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

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

Post by alietr » Sun Oct 15, 2017 5:49 pm

Congrats, Scarlett and especially congrats to Austin. The way Scarlett came out of the box swinging and once I knew she said she was a quiz bowler, I figured that had to be the end of Austin.

Normally, Andy, I would agree with you that 11/12 on FJs indicates you're very good at them, but this seems like an unprecedented streak of easy FJs, so I'm not sure how good that evidence is.

I will say that I was coming around on Austin's gameplay (the intros excepted), and he does seem like a genuine, fun guy.

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

Post by Linear Gnome » Sun Oct 15, 2017 6:19 pm

opusthepenguin wrote:
Sun Oct 15, 2017 10:50 am
OldSchoolChamp wrote:
Sun Oct 15, 2017 6:49 am
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?
The notation/terminology can get kind of squirrelly. I think of RWW, WWR, etc. as permutations with replacement. But you can also think of them as combinations if you label the players 1, 2, 3 based on their position after DJ! and ask the question, "Which players got the FJ! question right?" Telling me players 3 and 1 got the question right is the same as telling me players 1 and 3 got the question right.

In the combinatorics book out of which I used to teach, there's one particular formula that says "the number of combinations (blah blah blah) equals the number of permutations (blah blah blah)", which would bother the students because you'd expect there to be more permutations than combinations for given (blah blah blah). But the ground rules made it so that it would come out the same. One version of this is what I called the "MISSISSIPPI problem". The quantity 11!/(1!4!4!2!) counts the number of arrangements of the letters MISSISSIPPI. Thinking of it that way, it's a permutation (with some repeats allowed). You can also think of four boxes labeled M, I, S, and P, with 1 ping pong ball fitting into box M, four into I, four into S, and two into P. The number of ways to put ping pong balls numbered 1 to 11 into those boxes, with order *not* mattering, also is 11!/(1!4!4!2!). Since it's really the same counting problem in disguise, it's not surprising that the answer is the same, but I don't know if there's a simple answer to the question, "Are permutations or combinations being counted?"

Sorry if I should have spoilered that for graphic mathematical content.

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

Post by twelvefootboy » Sun Oct 15, 2017 8:42 pm

Linear Gnome wrote:
Sun Oct 15, 2017 6:19 pm
opusthepenguin wrote:
Sun Oct 15, 2017 10:50 am
OldSchoolChamp wrote:
Sun Oct 15, 2017 6:49 am
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?
The notation/terminology can get kind of squirrelly. I think of RWW, WWR, etc. as permutations with replacement. But you can also think of them as combinations if you label the players 1, 2, 3 based on their position after DJ! and ask the question, "Which players got the FJ! question right?" Telling me players 3 and 1 got the question right is the same as telling me players 1 and 3 got the question right.

In the combinatorics book out of which I used to teach, there's one particular formula that says "the number of combinations (blah blah blah) equals the number of permutations (blah blah blah)", which would bother the students because you'd expect there to be more permutations than combinations for given (blah blah blah). But the ground rules made it so that it would come out the same. One version of this is what I called the "MISSISSIPPI problem". The quantity 11!/(1!4!4!2!) counts the number of arrangements of the letters MISSISSIPPI. Thinking of it that way, it's a permutation (with some repeats allowed). You can also think of four boxes labeled M, I, S, and P, with 1 ping pong ball fitting into box M, four into I, four into S, and two into P. The number of ways to put ping pong balls numbered 1 to 11 into those boxes, with order *not* mattering, also is 11!/(1!4!4!2!). Since it's really the same counting problem in disguise, it's not surprising that the answer is the same, but I don't know if there's a simple answer to the question, "Are permutations or combinations being counted?"

Sorry if I should have spoilered that for graphic mathematical content.
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Re: Thursday, October 12, 2017 Game Recap and Discussion [SPOILERS]

Post by jeff6286 » Mon Oct 16, 2017 2:55 pm

I agree that the 11/12 fj record is not a hugely significant sample. What we don't know is if Austin had tracked his fj get rate over a longer period of time. I certainly don think he could be at 90%, but if he's 70-75% over time then there could be something to this argument, and if he feels good about the category then the big wager could become even more tempting.

However, I don't think any fj confidence level could ever overcome the huge potential value of playing infinite future games. He gambled on winning an extra $9,000 today while risking what could have been hundreds of thousands in the next 5-10 games. I don't think anyone could ever convince me that this bet is rational.

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

Post by OldSchoolChamp » Tue Oct 17, 2017 5:14 am

Linear Gnome wrote:
Sun Oct 15, 2017 6:19 pm
. . . I think of RWW, WWR, etc. as permutations with replacement. But you can also think of them as combinations if you label the players 1, 2, 3 based on their position after DJ! and ask the question, "Which players got the FJ! question right?" Telling me players 3 and 1 got the question right is the same as telling me players 1 and 3 got the question right.

