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Equation 13 · Part 4 · The Benchmarks That Don't Need the Image

=

Pchance=(1k)NP_{\mathrm{chance}} = \left(\frac{1}{k}\right)^{N}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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 Pchance=(1k)NP_{\mathrm{chance}} = \left(\frac{1}{k}\right)^{N}. 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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.