krueger_2024_identifying
In this mouselab risky-choice study, participants (2,368 in Experiment 1 and 404 in Experiment 2, MTurk adults) sequentially reveal payoff cells of a 4-outcome x 6-gamble payoff matrix by paying a per-click cost, then choose one gamble. Experiment 2 additionally manipulates whether expected values are displayed (EV-display, con vs exp). Both experiments record every trial across instruction blocks (practice) and the test block, with per-trial clicks, click times, reaction time, gambles, payoffs, and choice. The paper derives resource-rational heuristics via machine-learning/meta-RL strategy distillation and tests when people rely on heuristic vs rational strategies, fitting strategy-selection/RL cognitive models to the click-and-choice data.
Responses
85,124
3,058 held out
CORE effects
–
no effects simulated
CORE test NLL (avg)
0.555
rank 1 of 7 models
Best model
CORE
test NLL (avg) 0.555
Likelihood of human responses
| model | PNLL | test NLL (avg) | test responses | train NLL (avg) | train responses |
|---|---|---|---|---|---|
| CORE best | 1,696.0 | 0.5546 | 3,058 | 0.5654 | 82,066 |
| CORE (no prediction errors) | 1,756.1 | 0.5743 | 3,058 | 0.5561 | 82,066 |
| CORE (no phonemes) | 1,698.5 | 0.5554 | 3,058 | 0.5396 | 82,066 |
| CORE (no forgetting) | 1,924.9 | 0.6295 | 3,058 | 0.6649 | 82,066 |
| CORE (no hierarchy) | 3,932.4 | 1.2859 | 3,058 | 1.2960 | 82,066 |
| Transformer | 2,462.7 | 0.8053 | 3,058 | 0.8437 | 82,066 |
| Centaur | 2,828.7 | 0.9250 | 3,058 | – | – |
Experiments
| exp | task class | participants | responses | conditions | simulated | effects |
|---|---|---|---|---|---|---|
| exp0 | MouselabExperiment1 | 2,368 | 73,408 | 1 | no | – |
| exp1 | MouselabExperiment2 | 404 | 11,716 | 2 | no | – |
Behavioral effects
No behavioral effects were simulated for this study.
Transcript
You are choosing between gambles to earn points. Your bonus is $0.01 for every 5 points you earn. On each round, 6 gambles labeled A, B, C, D, E, F (left to right) are on offer. Each gamble pays off in one of 4 possible outcomes, numbered 1 to 4 from top to bottom. Each outcome has a chance of occurring, shown as a percentage. The payoff of each gamble under each outcome is shown in a cell of the table, but all cells start hidden. To reveal a cell, type its label: the gamble letter followed by the outcome number (e.g. A1 is gamble A under outcome 1). Each reveal costs 4 points. Revealed cells stay visible for the rest of the round, and you may reveal as many or as few as you like, in any order. When you are ready, choose a gamble by typing its letter: A, B, C, D, E, or F. The outcome is then drawn at random according to the chances, and you earn that gamble's payoff for that outcome minus the 4 points you paid for each reveal. Instruction block 1 (practice): Trial 1. Chances: 1:1%, 2:60%, 3:2%, 4:37%. You choose gamble A. Outcome 2 occurs. Your gamble pays 0 points. Net: 0 points. Trial 2. Chances: 1:12%, 2:32%, 3:45%, 4:11%. You choose gamble C. Outcome 4 occurs. Your gamble pays -38 points. Net: -38 points. Trial 3. Chances: 1:21%, 2:18%, 3:4%, 4:57%. You choose gamble F. Outcome 1 occurs. Your gamble pays -45 points. Net: -45 points. Instruction block 2 (practice): Trial 4. Chances: 