shahar_2019_improving
Participants (N=554, each with a baseline and a follow-up session) completed a two-stage decision task (two-step task) across two sessions a mean of 17.75 months apart (range 11.76–31.44 months). Each trial: first-stage choice between two stimuli, probabilistic transition (common/rare) to a second-stage state, then second-stage choice yielding binary reward (0/1). Trial count differed by session: 121 trials at baseline, 201 at follow-up; the source CSV ships ~118 and ~197 per participant after the authors' pre-processing (see Notes). Research question: whether combining reaction times with choices via drift-diffusion modeling improves the reliability of model-based vs model-free RL parameter estimates.
Responses
349,508
34,802 held out
CORE effects
1 / 1
CORE test NLL (avg)
0.474
rank 2 of 7 models
Best model
CORE (no phonemes)
test NLL (avg) 0.473
Likelihood of human responses
| model | PNLL | test NLL (avg) | test responses | train NLL (avg) | train responses |
|---|---|---|---|---|---|
| CORE | 16,505.4 | 0.4743 | 34,802 | 0.4766 | 314,706 |
| CORE (no prediction errors) | 16,562.2 | 0.4759 | 34,802 | 0.4773 | 314,706 |
| CORE (no phonemes) best | 16,459.2 | 0.4729 | 34,802 | 0.4733 | 314,706 |
| CORE (no forgetting) | 16,677.2 | 0.4792 | 34,802 | 0.4826 | 314,706 |
| CORE (no hierarchy) | 19,414.0 | 0.5578 | 34,802 | 0.5579 | 314,706 |
| Transformer | 17,485.0 | 0.5024 | 34,802 | 0.5030 | 314,706 |
| Centaur | 17,439.2 | 0.5011 | 34,802 | – | – |
Experiments
| exp | task class | participants | responses | conditions | simulated | effects |
|---|---|---|---|---|---|---|
| exp0 | TwoStageTask | 554 | 349,508 | 1 | yes | mb_choice_transition_reward_interaction |
Behavioral effects
| effect | experiment | paper | CORE | CORE (no prediction errors) | CORE (no phonemes) | CORE (no forgetting) | CORE (no hierarchy) |
|---|---|---|---|---|---|---|---|
mb_choice_transition_reward_interaction | exp0 | +0.251 | ✓ yes +0.015 | ✓ yes +0.016 | ✓ yes +0.013 | ✓ yes +0.018 | ✗ no +0.007 |
The transition × reward interaction on first-stage stay probability. Logistic regression: stay ~ transition * reward (paper coding: +1 common/-1 rare, +1 rewarded/-1 unrewarded). Prediction: positive interaction coefficient (more stay after common+rewarded and rare+unrewarded trials). | |||||||
Transcript
You are playing a game where you try to win as many play pounds as possible; you get a bonus based on your total. Each round has two stages. In the first stage you see two first-stage stimuli: press A for the first stimulus or B for the second. Your choice moves you to one of two second-stage states. In the second stage you see two second-stage stimuli in that state: press A for the first stimulus or B for the second. Win as many play pounds as you can. You begin the first session. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. 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The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press B. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press B. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state X. You see two second-stage stimuli. You press A. You win 0 play pounds. You see two first-stage stimuli. You press A. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press B. You win 1 play pound. You see two first-stage stimuli. You press B. The choice moves you to second-stage state Y. You see two second-stage stimuli. You press A. You win 1 play pound.