Demo 1 · How a reinforced loop becomes automatic

Each time a cue is followed by biting and then by immediate relief, the cue–biting link strengthens. Automaticity grows as a saturating function of the number of reinforced repetitions, A(n) = 1 − e−k n. Drag the number of repetitions and the reinforcement rate k, and watch why a long-standing habit feels impossible to stop by willpower: the curve is already near its ceiling.

50%90%0%50%100%0306090120reinforced repetitions (n)
After 30 reinforced repetitions at k = 0.05, automaticity is 78% — usually triggered before awareness. The link is still weak enough that deliberate attention can interrupt it before biting begins.

Demo 2 · Dose–response to tissue damage

Tissue damage scales with the dose of biting: how many episodes a day, how forcefully, and over how many years. The schematic nail plate shortens and the cuticle recedes in proportion to a saturating model, damage index = 1 − e−0.5L, with load L = (episodes ÷ 5) × force × years. Breaching the cuticle is what invites paronychia.

cuticledamage 63%
Load L = 2.00; tissue-damage index 63% (moderate — cuticle breached). The gradient is continuous: clinical attention tracks the dose — frequency, force, and duration — not the mere presence of the habit.

Demo 3 · Spontaneous vs treated cessation

A competing response reliably executed at the cue converts a would-be reinforced repetition into a non-reinforced one, so automaticity decays: A(m) = A0 e−d m. Natural remission is slow; a bitter coating alone is a little faster; full habit reversal paired with differential reinforcement of other behavior (DRO) is fastest, because it targets the automaticity directly (Azrin & Nunn, 1973).

10% of baseline0%50%100%015304560cues met with a competing response (m)
nonebitter coatinghabit reversal + DRO
Under habit reversal + DRO, the decay rate is d = 0.06. From an entrenched baseline of 0.95, automaticity after 20 cues is 0.286 (29%). Reaching 10% of baseline takes about 38 such cues. Starving the loop of reinforcement at every cue gives the steepest decline — the mechanism behind habit reversal's efficacy.