Equation 14 · Part 1 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

Symbol gamma_i

\gamma_i

\gamma_i

What this part means

the cache-read multiplier.

Its job in the formula

gamm $a_i$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol gamma_iArticle meaning

Where the article explains it

For vendor i , let $p^{\text{in}}_i$ and $p^{\text{out}}_i$ be the published input and output rates; let $\kappa_i$ be a tokenizer expansion factor, the number of tokens vendor i ’s own tokenizer needs to encode one fixed reference passage, normalised so $\kappa_i$ = 1 for whichever vendor is used as the baseline; let $h_i$ be the fraction of input served from cache and $\gamma_i$ the cache-read multiplier; and let $\rho_i$ be the ratio of total output tokens generated, visible answer plus hidden reasoning, to the visible answer alone.

The passage around this formula

Reading $p^{\text{in}}_i$ and $p^{\text{out}}_i$ off a rate card and comparing them directly across vendors is equivalent to assuming $\kappa_i$ , $\gamma_i$ , and $\rho_i$ are all equal to each other and to 1 across every vendor in the comparison. This article has just shown that one of those three, $\gamma_i$ , genuinely does converge close to 0.1 across all three companies’ published cards — the one term a naive comparison happens to get right…

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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 →

See this notation across published equations →

Sources cited in the article section

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