Do not do this!

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Do not do this!

Post by grapesmoker » Fri Jun 19, 2009 11:17 pm

I don't post often in the high school section, but I thought this merited addressing:
a terrible IS tossup wrote: Pencil and paper ready. Sheldon wants to know the odds that he throws a total of either 2 or 12 on a single throw of two fair, six-sided dice. The easiest way to calculate those odds, expressed as a ratio ”a to b,” is to total up the chances of his succeeding and failing, and expressing the ratio of those probabilities in lowest (*) terms. For 10 points—what are the odds of Sheldon throwing a 2 or a 12?

answer: 17 to 1 against or 17:1 (accept 1 to 17 or 1:17; do not accept “1/18”)
It is unacceptable and downright moronic to write a question that literally does not accept a mathematically correct and equivalent answer. I don't care that it says odds, this is just completely stupid. The probability of achieving the desired result is 1/18 and making people do a stupid trick to transform it into "odds notation" is beyond preposterous.
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Re: Do not do this!

Post by Important Bird Area » Sat Jun 20, 2009 12:24 am

Jerry, I've forwarded your concern to R., since now is the time of year when we discuss rules changes for next year's tournaments.

I've also set up a catchall thread for question-specific discussion of this year's IS sets.
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 12:31 am

But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
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Re: Do not do this!

Post by Sir Thopas » Sat Jun 20, 2009 12:40 am

Coach K wrote:But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
odds
  /ɒdz/ Show Spelled Pronunciation [odz] Show IPA
–noun (usually used with a plural verb)
1. the probability that something is so, will occur, or is more likely to occur than something else: The odds are that it will rain today.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 2:21 am

Coach K wrote:But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
It is a stupid trick. These are mathematically identical things. Saying "17 to one against" is the same as saying "one out of 18." The fact that this question demands odds rather than probabilities is stupid because they represent the same thing. It's like saying that Napoleon III is acceptable and Louis Napoleon is not, even though they are in fact the same person. You're just asking people to do a dumb transposition between forms instead of accepting the substance of the answer.
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 2:54 am

grapesmoker wrote:
Coach K wrote:But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
It is a stupid trick. These are mathematically identical things. Saying "17 to one against" is the same as saying "one out of 18." The fact that this question demands odds rather than probabilities is stupid because they represent the same thing. It's like saying that Napoleon III is acceptable and Louis Napoleon is not, even though they are in fact the same person. You're just asking people to do a dumb transposition between forms instead of accepting the substance of the answer.
Wel... technically, he is right. Odds are defined in a specific manner. However, that still does not detract from the poorness of the question. If you're doing math in such a short time, I doubt that you will be hanging on to every word of the question or watch out for tricky definitions. I'd say that, 95% of the time, questions like these in quizbowl and even most math competitions never ask for odds but rather probability (or in the case of math competitions, they say specifically what they mean). The question should reward knowledge of the material. If someone gets to the 1/18 part, then they know how to do it; and points should not be cheated from them due to a trick in semantics.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 4:17 am

kldaace wrote:Wel... technically, he is right. Odds are defined in a specific manner. However, that still does not detract from the poorness of the question. If you're doing math in such a short time, I doubt that you will be hanging on to every word of the question or watch out for tricky definitions. I'd say that, 95% of the time, questions like these in quizbowl and even most math competitions never ask for odds but rather probability (or in the case of math competitions, they say specifically what they mean). The question should reward knowledge of the material. If someone gets to the 1/18 part, then they know how to do it; and points should not be cheated from them due to a trick in semantics.
Again, he's not even right technically, since 1/18 is mathematically equivalent to 17 to 1 against. It doesn't matter that it says "odds" because these are literally the same thing. That's a problem on top of the fact that for the reasons you mention this question just plays horribly.

My point is: if you're writing a question, stop trying to be clever. Just reward knowledge and don't pull semantic tricks that make people hate the question.
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Re: Do not do this!

Post by Irreligion in Bangladesh » Sat Jun 20, 2009 4:22 am

Additionally, this one is no different than requiring an answer as a decimal and negging equivalent fractions (or vice versa), which is unfortunately common in the computational questions I've seen out of Illinois writers. Both restrictions may be valid in some non-quizbowl sense, mathematics-related or otherwise, but negging you for notation differences isn't fair. Extending from Jerry's example, we don't say "Do not give your answer as Louis Napoleon" in the middle of a tossup.
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 8:36 am

Sir Thopas wrote:
Coach K wrote:But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
odds
  /ɒdz/ Show Spelled Pronunciation [odz] Show IPA
–noun (usually used with a plural verb)
1. the probability that something is so, will occur, or is more likely to occur than something else: The odds are that it will rain today.
The common definition of odds and the mathematical definition of odds are very different things.

Probability is defined as the number of successes divided by the total number of outcomes.

