Do not do this!

[cvdwightw]

I hope R. does not mind me quoting a couple of choice segments from my private e-mail conversation with him regarding this question.

(stuff comparing this to converting between slope-intercept and standard form of a linear equation)

Computation questions like this strike me as computation for computation's sake; that is, there is no truly underlying mathematical concept other than "can you move some numbers around for me to get it in the form I specify?". I have always found slope-intercept form (or other fancy equation manipulation) to be a means toward making graphing easier (that is, a step in one process of graphing standard form equations), and not an end in itself...Perhaps you will respond that the mathematics involved in converting to slope-intercept form is plausible to test for exactly that reason; that is, it is a necessary step in something that does have mathematical or scientific relevance. To which I must respond: for what mathematically or scientifically relevant technique is conversion to odds a necessary step?

...this question (more than most computation questions, but really, all computation questions by NAQT have this issue) has the distinct disadvantage of possibly rewarding a player who has no idea at all how to do the problem (but can do arithmetic or, in this case, counting quickly) over a player who has a more advanced conceptual understanding of the problem...students who know how to do the problem are NOT going to do the computation you've asked for. They're going to find the probability of a 2, then find the probability of a 12, then realize they're mutually exclusive events and add them. In a large number of cases, the player will then assume that the concept being tested is "do you know what to do with mutually exclusive events" (since, after all, this is a reasonable assumption, as mutually exclusive events are mathematically relevant and taught in probability/statistics classes; certainly it's a far more reasonable assumption than "do you know how to make a table of successes and failures, add them, and compute their ratio?", which is what the question is actually asking the player to do, and is a far more basic skill that requires no conceptual understanding of probability or mutually exclusive events) and answer "1/18."

"17:1" is ambiguous; personally, I interpret that, given the question, as "17:1 for"; but then again, I'm not much of a gambler, and someone with a more extensive gambling background might interpret that as "it pays 17:1." I quote the one paragraph on "fair odds" from my textbook [Stirzaker, Elementary Probability, used in two upper-division probability courses at UCLA], page 13: "If the occurrence of some event is denoted by A, then Ac denotes the nonoccurrence of A...If the probability of A is p and the probability of Ac is q, then the odds against A are q:p...The odds on A are p:q." In other words, the order in which the two numbers are given necessarily matters. The correct answers to this question are, according to my textbook, _17:1 against_ or _1:17_ for. Since you're asking for the "odds that" something happens, it would be ridiculous to accept "17:1" by itself as that's not, according to my textbook, the odds that it happens. It would be like accepting "x = 2y+3" for the equation "y = 2x+3" or "1" for "-1." Again, if you're going to disallow an equivalent answer because it's not in the right form, it seems ludicrous to me to accept something that a textbook explicitly claims is not the right answer (unless there is some other reputable source that claims that _17:1_ and _1:17_ are equivalent, or you are arguing that the question does not specify whether it's odds on/for or odds against, in which case it's a systematically terrible question because the question does not have a unique answer).

Calculating things like odds or WHIP may be a valuable skill in some non-academic setting, but in those cases the emphasis is not on the mathematical skill required but rather the application to a non-academic setting...

[jonah]

I'd just like to point out two differences between the odds situation and various forms of lines. I don't think either are good questions, but there are these distinctions: firstly, I can't conceive of someone with a decent understanding of lines and their equations who doesn't know what slope-intercept form means, while I suspect there exist people who understand probability but don't know exactly the distinction between odds and ordinary probability (if it weren't for computation in Illinois Scholastic Bowl, I would be such a person).

Furthermore, not specifying what form a line's equation should be in opens the way to a ton of alternative forms, therefore either mandating an absurdly long and confusing answer line or opening the way to a lot of protests (and there might not be a neutral party qualified to adjudicate them, unfortunately). So if we ignore the fact that "give the equation of this described line" is a lousy question for other reasons common to all computation questions, there is still a good reason to specify what form it should be given in; on the other hand, probability/odds questions do not admit so many alternative forms, so there is much less an incentive to specify a constraint on form.

[Mechanical Beasts]

I don't see how comparing this problem to converting between slope-intercept form and standard form (whatever that is) of a linear equation suggests that this problem is any more legitimate. Indeed, that just illustrates precisely what's bogus about it. It's requiring one participant to answer using one convention over another without any real justification (it's not in the NAQT rules, you don't have a 1/1 craps arithmetic distribution, whatever) for preferring one convention over another. They are two different ways of representing the same line.

Now, i will submit that it is possible to create a question that is as legitimate as any computational math question can be out of this. Say that Mikey has ten dollars riding on this roll, and he wants to know what he'll get if he wins and the odds are fair (or something similar; I'm not a gambler). This rewards kids who knows how the "odds" form relates to the "probability" form. Similarly, asking for the y-intercept of a line (or the overhead costs of a firm, etc. etc.) rewards kids who can put a line into slope-intercept form but does not require them to use one arbitrary symbolic convention over another.

[grapesmoker]

While I appreciate Dwight's meticulousness, the shorter and more direct argument here is: notational issues should not matter. Different ways of denoting the same thing are logically equivalent and therefore effectively equivalent in terms of demonstrating the necessary knowledge.