Thursday, October 12, 2017 Game Recap and Discussion [SPOILERS]

[Golf]

In addition to the stellar performance by Scarlett, can I just say that that was the most exciting, competitive slugfest of a Jeopardy! match I’ve ever watched? Two great players with broad knowledge bases, slugging it out on the buzzer, seesawing the lead. A Jeopardy! classic.

I’m surprised, though, that amid all the richly deserved praise for Scarlett’s game, no one has mentioned Austin’s reckless overwager in FJ:

• Austin: 16600
  Scarlett: 21200
  Sean: 2800

Austin is not crushed, so he has no need to improve his score in order to win—just hold on tight and hope for a miss by the leader. Since he’s above 3/4 of her score, classic wagering theory holds he should bet at least 4601 to cover her. One thing he definitely must not do is fall below her swing-and-a-miss residue of 9199. If FJ had turned out to be a triple stumper, his whale bet of 16550 would have unnecessarily cost him the game and his winning streak.

None of which is to steal any glory from Scarlett. Girl, you totally rocked from start to finish. Looking forward to watching you for a good, long run.

Regular strategy also assumes you're an average player in Final Jeopardy. When you've already demonstrated you're 11-for-12 on the final clue of the game, well, you're allowed to throw regular strategy out the window a bit and be more aggressive.

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

[badgerfellow]

In addition to the stellar performance by Scarlett, can I just say that that was the most exciting, competitive slugfest of a Jeopardy! match I’ve ever watched? Two great players with broad knowledge bases, slugging it out on the buzzer, seesawing the lead. A Jeopardy! classic.

I’m surprised, though, that amid all the richly deserved praise for Scarlett’s game, no one has mentioned Austin’s reckless overwager in FJ:

• Austin: 16600
  Scarlett: 21200
  Sean: 2800

Austin is not crushed, so he has no need to improve his score in order to win—just hold on tight and hope for a miss by the leader. Since he’s above 3/4 of her score, classic wagering theory holds he should bet at least 4601 to cover her. One thing he definitely must not do is fall below her swing-and-a-miss residue of 9199. If FJ had turned out to be a triple stumper, his whale bet of 16550 would have unnecessarily cost him the game and his winning streak.

None of which is to steal any glory from Scarlett. Girl, you totally rocked from start to finish. Looking forward to watching you for a good, long run.

Regular strategy also assumes you're an average player in Final Jeopardy. When you've already demonstrated you're 11-for-12 on the final clue of the game, well, you're allowed to throw regular strategy out the window a bit and be more aggressive.

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

You have to figure, though, that the utility of winning 1 more game for Austin has diminished as he continues to win. He's already won a lot of money, a lot of games, and locked up a TOC spot. What's $1000 or $2000 more to him by then if he loses? May as well max out winnings then. Given he stated his main goal was to win 1 game, I think it's safe to say he was going to continue going big on Final when allowed, i.e. avoid a Clavin.

That said, I'm curious to see what he'll do for wagering in TOC. This field will be stacked. Looking forward to it.

[Golf]

In addition to the stellar performance by Scarlett, can I just say that that was the most exciting, competitive slugfest of a Jeopardy! match I’ve ever watched? Two great players with broad knowledge bases, slugging it out on the buzzer, seesawing the lead. A Jeopardy! classic.

I’m surprised, though, that amid all the richly deserved praise for Scarlett’s game, no one has mentioned Austin’s reckless overwager in FJ:

• Austin: 16600
  Scarlett: 21200
  Sean: 2800

Austin is not crushed, so he has no need to improve his score in order to win—just hold on tight and hope for a miss by the leader. Since he’s above 3/4 of her score, classic wagering theory holds he should bet at least 4601 to cover her. One thing he definitely must not do is fall below her swing-and-a-miss residue of 9199. If FJ had turned out to be a triple stumper, his whale bet of 16550 would have unnecessarily cost him the game and his winning streak.

None of which is to steal any glory from Scarlett. Girl, you totally rocked from start to finish. Looking forward to watching you for a good, long run.

Regular strategy also assumes you're an average player in Final Jeopardy. When you've already demonstrated you're 11-for-12 on the final clue of the game, well, you're allowed to throw regular strategy out the window a bit and be more aggressive.

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

You have to figure, though, that the utility of winning 1 more game for Austin has diminished as he continues to win. He's already won a lot of money, a lot of games, and locked up a TOC spot. What's $1000 or $2000 more to him by then? Given he stated his main goal was to win 1 game, I think it's safe to say he was going to continue going big on Final when allowed, i.e. avoid a Clavin.

That said, I'm curious to see what he'll do for wagering in TOC. This field will be stacked. Looking forward to it.