Odds is defined as the ratio of the probability of success to the probability of failure (which in practice simplifies to successes divided by failures).
kldaace wrote:
grapesmoker wrote:
Coach K wrote:But odds and probabilities are different, so 1/18 isn't a mathematically correct and equivalent answer. It isn't a "stupid trick", it's the definition of odds.
It is a stupid trick. These are mathematically identical things. Saying "17 to one against" is the same as saying "one out of 18." The fact that this question demands odds rather than probabilities is stupid because they represent the same thing. It's like saying that Napoleon III is acceptable and Louis Napoleon is not, even though they are in fact the same person. You're just asking people to do a dumb transposition between forms instead of accepting the substance of the answer.
Wel... technically, he is right. Odds are defined in a specific manner. However, that still does not detract from the poorness of the question. If you're doing math in such a short time, I doubt that you will be hanging on to every word of the question or watch out for tricky definitions. I'd say that, 95% of the time, questions like these in quizbowl and even most math competitions never ask for odds but rather probability (or in the case of math competitions, they say specifically what they mean). The question should reward knowledge of the material. If someone gets to the 1/18 part, then they know how to do it; and points should not be cheated from them due to a trick in semantics.
Saying "17 to 1 against" is the odds equivalent to saying the probability of "1 out of 18". Because the question is looking for odds, the probability is incorrect. If the odds were "one out of 18", then the event would have a probability of 1/19. One of the key points of the question is understanding the difference between odds and probability. An answer of "1 out of 18" shows a clear lack of understanding of what odds are.

Also, the suggestion that you wouldn't/shouldn't be hanging on to every word because you're working on a math problem is ridiculous. That's like saying "well you should take speed and velocity as correct answers because I didn't hear the question say vector quantity at the beginning".

And the definition of odds is not any trickier than any other definition in mathematics. Just because probability is asked for more, does not mean that it's unacceptable to ask for odds.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 11:21 am

Coach K wrote:The common definition of odds and the mathematical definition of odds are very different things.
So? First of all, the "mathematical" definition of odds, whatever that is, is equivalent to some "mathematical" definition of probability. They literally represent the same number, just like 5/2 and 2.5 represent the same number. Asking for one and not accepting the other is stupid and indefensible, because it basically trades on a semantic trick to deny a person points for the correct answer. Second, the question doesn't say which definition of odds is being used here (I'm accepting for the moment your incorrect premise that such a thing as the "mathematical" definition of odds exists, even though it doesn't). There's a colloquial understanding of odds, e.g. if I ask what are the odds of a fair coin coming up heads or tails, and someone says "50/50" or "1 in 2" I understand what that means because I am a human being capable of using language correctly. I do not then jump up and down and demand that the person answer my question in the form of "x to y against."

Why are you committed to defending such a terrible question?
Probability is defined as the number of successes divided by the total number of outcomes.

Odds is defined as the ratio of the probability of success to the probability of failure (which in practice simplifies to successes divided by failures).
It's not "defined" as such anywhere; odds are just a notational difference that's sometimes used instead of probability. If I'm in a poker hand and I'm a 3 to 2 favorite, I have a 60% chance or a 3/5 probability of winning. Those are the same numbers!

Also, the suggestion that you wouldn't/shouldn't be hanging on to every word because you're working on a math problem is ridiculous. That's like saying "well you should take speed and velocity as correct answers because I didn't hear the question say vector quantity at the beginning".
That's because speed and velocity are not the same thing!
And the definition of odds is not any trickier than any other definition in mathematics. Just because probability is asked for more, does not mean that it's unacceptable to ask for odds.
Look at that question: it begins, by saying "dude wants to know the odds of event x," and the desired number is trivial to calculate. Someone who is fast could immediately buzz, say "1/18" which is the correct answer, and be negged all because of your definitional zeal, which is misplaced because as I've already said a bunch of times, the definitions literally refer to the same number.

Nothing about that setup is consistent with the spirit of the game that rewards knowledge, so stop defending it and stop writing questions that trick people.
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Re: Do not do this!

Post by rjaguar3 » Sat Jun 20, 2009 11:43 am

styxman wrote:Extending from Jerry's example, we don't say "Do not give your answer as Louis Napoleon" in the middle of a tossup.
No, but in IHSA state series, about half the questions begin with one of the following:
  • Identify the n-word phrase...
  • Identify the k-letter <part of speech>...
  • Identify the x-syllable word...
...and, in addition to making the question REALLY transparent, this practice causes some of the rules-lawyering coaches to think that's enough justification to reject obviously equivalent answers like "Polish" and "Poland."

EDIT: I should also throw in that we lost a Masonic bowl regional championship match because a question asked for the standard form of some line, I gave the answer in the form Ax + By = C, but the paper had the auk-tastic answer of Ax + By + C = 0. Since the opposing coach was an infamous rules-lawyer, there was nothing we could do.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 11:53 am

rjaguar3 wrote:No, but in IHSA state series, about half the questions begin with one of the following:
  • Identify the n-word phrase...
  • Identify the k-letter <part of speech>...
  • Identify the x-syllable word...
...and, in addition to making the question REALLY transparent, this practice causes some of the rules-lawyering coaches to think that's enough justification to reject obviously equivalent answers like "Polish" and "Poland."

EDIT: I should also throw in that we lost a Masonic bowl regional championship match because a question asked for the standard form of some line, I gave the answer in the form Ax + By = C, but the paper had the auk-tastic answer of Ax + By + C = 0. Since the opposing coach was an infamous rules-lawyer, there was nothing we could do.
That's another thing not to do, although I've not seen many instances of this in NAQT.
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 12:19 pm

grapesmoker wrote:
Coach K wrote:The common definition of odds and the mathematical definition of odds are very different things.
So? First of all, the "mathematical" definition of odds, whatever that is, is equivalent to some "mathematical" definition of probability. They literally represent the same number, just like 5/2 and 2.5 represent the same number. Asking for one and not accepting the other is stupid and indefensible, because it basically trades on a semantic trick to deny a person points for the correct answer. Second, the question doesn't say which definition of odds is being used here (I'm accepting for the moment your incorrect premise that such a thing as the "mathematical" definition of odds exists, even though it doesn't). There's a colloquial understanding of odds, e.g. if I ask what are the odds of a fair coin coming up heads or tails, and someone says "50/50" or "1 in 2" I understand what that means because I am a human being capable of using language correctly. I do not then jump up and down and demand that the person answer my question in the form of "x to y against."

