Part 1 of 5 · 1 min read
Overview
In this module you will
- Explain what a reasoning model and a thinking budget are, and what they cost.
- Compare three ways to spend extra compute: think longer, try many times and vote, try many times and pick with a checker.
- Predict when voting helps, when it plateaus and when it makes things worse.
- Decide where in an agent extra thinking is worth the tokens and latency.
- Measure accuracy against cost, not accuracy alone.
Everything so far spends compute per step: one model call, one answer. But a model can spend more at answer time: by writing out its reasoning before it answers, by trying the same question several times, or by checking its candidates. This is called test-time compute (or inference-time compute). It is how current reasoning models get their gains, and it is also where agent bills and waiting times grow quickly. An agent builder has to decide where to buy accuracy with tokens and where not to.
About the examples
Everything here is an offline imitation. The "solver" is a program: a problem needs a number of steps; a step done "in the head" succeeds 75% of the time; a step written out costs 60 tokens and succeeds 93% of the time; and when something goes wrong, half of all wrong answers are the same "attractive" wrong answer. These numbers are my assumptions. Real reasoning models differ in how much they think, how errors cluster, and how a thinking budget is controlled by each provider. The point is the shape of the trade-offs, which holds more broadly than the specific percentages. No real model was called.