Probability Relations within Response Sequences under Ratio Reinforcement.

Mechner (1958) laid out the math of fixed-ratio schedules. The paper asked: what happens when every Nth response earns food?

It sketched the now-famous pattern: a pause after reward, then a fast run to the next payoff. No birds or data tables appear; the work is pure theory.

The model predicted two hallmarks we still teach today. First, post-reinforcement pauses grow with the ratio size. Second, once the bird starts, it finishes the burst at a high steady rate.

Mazur (1983) ran the experiment and confirmed the pause-plus-burst picture. The steady run speed stayed the same across FR, mixed, and random ratios; only the pause length changed.

Matthews et al. (1987) showed the same rules shape choice. Pigeons picked the sequence that started with the smaller ratio, even if it paid less often. The 1958 logic still held; the new twist was that the early ratio controlled preference.

Hamm et al. (1978) added a wrinkle. FR schedules locked pigeons into one response spot, while fixed-interval let them vary where they pecked. Same year, same lab, but the schedules acted differently on response form, not just rate.

When you set a token board or sticker chart, you are using FR mechanics. Expect a brief pause right after the payoff, then a quick stretch of work until the next token. If you see long pauses, shrink the ratio or add praise during the pause; the burst rate will likely stay high. This 1958 blueprint still guides everyday program tweaks.