Why are you committed to defending such a terrible question?
Probability is defined as the number of successes divided by the total number of outcomes.

Odds is defined as the ratio of the probability of success to the probability of failure (which in practice simplifies to successes divided by failures).
It's not "defined" as such anywhere; odds are just a notational difference that's sometimes used instead of probability. If I'm in a poker hand and I'm a 3 to 2 favorite, I have a 60% chance or a 3/5 probability of winning. Those are the same numbers!

Also, the suggestion that you wouldn't/shouldn't be hanging on to every word because you're working on a math problem is ridiculous. That's like saying "well you should take speed and velocity as correct answers because I didn't hear the question say vector quantity at the beginning".
That's because speed and velocity are not the same thing!
And the definition of odds is not any trickier than any other definition in mathematics. Just because probability is asked for more, does not mean that it's unacceptable to ask for odds.
Look at that question: it begins, by saying "dude wants to know the odds of event x," and the desired number is trivial to calculate. Someone who is fast could immediately buzz, say "1/18" which is the correct answer, and be negged all because of your definitional zeal, which is misplaced because as I've already said a bunch of times, the definitions literally refer to the same number.

Nothing about that setup is consistent with the spirit of the game that rewards knowledge, so stop defending it and stop writing questions that trick people.
Probability and odds are NOT the same thing in a mathematical sense, just like speed and velocity are not the same thing in a mathematical sense. It's not my fault that you lack understanding about the mathematical concepts underlying the question. Open any mathematics textbook that has a section on probability and odds and you will find the exact definitions I stated above. Probability and odds are frequently discussed hand-in-hand because they're related concepts, but they are not equivalent.
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Re: Do not do this!

Post by Sen. Estes Kefauver (D-TN) » Sat Jun 20, 2009 12:25 pm

Hilariously you are accusing someone with a math degree of not knowing basic mathematical concepts. Let me break it down for you: Jerry knows what he is talking about, and despite whatever you may argue, those 2 numbers are the exact same thing and to pore over every word looking for a technical loophole to punish knowledge is bad, and the fact that you are defending this suggests something like that you are more concerned with getting caught up in technicalities then the actual fact that this kind of writing is very bad.
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Re: Do not do this!

Post by Sen. Estes Kefauver (D-TN) » Sat Jun 20, 2009 12:28 pm

Also, if we stopped asking these awful computation tossups this would never be a problem again. Take heed, NAQT.
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Re: Do not do this!

Post by rjaguar3 » Sat Jun 20, 2009 12:29 pm

Coach K wrote:
grapesmoker wrote:
Coach K wrote:The common definition of odds and the mathematical definition of odds are very different things.
So? First of all, the "mathematical" definition of odds, whatever that is, is equivalent to some "mathematical" definition of probability. They literally represent the same number, just like 5/2 and 2.5 represent the same number. Asking for one and not accepting the other is stupid and indefensible, because it basically trades on a semantic trick to deny a person points for the correct answer. Second, the question doesn't say which definition of odds is being used here (I'm accepting for the moment your incorrect premise that such a thing as the "mathematical" definition of odds exists, even though it doesn't). There's a colloquial understanding of odds, e.g. if I ask what are the odds of a fair coin coming up heads or tails, and someone says "50/50" or "1 in 2" I understand what that means because I am a human being capable of using language correctly. I do not then jump up and down and demand that the person answer my question in the form of "x to y against."

Why are you committed to defending such a terrible question?
Probability is defined as the number of successes divided by the total number of outcomes.

Odds is defined as the ratio of the probability of success to the probability of failure (which in practice simplifies to successes divided by failures).
It's not "defined" as such anywhere; odds are just a notational difference that's sometimes used instead of probability. If I'm in a poker hand and I'm a 3 to 2 favorite, I have a 60% chance or a 3/5 probability of winning. Those are the same numbers!

Also, the suggestion that you wouldn't/shouldn't be hanging on to every word because you're working on a math problem is ridiculous. That's like saying "well you should take speed and velocity as correct answers because I didn't hear the question say vector quantity at the beginning".
That's because speed and velocity are not the same thing!
And the definition of odds is not any trickier than any other definition in mathematics. Just because probability is asked for more, does not mean that it's unacceptable to ask for odds.
Look at that question: it begins, by saying "dude wants to know the odds of event x," and the desired number is trivial to calculate. Someone who is fast could immediately buzz, say "1/18" which is the correct answer, and be negged all because of your definitional zeal, which is misplaced because as I've already said a bunch of times, the definitions literally refer to the same number.

Nothing about that setup is consistent with the spirit of the game that rewards knowledge, so stop defending it and stop writing questions that trick people.
Probability and odds are NOT the same thing in a mathematical sense, just like speed and velocity are not the same thing in a mathematical sense. It's not my fault that you lack understanding about the mathematical concepts underlying the question. Open any mathematics textbook that has a section on probability and odds and you will find the exact definitions I stated above. Probability and odds are frequently discussed hand-in-hand because they're related concepts, but they are not equivalent.
Speed and velocity are different quantities: one is a scalar, and the other is a vector. So I would neg 3i+4j if the question was asking for a speed of 5.