1:1%, 2:20%, 3:2%, 4:77%. You choose gamble C. Outcome 4 occurs. Your gamble pays 236 points. Net: 236 points. Trial 5. Chances: 1:73%, 2:7%, 3:3%, 4:17%. You choose gamble F. Outcome 1 occurs. Your gamble pays 206 points. Net: 206 points. Trial 6. Chances: 1:12%, 2:25%, 3:19%, 4:44%. You choose gamble C. Outcome 4 occurs. Your gamble pays 172 points. Net: 172 points. Trial 7. Chances: 1:3%, 2:71%, 3:25%, 4:1%. You choose gamble E. Outcome 3 occurs. Your gamble pays 240 points. Net: 240 points. Trial 8. Chances: 1:34%, 2:28%, 3:32%, 4:6%. You choose gamble C. Outcome 3 occurs. Your gamble pays 290 points. Net: 290 points. Instruction block 3 (practice): Trial 9. Chances: 1:17%, 2:3%, 3:7%, 4:73%. You reveal E4. E4 shows 188. You reveal B4. B4 shows -200. You reveal D4. D4 shows 250. You choose gamble D. Outcome 4 occurs. Your gamble pays 250 points. Net: 238 points (payoff minus 12 points for reveals). Trial 10. Chances: 1:1%, 2:65%, 3:22%, 4:12%. You reveal A2. A2 shows -163. You reveal C2. C2 shows -54. You reveal F2. F2 shows 100. You choose gamble E. Outcome 2 occurs. Your gamble pays -310 points. Net: -322 points (payoff minus 12 points for reveals). Trial 11. Chances: 1:9%, 2:48%, 3:39%, 4:4%. You reveal A2. A2 shows -248. You reveal B3. B3 shows 279. You reveal F3. F3 shows 74. You choose gamble B. Outcome 3 occurs. Your gamble pays 279 points. Net: 267 points (payoff minus 12 points for reveals). Test block: Trial 12. Chances: 1:44%, 2:6%, 3:2%, 4:48%. You reveal A4. A4 shows 8. You reveal A1. A1 shows -132. You reveal C4. C4 shows 18. You choose gamble E. Outcome 4 occurs. Your gamble pays -31 points. Net: -43 points (payoff minus 12 points for reveals). Trial 13. Chances: 1:2%, 2:1%, 3:47%, 4:50%. You reveal A4. A4 shows -156. You reveal C4. C4 shows 108. You reveal E4. E4 shows -48. You choose gamble C. Outcome 3 occurs. Your gamble pays 300 points. Net: 288 points (payoff minus 12 points for reveals). Trial 14. Chances: 1:6%, 2:48%, 3:3%, 4:43%. You reveal A2. A2 shows -61. You reveal F2. F2 shows 260. You reveal C2. C2 shows 69. You choose gamble F. Outcome 4 occurs. Your gamble pays -76 points. Net: -88 points (payoff minus 12 points for reveals). Trial 15. Chances: 1:17%, 2:28%, 3:38%, 4:17%. You reveal B3. B3 shows -56. You reveal D3. D3 shows 98. You reveal F3. F3 shows 29. You choose gamble D. Outcome 3 occurs. Your gamble pays 98 points. Net: 86 points (payoff minus 12 points for reveals). Trial 16. Chances: 1:1%, 2:12%, 3:42%, 4:45%. You reveal A4. A4 shows -8. You reveal C4. C4 shows -98. You reveal D4. D4 shows -272. You choose gamble A. Outcome 2 occurs. Your gamble pays -13 points. Net: -25 points (payoff minus 12 points for reveals). Trial 17. Chances: 1:46%, 2:33%, 3:5%, 4:16%. You reveal B1. B1 shows 92. You reveal E1. E1 shows 78. You reveal C1. C1 shows 518. You choose gamble C. Outcome 4 occurs. Your gamble pays -227 points. Net: -239 points (payoff minus 12 points for reveals). Trial 18. Chances: 1:35%, 2:22%, 3:32%, 4:11%. You reveal A3. A3 shows 123. You reveal F3. F3 shows -12. You reveal C3. C3 shows 237. You choose gamble C. Outcome 1 occurs. Your gamble pays 69 points. Net: 57 points (payoff minus 12 points for reveals). Trial 19. Chances: 1:4%, 2:23%, 3:71%, 4:2%. You