Symbol P_chance
hance is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
It is worth seeing precisely why an all-or-nothing rule across permutations is so stringent, and where the intuition needs a caveat. If a model’s answer on each rotated pass were an independent uniform guess among k options, the probability of passing all N rotations by chance would be . which for a four-option item run through all four rotations is (1/4)^4 , under half a percent. That is not a real prediction of model behavior — actual models are not memoryless guessers, and a model with a fixed positional bias will do considerably worse than this floor once the correct answer rotates away from its favored slot, while a model with genuine content understanding will pass…
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Symbol k
k occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol N
N is an input to the expression that computes the quantity on the left.
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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 13 · Foundation Models
The Benchmarks That Don't Need the Image
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
It is worth seeing precisely why an all-or-nothing rule across permutations is so stringent, and where the intuition needs a caveat. If a model’s answer on each rotated pass were an independent uniform guess among k options, the probability of passing all N rotations by chance would be . which for a four-option item run through all four rotations is (1/4)^4 , under half a percent. That is not a real prediction of model behavior — actual models are not memoryless guessers, and a model with a fixed positional bias will do considerably worse than this floor once the correct answer rotates away from its favored slot, while a model with genuine content understanding will pass…
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