Probability and odds are different ways of expressing the same number: a probability of 1/38 of winning on a single-number bet in roulette is exactly equivalent to 37:1 odds against winning.* They're just two different ways of stating the same thing.

Negging two equivalent ways of stating the same thing is just like negging "Polish" for "Poland" after "this country," or negging "deviant" for "deviance" after "this noun." It's asinine.

*Claim: For each probability p, 0 < p < 1, there is exactly one positive real N so that the odds of the event occurring is N : 1 for.

Proof: Let N = p/(1-p). Then the probability of the event occurring according to the N we just defined is (p/(1-p))/((p/(1-p))+1)=(p/(1-p))/(1/(1-p))=p.

Also, let N and M be odds numbers for probability p. We will show that N-M=0. We note that 0=N/(N+1)-M/(M+1) => 0=N(M+1)-M(N+1)=NM+N-MN-M=N-M, so N=M, hence uniqueness.
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 12:43 pm

Jeremy Gibbs Free Energy wrote:Hilariously you are accusing someone with a math degree of not knowing basic mathematical concepts. Let me break it down for you: Jerry knows what he is talking about, and despite whatever you may argue, those 2 numbers are the exact same thing and to pore over every word looking for a technical loophole to punish knowledge is bad, and the fact that you are defending this suggests something like that you are more concerned with getting caught up in technicalities then the actual fact that this kind of writing is very bad.
I guess my Masters in Mathematics is worthless then?

Those two numbers are not the same thing. They're not. This is not a technical loophole to punish knowledge. It's checking to make sure someone knows that probability and odds are different, something that you clearly do not know. They are different ways of talking about the same topic, but they are not equivalent.
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Re: Do not do this!

Post by Siverus Snape » Sat Jun 20, 2009 12:45 pm

Ahhh, Greg's doing real math again!!!
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 12:47 pm

rjaguar3 wrote:
*Claim: For each probability p, 0 < p < 1, there is exactly one positive real N so that the odds of the event occurring is N : 1 for.

Proof: Let N = p/(1-p). Then the probability of the event occurring according to the N we just defined is (p/(1-p))/((p/(1-p))+1)=(p/(1-p))/(1/(1-p))=p.

Also, let N and M be odds numbers for probability p. We will show that N-M=0. We note that 0=N/(N+1)-M/(M+1) => 0=N(M+1)-M(N+1)=NM+N-MN-M=N-M, so N=M, hence uniqueness.
This only proves that there is a one-to-one relationship between a given probability and its corresponding odds. A 1-to-1 relationship does not imply equivalence. I'm sure you can also show that the natural numbers and rational numbers can be placed in a 1-to-1 correspondence, but no one would try to state that 1 and 1/2 are equivalent.
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Re: Do not do this!

Post by Cheynem » Sat Jun 20, 2009 12:51 pm

We're getting into a forest for the trees situation here. On a definitional level, yes, probability and odds are not the same thing. But this begs the question: what sort of knowledge is this question meant to reward? Is it just that a person knows how to express something in "odds" as opposed to "probability"? That seems a little dubious in terms of question quality.
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Re: Do not do this!

Post by Huang » Sat Jun 20, 2009 1:07 pm

Coach K wrote:
Jeremy Gibbs Free Energy wrote:Hilariously you are accusing someone with a math degree of not knowing basic mathematical concepts. Let me break it down for you: Jerry knows what he is talking about, and despite whatever you may argue, those 2 numbers are the exact same thing and to pore over every word looking for a technical loophole to punish knowledge is bad, and the fact that you are defending this suggests something like that you are more concerned with getting caught up in technicalities then the actual fact that this kind of writing is very bad.
I guess my Masters in Mathematics is worthless then?

Those two numbers are not the same thing. They're not. This is not a technical loophole to punish knowledge. It's checking to make sure someone knows that probability and odds are different, something that you clearly do not know. They are different ways of talking about the same topic, but they are not equivalent.
Haha, where did Charlie state or even imply that your "Masters in Mathematics" was worthless? Sort of strange you would patronize someone on this board in a post and then automatically assume someone else is patronizing you in their post.

Anyways, you're absolutely right. If I gave an answer like 1/18 or 17 to 1 in Chinese, I would clearly not know what I'm talking about since the official language of the United States is English. How dare I not be aware of the official language of the country I'm playing quizbowl in!
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 1:10 pm

Coach K wrote:I guess my Masters in Mathematics is worthless then?
Any degree that leaves you apparently unable to understand that odds and probabilities represent the same number is worthless, yes. Don't pull rank on me.
Those two numbers are not the same thing. They're not. This is not a technical loophole to punish knowledge. It's checking to make sure someone knows that probability and odds are different, something that you clearly do not know. They are different ways of talking about the same topic, but they are not equivalent.
In mathematics, so I hear, argument by repetition is not an accepted proof method. Odds and probabilities are exactly the same. They are simply two different ways of encoding the same information. Do "1/18" and "17 to 1 against" represent the same number or not? If you answer affirmatively, then you'd better concede my point that this is a technical loophole; if you answer negatively, then you'd better explain yourself because you've just undermined statistics.
Coach K wrote:Probability and odds are NOT the same thing in a mathematical sense, just like speed and velocity are not the same thing in a mathematical sense. It's not my fault that you lack understanding about the mathematical concepts underlying the question. Open any mathematics textbook that has a section on probability and odds and you will find the exact definitions I stated above. Probability and odds are frequently discussed hand-in-hand because they're related concepts, but they are not equivalent.
Could you be any more wrong? They are exactly the same thing; in fact, there is no such thing as a "mathematical definition of odds," no matter what your high school math textbook might tell you. In fact, no field outside of gambling ever uses the language of odds (the word "odds" does not appear in 3 probability textbooks which I have just consulted and which I'll be happy to give you citations for). Odds and probabilities are logically equivalent; they must be if those words are to have any meaning whatsoever and we don't need to construct bijections or proofs to see this. What you are claiming is like saying that Zorn's Lemma and the Axiom of Choice are different even though they are logically identical and anything that can be proven with one can be proven with the other. Your inability to follow basic reason to a logical conclusion and your preference for dogmatic adherence to made-up definitions over reality is discouraging, and augurs poorly for your students. Fortunately I don't have to convince you since everyone in this thread understands that I'm right and you're wrong. Enjoy living in a world where Hesperus is not Phosphorus and referents are meaningless.
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Re: Do not do this!