reveal A3. A3 shows 74. You reveal D3. D3 shows 330. You reveal F3. F3 shows 3. You choose gamble D. Outcome 3 occurs. Your gamble pays 330 points. Net: 318 points (payoff minus 12 points for reveals). Trial 20. Chances: 1:21%, 2:30%, 3:3%, 4:46%. You reveal A4. A4 shows -129. You reveal D4. D4 shows -112. You reveal F4. F4 shows 12. You choose gamble F. Outcome 4 occurs. Your gamble pays 12 points. Net: 0 points (payoff minus 12 points for reveals). Trial 21. Chances: 1:30%, 2:1%, 3:60%, 4:9%. You reveal A3. A3 shows -129. You reveal B3. B3 shows 191. You reveal C3. C3 shows -29. You choose gamble B. Outcome 1 occurs. Your gamble pays 131 points. Net: 119 points (payoff minus 12 points for reveals). Trial 22. Chances: 1:51%, 2:17%, 3:1%, 4:31%. You reveal A1. A1 shows 121. You reveal D1. D1 shows -103. You reveal F1. F1 shows 106. You choose gamble A. Outcome 4 occurs. Your gamble pays 203 points. Net: 191 points (payoff minus 12 points for reveals). Trial 23. Chances: 1:73%, 2:1%, 3:18%, 4:8%. You reveal A1. A1 shows -226. You reveal D1. D1 shows -195. You reveal F1. F1 shows -99. You choose gamble E. Outcome 3 occurs. Your gamble pays 84 points. Net: 72 points (payoff minus 12 points for reveals). Trial 24. Chances: 1:5%, 2:42%, 3:15%, 4:38%. You reveal A2. A2 shows 139. You reveal C2. C2 shows 154. You reveal F2. F2 shows -188. You choose gamble C. Outcome 4 occurs. Your gamble pays 102 points. Net: 90 points (payoff minus 12 points for reveals). Trial 25. Chances: 1:40%, 2:9%, 3:12%, 4:39%. You reveal A1. A1 shows 104. You reveal A4. A4 shows -88. You reveal D1. D1 shows -19. You choose gamble C. Outcome 4 occurs. Your gamble pays 58 points. Net: 46 points (payoff minus 12 points for reveals). Trial 26. Chances: 1:1%, 2:50%, 3:6%, 4:43%. You reveal A2. A2 shows -21. You reveal E2. E2 shows 142. You reveal E4. E4 shows 182. You choose gamble E. Outcome 4 occurs. Your gamble pays 182 points. Net: 170 points (payoff minus 12 points for reveals). Trial 27. Chances: 1:3%, 2:1%, 3:77%, 4:19%. You reveal A3. A3 shows -8. You reveal F3. F3 shows -12. You reveal C3. C3 shows -119. You choose gamble A. Outcome 1 occurs. Your gamble pays -80 points. Net: -92 points (payoff minus 12 points for reveals). Trial 28. Chances: 1:21%, 2:3%, 3:62%, 4:14%. You reveal A3. A3 shows -106. You reveal C3. C3 shows 26. You reveal E3. E3 shows 14. You choose gamble C. Outcome 4 occurs. Your gamble pays -227 points. Net: -239 points (payoff minus 12 points for reveals). Trial 29. Chances: 1:9%, 2:10%, 3:61%, 4:20%. You reveal B3. B3 shows -77. You reveal D3. D3 shows 11. You reveal F3. F3 shows -148. You choose gamble E. Outcome 4 occurs. Your gamble pays 103 points. Net: 91 points (payoff minus 12 points for reveals). Trial 30. Chances: 1:35%, 2:11%, 3:1%, 4:53%. You reveal A4. A4 shows 195. You reveal A1. A1 shows 149. You reveal E4. E4 shows -140. You choose gamble A. Outcome 1 occurs. Your gamble pays 149 points. Net: 137 points (payoff minus 12 points for reveals). Trial 31. Chances: 1:1%, 2:4%, 3:1%, 4:94%. You reveal A4. A4 shows 182. You reveal D4. D4 shows 52. You reveal F4. F4 shows -154. You choose gamble A. Outcome 4 occurs. Your gamble pays 182 points. Net: 170 points (payoff minus 12 points for reveals).