In the combinatorics book out of which I used to teach . . .
Well as a software kind of guy, I tend to think more in powers of 2 rather than factorials. Instead of an (ordered) permutation or (unordered) combination of choices out of a box of pingpong balls labeled R or W, I just see a three-bit integer from 0 (000, WWW) to 7 (111, RRR). I seem to have triggered this whole discussion by using the word “combination” more in its common semantic meaning than in the strict combinatoric sense. Apologies for the confusion.

I did want to return, though, to the point about weighting the eight outcomes by their probabilities. Matt Knowles put his finger on it with the hypothetical scenario 20000/16000/13000. This is in fact an instance of Stratton’s Dilemma, notoriously the most difficult of decisions for a player in second place entering Final Jeopardy. In formal terms:
  • A > B > C
    B > (2/3)A
    B < 2C
    (A - B) > (B - C)
Or in plain English, B is not crushed by A for first place, is not locked over C for second place, but is closer to C than to A. Assuming A makes the classic shutout bet (12001 in the example scenario), A will always win the game with a right answer; so B’s strategy must be predicated on the assumption of a miss by A. Controversy swirls over whether B should bet big enough (> 10000) to shut C out, guaranteeing a win with a right answer (and of course a miss by A), or whether to bet small enough (< 3000) to stay ahead of C whenever C misses the question. Neither choice is perfect: the larger bet wins whenever A misses and B doesn’t—regardless of what C does—but loses if they both miss by falling below A’s shutout residue of 7999; the smaller avoids that catastrophe, but fails to cover C’s doubled score if C gets the question right. B cannot cater to both possibilities; hence the dilemma.

I have argued before on this board that the Stratton scenario is an exception to Boyd’s Rule: that the Stratton B player should opt for the smaller bet, risk getting caught from behind by C in favor of staying ahead of a miss by A. Looking at it in terms of the RW notation, A’s shutout bet guarantees a win for A in any of the scenarios RRR, RRW, RWR, RWW; either B or C will win with a sole get (WRW or WWR, respectively); the controversy revolves around the two remaining scenarios, WRR and WWW. The big Stratton bet wins for B in scenario WRR but loses (to A) in WWW; small Stratton, vice versa. My argument is precisely that WWW is more likely than WRR: that given the underlying assumption of a miss by the leader A (who presumably has already played the best game to this point), the other two players are more likely to both miss than to both answer correctly. I note that Matt Knowles reached the same conclusion in the post linked above.
Last edited by OldSchoolChamp on Tue Oct 17, 2017 3:04 pm, edited 1 time in total.
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Re: Thursday, October 12, 2017 Game Recap and Discussion [SPOILERS]

Post by OntarioQuizzer » Fri Dec 08, 2017 7:32 pm

TenPoundHammer wrote:
Thu Oct 12, 2017 8:37 pm
None of those TV titles rang any bells for me whatsoever except Jimmy Kimmel.

Saw no way to pick "Seal" on Inuit for $600 over any other fat aquatic northern animal. Especially since "whale" was overturned.

Thomas Stearns = ????? Explaining the category would've helped. I had no idea what they were going for until $800.

No, I didn't run Dolly Parton. Had no idea where Dollywood is, and didn't know there were any fires in TN recently.

NHO "doge" except in the meme sense. Nothing in that category rang any bells.

"Ashram" was undervalued at $800. It has only been a correct response once before according to the Archive.

I had "gumshoe" but clammed because I couldn't pull a tree with "hoe" or "gum" in it.

It's a Wonderful Life briefly surfaced, but I rejected it as having nothing objectionable.
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Re: Thursday, October 12, 2017 Game Recap and Discussion [SPOILERS]

Post by TenPoundHammer » Fri Dec 08, 2017 8:03 pm

OntarioQuizzer wrote:
Fri Dec 08, 2017 7:32 pm
TenPoundHammer wrote:
Thu Oct 12, 2017 8:37 pm
None of those TV titles rang any bells for me whatsoever except Jimmy Kimmel.

Saw no way to pick "Seal" on Inuit for $600 over any other fat aquatic northern animal. Especially since "whale" was overturned.

Thomas Stearns = ????? Explaining the category would've helped. I had no idea what they were going for until $800.

No, I didn't run Dolly Parton. Had no idea where Dollywood is, and didn't know there were any fires in TN recently.

NHO "doge" except in the meme sense. Nothing in that category rang any bells.

"Ashram" was undervalued at $800. It has only been a correct response once before according to the Archive.

I had "gumshoe" but clammed because I couldn't pull a tree with "hoe" or "gum" in it.

It's a Wonderful Life briefly surfaced, but I rejected it as having nothing objectionable.
12/8 Wheel spoiler
Show
When did TPH tape Wheel?
I taped November 9
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Re: Thursday, October 12, 2017 Game Recap and Discussion [SPOILERS]

Post by OntarioQuizzer » Fri Dec 08, 2017 8:27 pm

TenPoundHammer wrote:
Fri Dec 08, 2017 8:03 pm
OntarioQuizzer wrote:
Fri Dec 08, 2017 7:32 pm
TenPoundHammer wrote:
Thu Oct 12, 2017 8:37 pm
12/8 Wheel spoiler
Show
When did TPH tape Wheel?
I taped November 9
Still nothing objectionable about IAWL? ;)
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