Post by Sir Thopas » Sat Jun 20, 2009 1:26 pm

Coach K wrote:This only proves that there is a one-to-one relationship between a given probability and its corresponding odds. A 1-to-1 relationship does not imply equivalence. I'm sure you can also show that the natural numbers and rational numbers can be placed in a 1-to-1 correspondence, but no one would try to state that 1 and 1/2 are equivalent.
Yes, but if you have 1 pie and 1/2 a pie, those are describing different situations. This is emphatically not true with 1/18 and 17:1—both are describing the situation where a given possibility will occur once in every 18 iterations.
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Re: Do not do this!

Post by Matt Weiner » Sat Jun 20, 2009 1:28 pm

Yeah, this is a style of bad question that was really common like 10-15 years ago...something where the writer envisions smiling gleefully and explaining that TECHNICALLY you are incorrect because...not something that NAQT should be endorsing, obviously.
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Re: Do not do this!

Post by at your pleasure » Sat Jun 20, 2009 1:49 pm

The article linked in the other math thread should clarify this, but "odds notation" is not some mystical concept handed down to Moses with the ten commandments. It is simple one possible(and somewhat cumbersome) way of expressing how likely it is that something will happen. It seems the hight of absurdity to write a question to punish someone for giving a equally valid and accepted (and less cumbersome) description of the likelihood that the event will happen.
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Re: Do not do this!

Post by Deviant Insider » Sat Jun 20, 2009 2:00 pm

I'll throw in my two cents in here.

If I was moderating in a room and this question came up, I would not accept 1/18 as a correct answer. It stipulates a certain format early on, so students should answer in that format.

However, I have written about 500 computational tossups over the years, and I have never written one on odds. That's because it is an inconsequential topic that within a quizbowl tossup is more likely to trip up a student on a triviality than anything else.

If I was at a moderator's meeting before a tournament where the moderators had read the questions ahead of time, I would suggest changing the question so that it asked for the probability. If the consensus went against me, then I would go with the consensus, but I would raise the issue.

If I was an editor who was sent that question, I would make it a probability question and add a wrinkle to it so that it would not be as obvious to as many students. Two standard six-sided dice is a standard situation, and calculating a 2 or a 12 is a very simple problem within that standard situation, so I would make it a probability problem and add in a third die or make it so that the dice were not six-sided.
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 2:34 pm

Upon asking guidance from my biostatistics professor, odds and probability are not the same thing. Just sayin'. I don't think that this question is just in any way though. Math computational tossups as much as people hate them should be mathcomputation. I don't think it's fair that people lose points when they clearly were able to calculate the probability of such an event. I'm 98% sure that I've never heard a question ask for probability. Hence, whenever I go into a calculation question asking for the odds of something, I don't immediately recognize that odds is different from probability. The answer, as stated before, is cumbersome. I do realize that the question did state odds specifically, but it doesn't seem to reward mathematical knowledge in how to compute it. It trips people up because of just that one word, and people who have deep knowledge of probability might get it wrong. If this were a math theory question specifically asking for odds, then probability should not be accepted just as series is not accepted for sequence. But, if this were a math computation question, then leeway should be given to the person who gave the probability so as to award real knowledge of computation.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 2:37 pm

kldaace wrote:Upon asking guidance from my biostatistics professor, odds and probability are not the same thing.
I would be delighted to hear the justification for this. Do they or do they not represent the exact same information?
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Re: Do not do this!

Post by theMoMA » Sat Jun 20, 2009 2:38 pm

Jerry isn't saying they're literally the same thing, just that they're two equivalent modes of notation that point to the same referent. And that getting the correct mathematical notation in this situation should not be a requirement to answering the question, since both do the exact same thing (express 0.0555 in rational terms).
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Re: Do not do this!