You are choosing between gambles to earn points. Your bonus is $0.01 for every 5 points you earn. On each round, 6 gambles labeled A, B, C, D, E, F (left to right) are on offer. Each gamble pays off in one of 4 possible outcomes, numbered 1 to 4 from top to bottom. Each outcome has a chance of occurring, shown as a percentage. The payoff of each gamble under each outcome is shown in a cell of the table, but all cells start hidden. To reveal a cell, type its label: the gamble letter followed by the outcome number (e.g. A1 is gamble A under outcome 1). Each reveal costs 1 point. Revealed cells stay visible for the rest of the round, and you may reveal as many or as few as you like, in any order. When you are ready, choose a gamble by typing its letter: A, B, C, D, E, or F. The outcome is then drawn at random according to the chances, and you earn that gamble's payoff for that outcome minus the 1 point you paid for each reveal. A running expected value for each gamble is displayed next to its letter and updates as you reveal cells. You must wait at least 20 seconds each round before choosing; a countdown timer shows the remaining time. Instruction block 1 (practice): Trial 1. Chances: 1:16%, 2:19%, 3:14%, 4:51%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble A. Outcome 4 occurs. Your gamble pays 39 points. Net: 39 points. Trial 2. Chances: 1:23%, 2:20%, 3:41%, 4:16%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble C. Outcome 3 occurs. Your gamble pays 0 points. Net: 0 points. Trial 3. Chances: 1:21%, 2:18%, 3:4%, 4:57%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble F. Outcome 1 occurs. Your gamble pays -56 points. Net: -56 points. Instruction block 2 (practice): Trial 4. Chances: 1:19%, 2:18%, 3:38%, 4:25%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble E. Outcome 4 occurs. Your gamble pays 0 points. Net: 0 points. Trial 5. Chances: 1:20%, 2:13%, 3:32%, 4:35%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble F. Outcome 3 occurs. Your gamble pays 173 points. Net: 173 points. Trial 6. Chances: 1:37%, 2:14%, 3:33%, 4:16%. Expected-value display: A:0, B:0, C:0, D:0, E:0, F:0. You choose gamble C. Outcome 1 occurs. Your gamble pays 203 points. Net: 203 points. Instruction block 3 (practice): Trial 7. Chances: 1:27%, 2:19%, 3:18%, 4:36%. You reveal A4. A4 shows -36. You reveal B4. B4 shows -113. You reveal C4. C4 shows -20. You reveal D4. D4 shows 7. You reveal E4. E4 shows 100. You reveal F4. F4 shows 42. Expected-value display: A:-13, B:-41, C:-7, D:3, E:36, F:15. You choose gamble E. Outcome 3 occurs. Your gamble pays -59 points. Net: -65 points (payoff minus 6 points for reveals). Trial 8. Chances: 1:26%, 2:30%, 3:11%, 4:33%. You reveal A2. A2 shows 45. You reveal B2. B2 shows 60. You reveal C2. C2 shows 117. You reveal D2. D2 shows 8. You reveal E2. E2 shows -91. You reveal F2. F2 shows -4. Expected-value display: A:14, B:18, C:35, D:2, E:-27, F:-1. You choose gamble C. Outcome 4 occurs. Your gamble pays -49 points. Net: -55 points (payoff minus 6 points for reveals). Trial 9. Chances: 1:9%, 2:14%, 3:43%, 4:34%. You reveal A3. A3 shows 65. You reveal B3. B3 shows 66. You reveal C3. C3 shows 81. You reveal D3. D3 shows -21. You reveal E3. E3 shows -21. You reveal F3. F3 shows -30. You reveal A4. A4 shows -7. You reveal B4. B4 shows -124. You reveal C4. C4 shows -14. Expected-value display: A:26, B:-14, C:30, D:-9, E:-9, F:-13. You choose gamble C. Outcome 4 occurs. Your gamble pays -14 points. Net: -23 points (payoff minus 9 points for reveals). Test block: Trial 10. Chances: 1:29%, 2:22%, 3:26%, 4:23%. You reveal A1. A1 shows 27. You reveal B2. B2 shows 3. You reveal C3. C3 shows -68. You reveal D1. D1 