And of course there is correlation between math knowledge and success at test. The problem is that at the extremes the tails come apart. Kids that are better at multiplication will be better at the tests. But the kids who score maximum at the tests and the kids who win math olympiads, are probably two distinct groups. I am saying this as a former kid who did well at math olympiads, but often got B’s at high school, because of some stupid numeric mistake.
This is culture-dependent; e.g. in (some parts of Russian grading culture) making a numeric mistake might be counted similarly to other gaps in the reasoning. An attitude of mistake is a mistake is quite prevalent in grading for university admissions (in at least one of the few places they remain supplementing the standardized tests). Unsure how prevalent that was in olympiad grading, I never was competitive there (although did encounter this outlook a bit in my small stints of grading olympiad tasks).
[There is usually a bit of leniency if miscalculation happened to be in the last few calculations to be done. Otherwise, you are out of luck.]
In this culture poor calculation skills are punished, and you basically have to have them at a certain level in order to stay competitive. Another example of this phenomenon is competitive/olympiad programming—grading is done automatically, your solution has to pass the tests. It does not matter that you understand the idea (which is most of the time the difficult part); the implementation has to be correct.
[Depending on the competition: some give partial points for working on parts of the test set. Reiterating: this is a culture some popular competitions subscribe to and which I’ve had quite a bit of exposure to.]
Sidetrack: a coapproach to the mistake is a mistake is it doesn’t matter how you got the answer if it is correct. This is difficult to implement in grading because this makes cheating significantly easier, but has led to some of the most fun solutions I’ve had to math/programming problems. I vehemently despise the “you have to complete the task in exactly this way” problems.
I think your list of conditions is very restrictive; to the point at which it’s really difficult to find something matching it.
Most (all?) modern
difficultstrategy games rely on some version of “game knowledge” as part of it’s difficulty, expecting you to experiment with different approaches to find out what works best—this is a core part of the game loop, something specifically designed into the game to make it more fun. This is baked into the design on a fundamental level and is extremely difficult to separate out.Combine that with the one-shot nature and a strict time limit (so strict that in a large amount of cases this isn’t even enough to start making meaningful strategic decisions: either because learning all the systems takes longer or because you need to progress through the game enough to be aware of the later payoffs) and you are basically rolling a die on whenever you can land on a solution or not via some combination of prior gaming knowledge and luck—I don’t think you can meaningfully “try harder” to guess the decisions the game designers have made about the systems and obstacles you’ve not seen yet (besides playing more games beforehand of course, collecting game design principles trivia along the way).
Yes, you can bias the roll in your favor with genre savviness and experience; one of my friends has an absolutely uncanny ability of picking excellent builds in games with no prior information. He has also played games for some inordinate amount of time in order to build this intuition up.