Post by theMoMA » Sat Jun 20, 2009 2:41 pm

Also, it is especially horrible because a common understanding of the word "odds" stands in for general probability. The question assumes that you understand "odds" to mean a certain thing when in fact, it means multiple things.
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 2:41 pm

grapesmoker wrote:
kldaace wrote:Upon asking guidance from my biostatistics professor, odds and probability are not the same thing.
I would be delighted to hear the justification for this. Do they or do they not represent the exact same information?
They do. But it's represented in different ways is all.
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 2:47 pm

It's like if I said mixed fractions instead of improper fractions. Same idea; different ways of representing them. All technical.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 2:53 pm

kldaace wrote:It's like if I said mixed fractions instead of improper fractions. Same idea; different ways of representing them. All technical.
In other words, inconsequential. "Mixed fractions" and "improper fractions" are concepts that exist at the elementary school level and nowhere else. 5/2 and 2.5 and 2 and 1/2 represent the same number. They are equivalent according to any plausible concept of equivalence. Therefore, when one is an acceptable answer, they must all be acceptable. Any question written otherwise violates the basic notion of rewarding substantive knowledge in favor of parsing technicalities, and is therefore contrary to the spirit of the game.
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 2:58 pm

grapesmoker wrote:
kldaace wrote:It's like if I said mixed fractions instead of improper fractions. Same idea; different ways of representing them. All technical.
In other words, inconsequential. "Mixed fractions" and "improper fractions" are concepts that exist at the elementary school level and nowhere else. 5/2 and 2.5 and 2 and 1/2 represent the same number. They are equivalent according to any plausible concept of equivalence. Therefore, when one is an acceptable answer, they must all be acceptable. Any question written otherwise violates the basic notion of rewarding substantive knowledge in favor of parsing technicalities, and is therefore contrary to the spirit of the game.
Agreed. Technicalities shouldn't be written into such a question... it ruins the game when someone knows how to do a problem well and accurately but loses points due to a technical definition.
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Re: Do not do this!

Post by Important Bird Area » Sat Jun 20, 2009 3:14 pm

grapesmoker wrote:
kldaace wrote:It's like if I said mixed fractions instead of improper fractions. Same idea; different ways of representing them. All technical.
In other words, inconsequential. "Mixed fractions" and "improper fractions" are concepts that exist at the elementary school level and nowhere else. 5/2 and 2.5 and 2 and 1/2 represent the same number. They are equivalent according to any plausible concept of equivalence. Therefore, when one is an acceptable answer, they must all be acceptable. Any question written otherwise violates the basic notion of rewarding substantive knowledge in favor of parsing technicalities, and is therefore contrary to the spirit of the game.
In possibly related news:
NAQT correctness guidelines wrote:Fractional answers must be given in lowest terms, unless otherwise specified in the question. They may, however, be in improper form.
So the present standard is that 5/2, 2.5, and 2 1/2 are all acceptable, but 10/4 is not. Should we consider changing this?
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Re: Do not do this!

Post by kayli » Sat Jun 20, 2009 3:22 pm

bt_green_warbler wrote: So the present standard is that 5/2, 2.5, and 2 1/2 are all acceptable, but 10/4 is not. Should we consider changing this?
That's a really tough call. Mathematical norm is to put it in simplest fractional terms, but the person would obviously know what he's talking about... If we're in the realm of rewarding knowledge, then 10/4 should be accepted provided. Hopefully, no one would be a buttberet and say 170/68 or something, but you really can't punish correctness...

My vote: Aceept.
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Re: Do not do this!

Post by grapesmoker » Sat Jun 20, 2009 3:25 pm

bt_green_warbler wrote:So the present standard is that 5/2, 2.5, and 2 1/2 are all acceptable, but 10/4 is not. Should we consider changing this?
Absolutely! Again, these are the same number. I don't know what this "mathematical norm" is that Kay speaks of but it's nothing more than custom. Any answer that is equivalent to the correct answer must be acceptable.
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Re: Do not do this!

Post by Coach K » Sat Jun 20, 2009 3:26 pm

grapesmoker wrote:
Coach K wrote:I guess my Masters in Mathematics is worthless then?
Any degree that leaves you apparently unable to understand that odds and probabilities represent the same number is worthless, yes. Don't pull rank on me.
Those two numbers are not the same thing. They're not. This is not a technical loophole to punish knowledge. It's checking to make sure someone knows that probability and odds are different, something that you clearly do not know. They are different ways of talking about the same topic, but they are not equivalent.
In mathematics, so I hear, argument by repetition is not an accepted proof method. Odds and probabilities are exactly the same. They are simply two different ways of encoding the same information. Do "1/18" and "17 to 1 against" represent the same number or not? If you answer affirmatively, then you'd better concede my point that this is a technical loophole; if you answer negatively, then you'd better explain yourself because you've just undermined statistics.
Coach K wrote:Probability and odds are NOT the same thing in a mathematical sense, just like speed and velocity are not the same thing in a mathematical sense. It's not my fault that you lack understanding about the mathematical concepts underlying the question. Open any mathematics textbook that has a section on probability and odds and you will find the exact definitions I stated above. Probability and odds are frequently discussed hand-in-hand because they're related concepts, but they are not equivalent.
Could you be any more wrong? They are exactly the same thing; in fact, there is no such thing as a "mathematical definition of odds," no matter what your high school math textbook might tell you. In fact, no field outside of gambling ever uses the language of odds (the word "odds" does not appear in 3 probability textbooks which I have just consulted and which I'll be happy to give you citations for). Odds and probabilities are logically equivalent; they must be if those words are to have any meaning whatsoever and we don't need to construct bijections or proofs to see this. What you are claiming is like saying that Zorn's Lemma and the Axiom of Choice are different even though they are logically identical and anything that can be proven with one can be proven with the other. Your inability to follow basic reason to a logical conclusion and your preference for dogmatic adherence to made-up definitions over reality is discouraging, and augurs poorly for your students. Fortunately I don't have to convince you since everyone in this thread understands that I'm right and you're wrong. Enjoy living in a world where Hesperus is not Phosphorus and referents are meaningless.
My degree was only mentioned in response to someone else insinuating that my actions were "hilarious" because I was arguing with someone who had a degree in math. My apologies if that offended anyone.