shows -18. You reveal E2. E2 shows -146. You reveal F4. F4 shows -101. Expected-value display: A:8, B:1, C:-18, D:-5, E:-32, F:-23. You choose gamble A. Outcome 2 occurs. Your gamble pays 29 points. Net: 23 points (payoff minus 6 points for reveals). Trial 11. Chances: 1:23%, 2:32%, 3:29%, 4:16%. You reveal A2. A2 shows 13. You reveal B2. B2 shows -25. You reveal C2. C2 shows 81. You reveal D2. D2 shows 4. You reveal E2. E2 shows -24. You reveal F2. F2 shows -10. You reveal C3. C3 shows -88. You reveal D3. D3 shows 37. Expected-value display: A:4, B:-8, C:0, D:12, E:-8, F:-3. You choose gamble D. Outcome 1 occurs. Your gamble pays 57 points. Net: 49 points (payoff minus 8 points for reveals). Trial 12. Chances: 1:13%, 2:20%, 3:22%, 4:45%. You reveal A4. A4 shows 138. You reveal B4. B4 shows -20. You reveal C4. C4 shows 55. You reveal D4. D4 shows -19. You reveal F4. F4 shows -19. You reveal E4. E4 shows -23. You reveal A3. A3 shows 59. You reveal C3. C3 shows -70. Expected-value display: A:75, B:-9, C:9, D:-9, E:-10, F:-9. You choose gamble A. Outcome 4 occurs. Your gamble pays 138 points. Net: 130 points (payoff minus 8 points for reveals). Trial 13. Chances: 1:45%, 2:20%, 3:18%, 4:17%. You reveal A1. A1 shows 40. You reveal B1. B1 shows -1. You reveal C1. C1 shows 19. You reveal D2. D2 shows -38. You reveal D1. D1 shows 112. You reveal E1. E1 shows 19. You reveal F1. F1 shows 75. You reveal F2. F2 shows 86. You reveal A2. A2 shows 47. You reveal D3. D3 shows -87. Expected-value display: A:27, B:0, C:9, D:27, E:9, F:51. You choose gamble F. Outcome 3 occurs. Your gamble pays 65 points. Net: 55 points (payoff minus 10 points for reveals). Trial 14. Chances: 1:20%, 2:30%, 3:19%, 4:31%. You reveal A2. A2 shows -77. You reveal B2. B2 shows 73. You reveal C2. C2 shows -11. You reveal D2. D2 shows 60. You reveal E2. E2 shows -57. You reveal F2. F2 shows 2. You reveal B4. B4 shows 24. You reveal A4. A4 shows 31. You reveal D4. D4 shows -144. You reveal E4. E4 shows -34. You reveal B1. B1 shows 30. Expected-value display: A:-13, B:35, C:-3, D:-27, E:-28, F:1. You choose gamble B. Outcome 2 occurs. Your gamble pays 73 points. Net: 62 points (payoff minus 11 points for reveals). Trial 15. Chances: 1:14%, 2:45%, 3:5%, 4:36%. You reveal A1. A1 shows -85. You reveal A2. A2 shows -103. You reveal B2. B2 shows 20. You reveal C2. C2 shows 12. You reveal D2. D2 shows 8. You reveal E2. E2 shows 1. You reveal F2. F2 shows -43. You reveal B4. B4 shows -133. You reveal C4. C4 shows -24. You reveal D4. D4 shows 127. You reveal E4. E4 shows 45. You reveal F4. F4 shows 36. You reveal D1. D1 shows -82. You reveal D3. D3 shows 62. Expected-value display: A:-58, B:-39, C:-3, D:41, E:17, F:-6. You choose gamble D. Outcome 2 occurs. Your gamble pays 8 points. Net: -6 points (payoff minus 14 points for reveals). Trial 16. Chances: 1:40%, 2:14%, 3:20%, 4:26%. You reveal A1. A1 shows -33. You reveal B1. B1 shows -36. You reveal C1. C1 shows -64. You reveal D1. D1 shows -39. You reveal E1. E1 shows -109. You reveal F1. F1 shows 24. You reveal A3. A3 shows 61. You reveal B3. B3 shows -11. You reveal C3. C3 shows 147. You reveal D3. D3 shows 71. You reveal E3. E3 shows 140. You reveal F3. F3 shows 2. You reveal C4. C4 shows 64. You reveal E4. E4 shows -76. Expected-value display: A:-1, B:-17, C:20, D:-1, E:-35, F:10. You choose gamble C. Outcome 1 occurs. Your gamble pays -64 points. Net: -78 points (payoff minus 14 points for reveals). Trial 17. Chances: 1:6%, 2:31%, 3:35%, 4:28%. You reveal A3. A3 shows -64. You reveal A2. A2 shows 36. You reveal B2. B2 shows -62. You reveal B3. B3 shows -38. You reveal C3. C3 shows 68. You reveal C2. C2 shows 14. You reveal D2. D2 