But none of that should matter. The goal in each and every game is to win, that's it. If you do not win the current game you have no more opportunities to win the next. And then next. And so on. Therefore each and every game has absolutely nothing to do with what happened prior. And it has nothing to do with his goals going in.

If a contestant does not give themselves to best possible chance to win each and every game then they are not playing optimally. The only deviation from this would be if a weak player in the lead going into FJ has a wheelhouse category and decides the extra money is worth sacrificing some winning chances because it's highly unlikely they will win the next game.

[MarkBarrett]

In addition to the stellar performance by Scarlett, can I just say that that was the most exciting, competitive slugfest of a Jeopardy! match I’ve ever watched? Two great players with broad knowledge bases, slugging it out on the buzzer, seesawing the lead. A Jeopardy! classic.

I’m surprised, though, that amid all the richly deserved praise for Scarlett’s game, no one has mentioned Austin’s reckless overwager in FJ:

• Austin: 16600
  Scarlett: 21200
  Sean: 2800

Austin is not crushed, so he has no need to improve his score in order to win—just hold on tight and hope for a miss by the leader. Since he’s above 3/4 of her score, classic wagering theory holds he should bet at least 4601 to cover her. One thing he definitely must not do is fall below her swing-and-a-miss residue of 9199. If FJ had turned out to be a triple stumper, his whale bet of 16550 would have unnecessarily cost him the game and his winning streak.

None of which is to steal any glory from Scarlett. Girl, you totally rocked from start to finish. Looking forward to watching you for a good, long run.

Regular strategy also assumes you're an average player in Final Jeopardy. When you've already demonstrated you're 11-for-12 on the final clue of the game, well, you're allowed to throw regular strategy out the window a bit and be more aggressive.

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

You have to figure, though, that the utility of winning 1 more game for Austin has diminished as he continues to win. He's already won a lot of money, a lot of games, and locked up a TOC spot. What's $1000 or $2000 more to him by then if he loses? May as well max out winnings then. Given he stated his main goal was to win 1 game, I think it's safe to say he was going to continue going big on Final when allowed, i.e. avoid a Clavin.

That said, I'm curious to see what he'll do for wagering in TOC. This field will be stacked. Looking forward to it.

With $411K in winnings does 5K for showing up or 10K for making the cut seem like that big of a deal? Austin may play like that is chump change and only finals money matters. For most players I would expect a 0 wager for 20K or above going into the FJ! round of the quarterfinals. Austin comes off as someone that won't be able to resist betting for the outright win into the semis.

I could see him working his DD magic and leading 22K to 13K and instead of sitting on the total betting that 4K for the win. That's fine as 18K would almost have to be enough also, but 22K would seem to be a guaranteed wildcard spot based on past history.

Austin could also get burned being too aggressive in his match and going 0/1 on DDs although only once in thirteen games did he only play 1 DD, while having at least 2 in all his other matches. Overall Austin's DD and FJ success pattern indicates he is much more likely than unlikely to play in the semis.

What won't happen is an underwager being too conservative as that would not seem to be in the cards.

[AndyTheQuizzer]

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

For someone who alleges to be so versed in mathematics, you have such little backing in statistical knowledge.

Stats 101 will tell you that in a situation such as this, if you're going 11 for 12 in Final Jeopardy -- you are above average in Final Jeopardy to any degree of statistical significance.

[twelvefootboy]

First of all, hearty congratulations to both Austin and of course Scarlett. What a game and what a win! As OSC says (and he knows wherefrom he speaks) it was a game for the ages.

Count me on the Scarlett bandwagon. Here's how good the game was IMHO: I queued up the Nationals/Cubs game to watch and decided to watch J! while I built up DVR backlog. I queued up exactly at the middle of the 5th inning, Nats up 4-1. Watched J!, switched back and accidentally caught the 7-4 score and didn't care. The bottom of the 5th inning (that I therefore missed completely) has turned out to be an epic event for baseball that will be remembered for decades. But, I have no regrets - I got to see an awesome clicker cage fight on DVR delay that taped months ago .
I'm just now able to get online, and will soon feast on the Friday game - best of retro luck to Scarlett! And real luck for the Astros and ugh! Dodgers. Thanks for sharing with us mooks on the board as well!

[hbomb1947]

Austin could also get burned being too aggressive in his match and going 0/1 on DDs although only once in thirteen games did he only play 1 DD, while having at least 2 in all his other matches.

But his opponents during his run rarely hunted for the DD's. Anecdotally in my memory, hunting is much more commonly seen in TOC's than in regular play. Austin stated in some interview that he prefers playing the boards top to bottom in each category, for the same reason that many other contestants do (not wanting to risk landing on a DD when he doesn't know what the category is about). That's perfectly fine, but if he sticks rigidly to that approach in the TOC, he leaves himself more vulnerable to having the DD's picked off by his opponents.

