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Equation 18 · Part 4 · How AI Inference Serving Actually Works

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E[tokens per round]=1−αγ+11−α.\mathbb{E}[\text{tokens per round}] = \frac{1-\alpha^{\gamma+1}}{1-\alpha}.
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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

The size of the win has a clean shape. Model the draft’s acceptance probability as α\alpha per token, roughly constant and independent across the γ\gamma tokens proposed in a round — an idealization real traffic does not fully satisfy, but a useful one for seeing the ceiling. The expected number of tokens accepted per verification round is then E[tokens per round]=1−αγ+11−α\mathbb{E}[\text{tokens per round}] = \frac{1-\alpha^{\gamma+1}}{1-\alpha}. This rises with both α\alpha and γ\gamma , but with steeply diminishing returns in γ\gamma for any α\alpha below one: drafting fifty tokens ahead does not buy anywhere near fifty accepted tokens, because the marginal proposal deep into a long draft is unlikely to be exactly what the target would have generated. The bottleneck decode…

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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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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