breslav_2022_shuffle
Single experiment (exp0, N = 304): 304 children (ages 4–13) each completed 50 trials of a sequential-choice task choosing between an advantageous and a disadvantageous deck (one backed with stripes, the other with dots; which pattern was the advantageous deck was randomly assigned per child and is not recorded) under partial feedback of M&M wins/losses. Both decks carried hidden alternating win/loss structure (incidental nonrandom sequences), and the key question was whether children's choices track this incidental structure versus the decks' expected value. The binary deck choice per trial is the response; the paper also fits a formal switch model to switching behavior, with θ-binning of individual differences across development (hence the cognitive-modeling tag).
Responses
15,200
1,500 held out
CORE effects
1 / 1
CORE test NLL (avg)
0.506
rank 2 of 7 models
Best model
CORE (no phonemes)
test NLL (avg) 0.504
Likelihood of human responses
| model | PNLL | test NLL (avg) | test responses | train NLL (avg) | train responses |
|---|---|---|---|---|---|
| CORE | 759.4 | 0.5063 | 1,500 | 0.5197 | 13,700 |
| CORE (no prediction errors) | 766.4 | 0.5109 | 1,500 | 0.5212 | 13,700 |
| CORE (no phonemes) best | 756.4 | 0.5043 | 1,500 | 0.5093 | 13,700 |
| CORE (no forgetting) | 766.4 | 0.5109 | 1,500 | 0.5184 | 13,700 |
| CORE (no hierarchy) | 911.0 | 0.6074 | 1,500 | 0.6072 | 13,700 |
| Transformer | 796.2 | 0.5308 | 1,500 | 0.5349 | 13,700 |
| Centaur | 772.7 | 0.5151 | 1,500 | – | – |
Experiments
| exp | task class | participants | responses | conditions | simulated | effects |
|---|---|---|---|---|---|---|
| exp0 | ChildrensGamblingTask | 304 | 15,200 | 1 | yes | deplete_replenish_bias |
Behavioral effects
| effect | experiment | paper | CORE | CORE (no prediction errors) | CORE (no phonemes) | CORE (no forgetting) | CORE (no hierarchy) |
|---|---|---|---|---|---|---|---|
deplete_replenish_bias | exp0 | – | ✓ yes +0.106 | ✓ yes +0.111 | ✓ yes +0.135 | ✓ yes +0.106 | ✓ yes +0.155 |
Within the low-Theta (deplete-replenish) tertile, P(switch|win) > P(switch|loss) via paired t-test. Expected: positive mean difference, p < .05. | |||||||
Transcript
You are playing a card game for M&M's with a grown-up on the other side of the table. A cylinder on the table already holds your 10 M&M's. Two face-down decks sit in front of you: one deck of cards is backed with black and white stripes, the other is backed with black dots on a white background. On each of 50 turns you pick one whole deck and the grown-up turns over that deck's top card. Every card shows, on its top half, how many M&M's you win, and on its bottom half, how many M&M's you lose; the difference between the two is the net M&M's you keep. The grown-up adds or removes M&M's from your cylinder to match. Your goal is to finish with as many M&M's as possible. As a demonstration you are first shown three example cards from each deck, never scored: the stripe deck's examples give +1, +1 and 0 net M&M's; the dot deck's examples give +2, +2 and -2 net M&M's. On each turn press A for the dot-backed deck or B for the stripe-backed deck. You press A and pick the dot-backed deck. Its top card shows 2 M&M's won and 0 M&M's lost, a net of +2 M&M's. Your cylinder now holds 12 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 13 M&M's. You press A and pick the dot-backed deck. Its top card shows 2 M&M's won and 6 M&M's lost, a net of -4 M&M's. Your cylinder now holds 9 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 9 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 10 M&M's. You press A and pick the dot-backed deck. Its top card shows 2 M&M's won and 0 M&M's lost, a net of +2 M&M's. Your cylinder now holds 12 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 12 M&M's. You press A and pick the dot-backed deck. Its top card shows 2 M&M's won and 4 M&M's lost, a net of -2 M&M's. Your cylinder now holds 10 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 11 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 11 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 11 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 12 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 12 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 12 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 13 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 14 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 15 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 15 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 15 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 16 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 16 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 17 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 18 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 19 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 19 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 19 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 19 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 20 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 21 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 21 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 21 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 22 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 23 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 24 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 24 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 24 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 25 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 25 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 26 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 26 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 26 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 27 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 28 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 28 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 29 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 29 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 30 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 30 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 0 M&M's lost, a net of +1 M&M's. Your cylinder now holds 31 M&M's. You press B and pick the stripe-backed deck. Its top card shows 1 M&M's won and 1 M&M's lost, a net of +0 M&M's. Your cylinder now holds 31 M&M's. The 50 choices are over. You end with 31 M&M's.