Choose lookahead by committed output per unit cost

Let A be the number of consecutive proposals accepted before the first rejection, capped at draft length γ. A token accepted at a later position is not committed if an earlier proposal failed, because its history is wrong. Thus E[A] is a sum of prefix-survival probabilities, not the sum of all independently reported per-position accepts. Under the simplifying assumption of a common constant conditional acceptance α along the accepted path, Pr(A≥i)=α^i. The real history-dependent process need not have that property, even when its aggregate acceptance average is α.

Ignoring EOS and length caps, the standard round emits A+1 tokens: one residual correction after a rejection, or a bonus target token if every proposal passes. The expected count is 1+α+…+α^γ in the constant-acceptance model. At α=1 it isγ+1, and at α=0 it is one. Handle the α=1 endpoint directly rather than evaluate a closed form with a zero denominator. Early stopping or a different verifier can change the count, so a measured number of output tokens must identify which round and stopping convention was used.

A simple sequential round budget includes γ draft steps, one target verification pass at that block length, and coordination or sampling overhead. Divide that cost by the expected committed count only under a sustained repeated-round model with suitable stable averages. A target pass scoring a long block can take more time than one ordinary decode step, and memory pressure or synchronization can add costs. If phases overlap, use the actual critical-path model instead of adding them blindly. State whether prefill, compilation, tokenizer work, and request queueing are included in the reported interval.

Compare against the same target decoding workload, hardware, batch conditions, and output contract. A two-times reduction in target invocations does not imply a two-times speedup when the draft or verification kernel is expensive. Conversely, extra arithmetic can help a memory-bound workload if it amortizes weight access effectively. Sweep a bounded range of γ values while measuring accepted-prefix distributions, stage times, peak memory, and latency tails. A higher acceptance rate with a slower draft can lose to a less accurate but much cheaper proposal mechanism.

Acceptance varies across prompt type, context length, decoding temperature, and position within a response. Dynamic lookahead can use recent evidence to choose γ, but its changing cost and selection policy must be evaluated on held-out or representative traces. Avoid substituting one global α into every latency percentile or assuming a longer proposal always adds useful work. Include EOS-heavy short requests and low-acceptance domains. Pinned backends can implement confidence-based proposal stopping without changing verification, but their precise schedule and overhead remain implementation details to measure, not a universal optimum.

The probability lab shows why a binomial count is another quantity. Reset, set both lab p=0.8 and n=3, predict its mean and all-three bar, then inspect. Its mean is 2.4 successes and its all-three probability 0.512. Under the separate independent-prefix toy model, E[A] is 0.8+0.64+0.512=1.952, not 2.4, because success after a prior failure is unusable. The instrument does not model prefix stopping or round cost. Use its exact independent bars to compare those definitions, then calculate the committed-prefix expectation explicitly.