shows 74. You reveal D3. D3 shows 51. You reveal E3. E3 shows -33. You reveal E2. E2 shows 0. Expected-value display: A:-11, B:-33, C:28, D:41, E:-12, F:0. You choose gamble D. Outcome 3 occurs. Your gamble pays 51 points. Net: 41 points (payoff minus 10 points for reveals). Trial 18. Chances: 1:30%, 2:22%, 3:8%, 4:40%. You reveal A4. A4 shows 112. You reveal B4. B4 shows -22. You reveal C4. C4 shows -4. You reveal D4. D4 shows -108. You reveal E4. E4 shows -63. You reveal F4. F4 shows 30. You reveal A1. A1 shows -96. You reveal D1. D1 shows 47. You reveal F1. F1 shows 28. Expected-value display: A:16, B:-9, C:-2, D:-29, E:-25, F:20. You choose gamble F. Outcome 4 occurs. Your gamble pays 30 points. Net: 21 points (payoff minus 9 points for reveals). Trial 19. Chances: 1:15%, 2:31%, 3:28%, 4:26%. You reveal A2. A2 shows 116. You reveal B2. B2 shows -83. You reveal A3. A3 shows -145. You reveal B3. B3 shows 63. You reveal C2. C2 shows -48. You reveal D2. D2 shows -153. You reveal E2. E2 shows -19. You reveal F2. F2 shows -15. You reveal D3. D3 shows 42. You reveal D4. D4 shows -6. You reveal A4. A4 shows 65. Expected-value display: A:12, B:-8, C:-15, D:-37, E:-6, F:-5. You choose gamble A. Outcome 3 occurs. Your gamble pays -145 points. Net: -156 points (payoff minus 11 points for reveals). Trial 20. Chances: 1:5%, 2:47%, 3:28%, 4:20%. You reveal A2. A2 shows 68. You reveal B2. B2 shows 33. You reveal C2. C2 shows 81. You reveal D2. D2 shows -31. You reveal E2. E2 shows 134. You reveal F2. F2 shows 13. You reveal E3. E3 shows 23. Expected-value display: A:32, B:16, C:38, D:-15, E:69, F:6. You choose gamble E. Outcome 3 occurs. Your gamble pays 23 points. Net: 16 points (payoff minus 7 points for reveals). Trial 21. Chances: 1:31%, 2:14%, 3:41%, 4:14%. You reveal A3. A3 shows 65. You reveal B3. B3 shows 14. You reveal D3. D3 shows 68. You reveal C3. C3 shows 45. You reveal E3. E3 shows 43. You reveal F3. F3 shows -74. You reveal D1. D1 shows -19. You reveal A1. A1 shows -17. You reveal E1. E1 shows -145. You reveal C1. C1 shows -75. You reveal D2. D2 shows -48. You reveal F1. F1 shows 57. You reveal F2. F2 shows 46. Expected-value display: A:21, B:6, C:-5, D:15, E:-27, F:-6. You choose gamble F. Outcome 1 occurs. Your gamble pays 57 points. Net: 44 points (payoff minus 13 points for reveals). Trial 22. Chances: 1:31%, 2:33%, 3:9%, 4:27%. You reveal A2. A2 shows -3. You reveal B2. B2 shows -132. You reveal C2. C2 shows 45. You reveal D2. D2 shows 78. You reveal E2. E2 shows 5. You reveal F2. F2 shows 2. You reveal D1. D1 shows -120. You reveal D4. D4 shows 56. Expected-value display: A:-1, B:-44, C:15, D:4, E:2, F:1. You choose gamble D. Outcome 1 occurs. Your gamble pays -120 points. Net: -128 points (payoff minus 8 points for reveals). Trial 23. Chances: 1:25%, 2:11%, 3:47%, 4:17%. You reveal A3. A3 shows -71. You reveal B3. B3 shows 31. You reveal C3. C3 shows -34. You reveal D3. D3 shows -6. You reveal E3. E3 shows -5. You reveal F3. F3 shows 13. You reveal B1. B1 shows -114. Expected-value display: A:-33, B:-14, C:-16, D:-3, E:-2, F:6. You choose gamble D. Outcome 2 occurs. Your gamble pays -61 points. Net: -68 points (payoff minus 7 points for reveals). Trial 24. Chances: 1:19%, 2:51%, 3:10%, 4:20%. You reveal A2. A2 shows 93. You reveal B2. B2 shows 107. You reveal C2. C2 shows -71. You reveal B4. B4 shows 73. Expected-value display: A:47, B:69, C:-36, D:0, E:0, F:0. You choose gamble B. Outcome 2 occurs. Your gamble pays 107 points. Net: 103 points (payoff minus 4 points for reveals). Trial 25. Chances: 1:48%, 2:25%, 3:24%, 4:3%. You reveal A1. A1 shows 11. You reveal B1. B1 shows -192. You reveal C1. C1 shows -3. You reveal D1. D1 