[Golf]

No, no you are not. Just because you have answered a very small number of selected clue correctly does not mean you sacrifice winning chances in a game of Jeopardy. You've been duped by an insignificant sample size and ignored basic strategy.

For someone who alleges to be so versed in mathematics, you have such little backing in statistical knowledge.

Stats 101 will tell you that in a situation such as this, if you're going 11 for 12 in Final Jeopardy -- you are above average in Final Jeopardy to any degree of statistical significance.

Sure you are above average, but a whopping 12 trials doesn't mean you simply wager everything and sacrifice the TS win scenario. Again, a few extra dollars in a win doesn't justify throwing the TS win down the toilet.

Regardless, advanced math isn't necessary to understand proper wagering in 99%+ of scenarios such as this one.

[OldSchoolChamp]

In my post upthread, I said:

I’m surprised, though, that amid all the richly deserved praise for Scarlett’s game, no one has mentioned Austin’s reckless overwager in FJ . . .

Well, I seem to have remedied that situation.

I’ve stated before Chernicoff’s First Law of Final Jeopardy Wagering: Bet with a purpose. Choose a target and aim for it. If you’re betting aggressively, choose the number you want to reach with a hit; if you’re betting defensively, choose the number you want to safeguard even with a miss. But have a target in sight (preferably one more tactically constructive than “a nice, round $20,000”).

To that I would now add Chernicoff’s Second Law: Bet to maximize your chances of winning the present game. It has nothing to do with your past FJ history or your feelings about the category. Winning this game is paramount, because it represents the potential opportunity cost of an indefinite chain of future wins. If my friend Ken had lost his first game, the loss would have cost him two-and-a-half million dollars (and he would never have known it).

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game. The reason a runaway is a runaway is that a sufficiently small bet guarantees the win in all eight scenarios. The fundamental reason behind the leader’s classic shutout bet is that it wins the game in four of the eight scenarios—all those including a right answer by the leader. The reason Austin’s bet in this game was bad is that it needlessly sacrificed the win in one of the eight scenarios: namely, the triple miss (WWW). In that sense, it’s tantamount to a Clavin: giving away winning chances that are yours by right. As it happened, the mistake didn’t cost Austin anything, because it didn’t happen to affect the outcome in the particular right-and-wrong scenario that actually occurred. But with a different question and a different combination of right and wrong answers, it could have cost him a game (and who knows how many future games?) that he should have won.

[opusthepenguin]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

The Nitpicker's Club would like to inform you that this is incorrect. For two reasons.

Spoiler

1. This is not true for "any Final Jeopardy scenario," only those with three players. Several scenarios each year involve only two players. Very occasionally they involve one. Way back when, there were some 4-player games too.

2. I believe what you list are permutations, not combinations.

The proper response to any objection from the Nitpicker's Club is to say that you could care less.

[AFRET CMS]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

The Nitpicker's Club would like to inform you that this is incorrect. For two reasons.

Spoiler

1. This is not true for "any Final Jeopardy scenario," only those with three players. Several scenarios each year involve only two players. Very occasionally they involve one. Way back when, there were some 4-player games too.

2. I believe what you list are permutations, not combinations.

The proper response to any objection from the Nitpicker's Club is to say that you could care less.

Which is the perfect response, since the nitpicker would be forced to reply

Spoiler

that you actually meant you couldn't care less

thus guaranteeing the discussion won't be laid to rest yet.

[MattKnowles]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game.

That statement would only be true if those combinations each had an equal chance of occurring. The cases of RRR and WWW both occur twice as frequently as some of the other cases.

You're right that Austin's wager was too high in this case. If he wagered low he should have had about a 48% chance to win and if he wagered high he only gets a 19% chance to win. He doesn't gain anything from wagering that high unless his opponent makes an irregular bet. Edit: These numbers aren't really that accurate. Austin showed that he had a higher chance of answering FJ correctly than a typical contestant and I don't know what the actual probabilities would be.

[seaborgium]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game.

That statement would only be true if those combinations each had an equal chance of occurring. The cases of RRR and WWW both occur twice as frequently as some of the other cases.

I don't see any part of his statement that claims or assumes all those outcomes are equally likely.

[MattKnowles]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game.

That statement would only be true if those combinations each had an equal chance of occurring. The cases of RRR and WWW both occur twice as frequently as some of the other cases.

I don't see any part of his statement that claims or assumes all those outcomes are equally likely.

The object of the Final Jeopardy wager is to maximize the chance of winning the game. Maximizing the number of combinations only maximizes the chances of winning if all the scenarios are equally likely.

The chance of each combination is not actually 12.5% but closer to RRR = 20%, WWW = 20%, RRW = RWR = RWW = WRR = WRW = WWR = 10%.