Allow me to clarify my statements from before (in regard to probability and odds not being the same thing).

The original question seems to me to be designed to evaluate two things:

1. Do you know the probability that this event occurs?
2. Do you know that while odds and probability talk about the same kind of things, one compares your number of successes to a total number of outcomes and the other compares your number of successes to your number of failures?

Of course a probability of 1/18 and odds of 1/17 mean the same thing. They're two different ways of explaining the same concept. However, a probability of 1/18 and odds of 1/18 do not mean the same thing. If a question asks for the odds of something and you answer "1/18", you're saying that there is a probability of 1/19 that the event occurs. Answering 1/18 shows that you know the first concept the question is looking at, but not the second.

And you're again right that odds are mostly discussed among gambling circles, but it's certainly something that has come up in many math classes that I have taken. I can cite several textbooks of my own that discuss it using the definition above. If you want to argue that we shouldn't ask questions about odds, I can certainly get behind that. Probability is far more useful and has many more applications.

Like I said, I can get behind not asking questions about odds. But if we are asking them, then their corresponding probabilities are not acceptable answers because it's impossible to know whether your answer of "1/18" is referring to the probability or the odds.

And I certainly agree with you that it's bad question writing if that level of ambiguity is introduced (which is why I'm okay with not asking about odds at all). It's like asking a question on Zeus and not accepting Jupiter. But if odds are an acceptable thing to ask about, then their corresponding probabilities are wrong. Yay mathcomp?
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Re: Do not do this!

Post by Cheynem » Sat Jun 20, 2009 3:35 pm

Yeah, I would just add that it seems like the question definitely is asking for those two criteria. My problem is that one (knowing how to calculate probability into odds or the difference between them) is frankly rather trivial and not something that a neg or points should actually hinge upon knowing. If you're going to allow math calc, it seems like the actual point is to reward mathematical knowledge, not technical ways of how to say the answer. If one were to ask on a math theory tossup or bonus about probability or odds (which would be kind of stupid) as terms, then you can get more technical, I guess.
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Re: Do not do this!

Post by Deckard Cain » Sat Jun 20, 2009 4:06 pm

For what it's worth, the class in combinatorics at Missouri S&T does not even define "odds" other than to say that it's an equivalent notation to probability, and in fact the professor even explicitly compared it to expressing a number as a improper fraction versus expressing the same number as a mixed number; 17:1 is equivalent to 1/18 in precisely the same way that 2.5 is equivalent to 5/2.

In short, I agree with Jerry both that this is a dumb question and that 1/18 is an equivalent answer that should be acceptable.
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Re: Do not do this!

Post by master15625 » Sat Jun 20, 2009 4:31 pm

grapesmoker wrote:
bt_green_warbler wrote:So the present standard is that 5/2, 2.5, and 2 1/2 are all acceptable, but 10/4 is not. Should we consider changing this?
Absolutely! Again, these are the same number. I don't know what this "mathematical norm" is that Kay speaks of but it's nothing more than custom. Any answer that is equivalent to the correct answer must be acceptable.
I do think however, that if they at the beginning of the question says, "You want to find the probability in reduced form..." then they shouldn't accept 10/4 or 170/68.

EDIT: Yeah those aren't proper probabilities, more like 4/10 or 68/170 shouldn't be accepted.

Shcool wrote:If I was an editor who was sent that question, I would make it a probability question and add a wrinkle to it so that it would not be as obvious to as many students. Two standard six-sided dice is a standard situation, and calculating a 2 or a 12 is a very simple problem within that standard situation, so I would make it a probability problem and add in a third die or make it so that the dice were not six-sided.
If you had 3 dice and wanted a 12, that would be a question of some trickty casework, which would make this question to hard to solve in the allotted time. So, it can stick to 3 dice but maybe should use 15, or something.
Last edited by master15625 on Sat Jun 20, 2009 4:34 pm, edited 1 time in total.
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Re: Do not do this!

Post by DumbJaques » Sat Jun 20, 2009 4:32 pm

For the record I agree with Jerry's line of reasoning 100%, but for those of you insisting on disagreeing with it, I'd ask you to consider whether the word "odds" has a universal, 1 to 1 definition as an entity unique from probability. It should be obvious that it does not, and that the convention of expressing odds in a different way is very hardly universal. If the question had specifically said "you cannot express your answer in terms of fractional probability but must give it in the form of a ratio," well, I guess that would change things slightly, but obviously the question would be unforgivably dumb(er) and unlike anything that's normally done in quizbowl. But if it doesn't say something like this, then you can't just argue that because odds can denote a certain way of expressing something that a logically equivalent way is somehow incorrect, particularly since odds seems to have a nebulous definition anyway.
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Re: Do not do this!

Post by Wall of Ham » Sat Jun 20, 2009 4:45 pm

After taking 12 years of grade school math and 2 years of collegiate math, I have never learned nor used probability expressed in "odds" in an academic setting.

In fact, the only time I've ever encountered "odds" was in sports bettings, when Vegas would give the "odds" of a horse race or a NBA team winning the championship. The whole point of using "odds" ever is to make it easier to understand how much money you'd win.

Many math calc proponents argue that it should be included due to its part in the curriculum. But "odds" have no part in that curriculum, unless they are teaching about gambling. Thus the use of "odds" should be eliminated.


(This is only a side argument to the fact that 1/18 and 17 to 1 are mathmatically equivalent, since that argument doesn't seem to be working)

("odds" in quotation marks to distinguish from common definition)
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Re: Do not do this!

