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Equation 13 · Part 6 · The Benchmarks That Don't Need the Image

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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