Edit: Using the numbers listed above it essentially amounts to maximizing the number of combinations that lead to your winning the game and my point is essentially moot. For a better example lets assume there is a player in second place and they hit a category they know they will answer incorrectly and the chance of them getting it right is nearly 0%. The approximate chance of RRR = RRW = WRR = WRW = 0%, RWR = 30%, RWW = 20%, WWR = 20%, WWW = 30%, if the scores are 20,000/16,000/13,000 they can expect to win in the scenarios WRW, WWW if they bet small. If they bet medium/big they can expect to win in the scenarios WRR, WRW, and they can expect to win a WWW some of the time. If you maximize the number of combinations you would bet medium/big but you should be maximizing the chance of winning and betting small.

[seaborgium]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game.

That statement would only be true if those combinations each had an equal chance of occurring. The cases of RRR and WWW both occur twice as frequently as some of the other cases.

I don't see any part of his statement that claims or assumes all those outcomes are equally likely.

The object of the Final Jeopardy wager is to maximize the chance of winning the game. Maximizing the number of combinations only maximizes the chances of winning if all the scenarios are equally likely.

The chance of each combination is not actually 12.5% but closer to RRR = 20%, WWW = 20%, RRW = RWR = RWW = WRR = WRW = WWR = 10%.

I get what you're saying now, but I don't think there's any circumstance in which a trailing player can maximize the number of right/wrong outcomes in which they win without also giving themselves the best statistical chance of winning.

[MattKnowles]

I get what you're saying now, but I don't think there's any circumstance in which a trailing player can maximize the number of right/wrong outcomes in which they win without also giving themselves the best statistical chance of winning.

You're right. I edited my previous post to give a forced example of a scenario where that could occur.

[BobF]

It was *Miss Scarlett in the studio with the buzzer as Austin was Mr. Boddy.

Austin was given some bonus money with the whale reversal happening after his DD miss. If the judges had handled matters sooners Austin would have been at zero to start the second segment instead of 1200.

*Scarlett Sims could be a Miss or Ms. and Miss Scarlet in the board game Clue is one T.

Scarlett Sims from Tennessee took names and numbers in the Dolly Parton category.

Austin's opening looked like this thing: https://www.youtube.com/watch?v=pPpQoCDS_tw

For the FJ! round let's just say I've seen that movie more than once so not going to miss it.

have never seen the movie, but got it correct because what other holiday film came out in 1947?

It's a Wonderful Life was 1946. It was one of the films I studied in a film course I took as an elective in college.

[OldSchoolChamp]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

The Nitpicker's Club would like to inform you that this is incorrect. For two reasons.

Spoiler

1. This is not true for "any Final Jeopardy scenario," only those with three players. Several scenarios each year involve only two players. Very occasionally they involve one. Way back when, there were some 4-player games too.

2. I believe what you list are permutations, not combinations.

The proper response to any objection from the Nitpicker's Club is to say that you could care less.

Which is the perfect response, since the nitpicker would be forced to reply

Spoiler

that you actually meant you couldn't care less

thus guaranteeing the discussion won't be laid to rest yet.

. . . as well as that

Spoiler

Yes, they are combinations and not permutations. The permutations of three objects are 3! = 6:

• 1 2 3
  1 3 2
  2 1 3
  2 3 1
  3 1 2
  3 2 1

The combinations of three binary choices are 2^3 = 8, as listed in my earlier post.

[OldSchoolChamp]

In any Final Jeopardy scenario, there are eight possible combinations of hit-and-miss outcomes:

• R R R
  R R W
  R W R
  R W W
  W R R
  W R W
  W W R
  W W W

The object of the Final Jeopardy wager is to maximize the number of these combinations that lead to your winning the game.

That statement would only be true if those combinations each had an equal chance of occurring. The cases of RRR and WWW both occur twice as frequently as some of the other cases.

Yes, I was aware of this oversimplification when I wrote it, and I knew I could count on somebody in the chorus astute enough to point it out. Yes, you’re right: the true aim of the FJ wager is to maximize the sum of the winning scenarios, weighted by their probabilities. I just didn’t want to burden my earlier argument with this level of detail. The thrust of the argument remains the same, however: that considering the outcomes in terms of the eight possible right/wrong scenarios is the right way to think about FJ betting.

[opusthepenguin]

Yes, they are combinations and not permutations. The permutations of three objects are 3! = 6:

• 1 2 3
  1 3 2
  2 1 3
  2 3 1
  3 1 2
  3 2 1

The combinations of three binary choices are 2^3 = 8, as listed in my earlier post.

Yeah, I may have screwed up there. But help me out if you know this one. I thought the point of combinations was that order doesn't matter. I.e. RWW is no different from WWR or WRW as an outcome. Is that wrong?