shows -131. You reveal E1. E1 shows 0. You reveal F1. F1 shows 63. You reveal F2. F2 shows 101. Expected-value display: A:5, B:-92, C:-1, D:-63, E:0, F:55. You choose gamble F. Outcome 2 occurs. Your gamble pays 101 points. Net: 94 points (payoff minus 7 points for reveals). Trial 26. Chances: 1:8%, 2:33%, 3:16%, 4:43%. You reveal A4. A4 shows -98. You reveal B4. B4 shows 115. You reveal C4. C4 shows -44. You reveal D4. D4 shows -8. You reveal E4. E4 shows 33. You reveal F4. F4 shows -7. You reveal B2. B2 shows 43. Expected-value display: A:-42, B:64, C:-19, D:-3, E:14, F:-3. You choose gamble B. Outcome 2 occurs. Your gamble pays 43 points. Net: 36 points (payoff minus 7 points for reveals). Trial 27. Chances: 1:30%, 2:28%, 3:7%, 4:35%. You reveal A4. A4 shows 34. You reveal B4. B4 shows 60. You reveal C4. C4 shows -124. You reveal D4. D4 shows 8. You reveal E4. E4 shows -30. You reveal F4. F4 shows 180. You reveal F1. F1 shows 62. You reveal B1. B1 shows -78. Expected-value display: A:12, B:-2, C:-43, D:3, E:-10, F:82. You choose gamble F. Outcome 2 occurs. Your gamble pays -37 points. Net: -45 points (payoff minus 8 points for reveals). Trial 28. Chances: 1:15%, 2:13%, 3:43%, 4:29%. You reveal A3. A3 shows -83. You reveal B3. B3 shows -200. You reveal C3. C3 shows 54. You reveal D3. D3 shows 89. You reveal E3. E3 shows 118. You reveal F3. F3 shows -117. You reveal E4. E4 shows -19. You reveal D4. D4 shows -56. Expected-value display: A:-36, B:-86, C:23, D:22, E:45, F:-50. You choose gamble E. Outcome 4 occurs. Your gamble pays -19 points. Net: -27 points (payoff minus 8 points for reveals). Trial 29. Chances: 1:10%, 2:54%, 3:15%, 4:21%. You reveal A2. A2 shows -102. You reveal B2. B2 shows 110. You reveal C2. C2 shows 161. You reveal D2. D2 shows -24. You reveal E2. E2 shows -71. You reveal F2. F2 shows 37. You reveal B4. B4 shows -16. You reveal C4. C4 shows 17. Expected-value display: A:-55, B:56, C:91, D:-13, E:-38, F:20. You choose gamble C. Outcome 2 occurs. Your gamble pays 161 points. Net: 153 points (payoff minus 8 points for reveals).
You are choosing between gambles to earn points. Your bonus is $0.01 for every 5 points you earn. On each round, 6 gambles labeled A, B, C, D, E, F (left to right) are on offer. Each gamble pays off in one of 4 possible outcomes, numbered 1 to 4 from top to bottom. Each outcome has a chance of occurring, shown as a percentage. The payoff of each gamble under each outcome is shown in a cell of the table, but all cells start hidden. To reveal a cell, type its label: the gamble letter followed by the outcome number (e.g. A1 is gamble A under outcome 1). Each reveal costs 4 points. Revealed cells stay visible for the rest of the round, and you may reveal as many or as few as you like, in any order. When you are ready, choose a gamble by typing its letter: A, B, C, D, E, or F. The outcome is then drawn at random according to the chances, and you earn that gamble's payoff for that outcome minus the 4 points you paid for each reveal. Instruction block 1 (practice): Trial 1. Chances: 1:16%, 2:19%, 3:14%, 4:51%. You choose gamble A. Outcome 1 occurs. Your gamble pays 7 points. Net: 7 points. Trial 2. Chances: 1:23%, 2:20%, 3:41%, 4:16%. You choose gamble C. Outcome 2 occurs. Your gamble pays -18 points. Net: -18 points. Trial 3. Chances: 1:21%, 2:18%, 3:4%, 4:57%. You choose gamble F. Outcome 4 occurs. Your gamble pays 5 points. Net: 5 points. Instruction block 2 (practice): Trial 4. Chances: 1:19%, 2:18%, 3:38%, 4:25%. You choose gamble E. Outcome 1 occurs. Your gamble pays 150 points. Net: 150 points. Trial 5. Chances: 1:20%, 2:13%, 3:32%, 4:35%. You choose gamble F. Outcome 4 occurs. Your gamble