problem clues will also affect her strategic choices.
James’s traditional strategy is to be the best strategy, and Emma’s chances of using the mid-office are as low as negligible. (I can also note here that the third-placed Jay did not enter the scope of our discussion because Jay was able to finally turn over only in Emma and James. The answer is that in the case of Jay’s correct answer, this possibility is a small part of the blue square that is itself small.)
So, considering all of the above, I think James made the wrong decision.
Of course, if Emma really figured it out, she might realize that James’s mid-game bureau’s threat to her might make it possible to use James Central’s mid-office and James. The Central Bureau of the Bureau of the bet was killed. Emma’s last big bet means that she either adopts a traditional strategy or uses a mid-office in the bureau.
But no matter what she thinks, James correctly predicted her bet and made the best bet on this prediction, but that doesn’t mean James’ bet can win.
This article is from WeChat public account:Wait But Why(ID:wbwtimurban)< span class = "text-remarks">, author: Tim Urban, the compiler: Panda Xie Jun, edit: Vivid & Las