Post by Rococo A Go Go » Sat Jun 20, 2009 4:59 pm

I demand a 3/3 Gambling distribution!!!! :wink:

In all seriousness, I don't know of a good reason for asking a question like this, especially if you're just going to disqualify certain ways to say an answer because of a technicality.
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Re: Do not do this!

Post by Mechanical Beasts » Sat Jun 20, 2009 9:32 pm

Jeremy Gibbs Free Energy wrote:Also, if we stopped asking these awful computation tossups this would never be a problem again. Take heed, NAQT.
Yeah. If you don't accept two answers that mean the very same thing, then you are doing something terrible. If I were a math textbook and define "odds" and "probability" to be two different things, how am I any better than a "literature textbook" defining Mark Twain as "Sam Clemens's pen name" and Sam Clemens as "the author of this stuff?" Then, if you say "For 10 points, give the PEN NAME OF THE AUTHOR OF" at the end of the question, you can declare "hey, buddy, you buzzed and said the real name instead of the pen name" or vice versa. How clever! How rewarding of knowledge!

Leaving aside the fact that your ability to calculate probabilities quickly doesn't reward knowledge at all, what REALLY doesn't reward knowledge is penalizing someone for using different notation. If you, as the question writer, decide "I'll arbitrarily prefer this notational convention over this other one because I have stuck my thumb so far up my butt I can't breathe," then you have done a bad thing and should stop doing that thing.

I feel strongly about this subject.
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Re: Do not do this!

Post by jonpin » Sun Jun 21, 2009 12:02 am

Coach K wrote:Saying "17 to 1 against" is the odds equivalent to saying the probability of "1 out of 18". Because the question is looking for odds, the probability is incorrect. If the odds were "one out of 18", then the event would have a probability of 1/19. One of the key points of the question is understanding the difference between odds and probability. An answer of "1 out of 18" shows a clear lack of understanding of what odds are.
If you're going to take the pedantic approach, the underlined statement is meaningless. Similarly, the question as written begins "Sheldon wants to know the odds that he throws a total of either 2 or 12..." This is bad mathematics. If you're going to insist on odds as being different from probabilty, use it correctly. It's impossible for the odds of something to be "one out of 18" as odds are always odds for (successes to failures) or odds against (failures to successes), both with the linking word "to". Thus, I'd prefer the answer to the question be "1 to 17". If you want "17 to 1", you should emphasize "odds against" from the beginning.

Or, you know, NAQT could choose not to write this question ever again, given that it's trivial except in that it has a trick.
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Re: Do not do this!

Post by The King's Flight to the Scots » Sun Jun 21, 2009 10:35 am

People have alluded to this before, but I think the big problem is that to get a comp math problem before the other team, you HAVE to ignore everything that doesn't lead to the answer and listen for the numbers. You don't have time to contemplate the difference between "odds" and "probability". If NAQT thinks that this skill should be rewarded, it shouldn't maliciously penalize players with a trivial hose.
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Re: Do not do this!

Post by cvdwightw » Sun Jun 21, 2009 5:48 pm

This thread is terrible and stupid.

Are odds and probabilities the same? No.
Do they represent the exact same thing? Yes.
Are students who actually know what they're doing with probability going to eschew the "this is how you do the problem" in favor of an easier strategy of adding two mutually exclusive probabilities? Yes.
Should we punish students for not doing what frankly amounts to an extra computation? No.
Is it extremely likely that a student will buzz in with the "do not accept" answer, leading to the other team saying something absolutely wrong on the rebound (because their purported answer of 1/18 has already been ruled wrong)? Yes.

No student, trying to win a computation race, is going to take the extra computation time to go from (1 in 18 chance) to (1:17 odds for).

Furthermore, as has been pointed out, 17:1 and 1:17 are not equivalent odds. This question is thus systematically terrible, as it both manages to punish knowledge (that 1 in 18 and 1:17 mean the same thing) and reward wrong knowledge (awarding 10 points for saying that the odds are 17:1 for).

Regardless of all other points, any question that has the potential to punish the non-answering team for the answering team's "wrong" answer is terrible. I hope this is intuitively obvious.
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Ben Dillon
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Re: Do not do this!

Post by Ben Dillon » Sun Jun 21, 2009 9:37 pm

As a math teacher, I'll throw in my one-fiftieth of a dollar here.

Be careful of the argument along the lines that "everyone knows what odds mean in the real world, therefore it's equivalent to probability". Every subject has in it technical jargon that may be used differently from the way the same terms are used in the real world. For example, "color" has a specific meaning to a nuclear physicist, "check" has a specific meaning to a poker player, and "thrill" has a specific meaning to a doctor.

The question could be worded as "How likely is the event?", in which case either odds or probability could be taken for answers. Then, if the question ended up asking for odds, the answer could specify to accept probability before that point to avoid the hose.

That all stated, I agree the question is bad because it makes students jump through an extra hoop. This type of question should have been sent to an electric chair long before it made it into a set.
Ben Dillon, Saint Joseph HS
Indiana State Quiz Bowl Board

"Why, sometimes I've believed as many as
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Mechanical Beasts
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Re: Do not do this!

Post by Mechanical Beasts » Sun Jun 21, 2009 10:06 pm

Are different meanings of the word "odds" as different as color charge and hey that hotel is blue? Are these many meanings different enough, moreover, to justify asking for odds instead of just accepting anything that refers to how likely the event is? I don't see how.
Andrew Watkins

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