pays 68 points. Net: 68 points. Trial 6. Chances: 1:37%, 2:14%, 3:33%, 4:16%. You choose gamble C. Outcome 2 occurs. Your gamble pays -136 points. Net: -136 points. Instruction block 3 (practice): Trial 7. Chances: 1:27%, 2:19%, 3:18%, 4:36%. You reveal A1. A1 shows 67. You reveal B2. B2 shows 40. You reveal D3. D3 shows -84. You choose gamble A. Outcome 1 occurs. Your gamble pays 67 points. Net: 55 points (payoff minus 12 points for reveals). Trial 8. Chances: 1:26%, 2:30%, 3:11%, 4:33%. You reveal E1. E1 shows -95. You reveal C3. C3 shows 28. You reveal B3. B3 shows 49. You choose gamble D. Outcome 3 occurs. Your gamble pays -54 points. Net: -66 points (payoff minus 12 points for reveals). Trial 9. Chances: 1:9%, 2:14%, 3:43%, 4:34%. You reveal F3. F3 shows -30. You reveal E4. E4 shows 23. You reveal B3. B3 shows 66. You choose gamble B. Outcome 3 occurs. Your gamble pays 66 points. Net: 54 points (payoff minus 12 points for reveals). Test block: Trial 10. Chances: 1:29%, 2:22%, 3:26%, 4:23%. You choose gamble D. Outcome 1 occurs. Your gamble pays -18 points. Net: -18 points. Trial 11. Chances: 1:23%, 2:32%, 3:29%, 4:16%. You reveal E3. E3 shows -86. You reveal C2. C2 shows 81. You reveal A1. A1 shows -50. You choose gamble C. Outcome 1 occurs. Your gamble pays -163 points. Net: -175 points (payoff minus 12 points for reveals). Trial 12. Chances: 1:13%, 2:20%, 3:22%, 4:45%. You choose gamble F. Outcome 2 occurs. Your gamble pays -42 points. Net: -42 points. Trial 13. Chances: 1:45%, 2:20%, 3:18%, 4:17%. You choose gamble D. Outcome 1 occurs. Your gamble pays 112 points. Net: 112 points. Trial 14. Chances: 1:20%, 2:30%, 3:19%, 4:31%. You choose gamble B. Outcome 4 occurs. Your gamble pays 24 points. Net: 24 points. Trial 15. Chances: 1:14%, 2:45%, 3:5%, 4:36%. You choose gamble D. Outcome 3 occurs. Your gamble pays 62 points. Net: 62 points. Trial 16. Chances: 1:40%, 2:14%, 3:20%, 4:26%. You choose gamble A. Outcome 4 occurs. Your gamble pays 13 points. Net: 13 points. Trial 17. Chances: 1:6%, 2:31%, 3:35%, 4:28%. You choose gamble E. Outcome 4 occurs. Your gamble pays -23 points. Net: -23 points. Trial 18. Chances: 1:30%, 2:22%, 3:8%, 4:40%. You choose gamble F. Outcome 2 occurs. Your gamble pays -47 points. Net: -47 points. Trial 19. Chances: 1:15%, 2:31%, 3:28%, 4:26%. You choose gamble C. Outcome 2 occurs. Your gamble pays -48 points. Net: -48 points. Trial 20. Chances: 1:5%, 2:47%, 3:28%, 4:20%. You choose gamble B. Outcome 2 occurs. Your gamble pays 33 points. Net: 33 points. Trial 21. Chances: 1:31%, 2:14%, 3:41%, 4:14%. You choose gamble D. Outcome 1 occurs. Your gamble pays -19 points. Net: -19 points. Trial 22. Chances: 1:31%, 2:33%, 3:9%, 4:27%. You choose gamble A. Outcome 2 occurs. Your gamble pays -3 points. Net: -3 points. Trial 23. Chances: 1:25%, 2:11%, 3:47%, 4:17%. You choose gamble B. Outcome 3 occurs. Your gamble pays 31 points. Net: 31 points. Trial 24. Chances: 1:19%, 2:51%, 3:10%, 4:20%. You choose gamble E. Outcome 3 occurs. Your gamble pays -43 points. Net: -43 points. Trial 25. Chances: 1:48%, 2:25%, 3:24%, 4:3%. You choose gamble F. Outcome 3 occurs. Your gamble pays -177 points. Net: -177 points. Trial 26. Chances: 1:8%, 2:33%, 3:16%, 4:43%. You choose gamble B. Outcome 4 occurs. Your gamble pays 115 points. Net: 115 points. Trial 27. Chances: 1:30%, 2:28%, 3:7%, 4:35%. You choose gamble D. Outcome 2 occurs. Your gamble pays -12 points. Net: -12 points. Trial 28. Chances: 1:15%, 2:13%, 3:43%, 4:29%. You choose gamble C. Outcome 1 occurs. Your gamble pays 8 points. Net: 8 points. Trial 29. Chances: 1:10%, 2:54%, 3:15%, 4:21%. You choose gamble E. Outcome 3 occurs. Your gamble pays 70 points. Net: 70 points.