A tone plays. Sometimes it's followed by an air puff to the eye; sometimes it isn't. Fifty-fifty. After a long run of unreinforced trials — four consecutive misses — what happens to explicit expectancy and the conditioned blink response?
Explicit expectancy climbs. The gambler's fallacy: four misses, the puff must be due. Meanwhile the conditioned blink weakens. Standard extinction: each unreinforced trial thins the association. The graphs cross. At the end of a long miss run, the person is maximally convinced the puff is coming — and minimally likely to blink when it does.
Two systems, same evidence, opposite conclusions.
Pierre Perruchet ran the eyeblink experiment in 1985 with a 50% partial reinforcement schedule. Participants knew the schedule. His innovation was to analyze by run length: after N consecutive reinforced trials, or N consecutive unreinforced trials, where are both measures?
The conditioned response follows Rescorla-Wagner learning: each reinforced trial strengthens the association by a fraction of the remaining gap to maximum; each unreinforced trial weakens it by a fraction of the current strength. The association is tracking cumulative prediction error.
Explicit expectancy follows the gambler's fallacy: random sequences look streaky, and streaks feel like they should end. After four consecutive misses, subjects reported strong belief the puff was coming. After four consecutive hits, they expected a miss. The explicit system is reasoning about the run, not the base rate.
Neither reasoning strategy is simply wrong. The explicit system asks: given this run, what does the next trial look like? (It answers incorrectly — the trials are independent.) The conditioned system asks: across all trials, how often has tone predicted puff? (It answers correctly on average, but slowly.) They don't communicate. The crossing is structural, not a mistake.
In the simulation: the puff % slider changes the reinforcement probability. At 50%, crossings are frequent — the two curves constantly diverge and reconverge as runs develop and reverse. At higher or lower probabilities, one system dominates more persistently. The dots mark where the curves crossed.