
==============================================================================
RANGES: the favoured number as the range grows
==============================================================================

--- 1-10  (n=239 of 239 answers parsed) ---
top three: 7 (223, 93.3%)   4 (5, 2.1%)   5 (5, 2.1%)     uniform would be 10.0% each
spread: 5 distinct values of 10 possible; entropy 0.48 of 3.32 bits (14% of uniform)
per-model favourite:
  claude-fable-5.1           7  20/20
  claude-opus-5              7  20/20
  claude-sonnet-5            7  20/20
  deepseek-v4-flash-0731     7  19/20
  deepseek-v4-pro-0813       7  10/20
  gemini-3.8-flash           7  20/20
  gpt-6-astra                7  20/20
  qwen3.8-flash              7  19/19
  qwen3.8-max-0902           7  20/20
  grok-4.6                   7  15/20
  glm-5.3                    7  20/20
  glm-5.3-flash              7  20/20

--- 1-20  (n=233 of 237 answers parsed) ---
top three: 14 (66, 28.3%)   17 (54, 23.2%)   7 (48, 20.6%)     uniform would be 5.0% each
spread: 12 distinct values of 20 possible; entropy 2.47 of 4.32 bits (57% of uniform)
per-model favourite:
  claude-fable-5.1          14  16/20
  claude-opus-5             17  15/20
  claude-sonnet-5           14  12/20
  deepseek-v4-flash-0731    17  11/20
  deepseek-v4-pro-0813      15   6/16
  gemini-3.8-flash          14  20/20
  gpt-6-astra               13  10/20
  qwen3.8-flash              7  11/17
  qwen3.8-max-0902          13  17/20
  grok-4.6                   7   6/20
  glm-5.3                    7  11/20
  glm-5.3-flash              7  13/20

--- 1-30  (n=235 of 235 answers parsed) ---
top three: 17 (188, 80.0%)   14 (11, 4.7%)   7 (8, 3.4%)     uniform would be 3.3% each
spread: 12 distinct values of 30 possible; entropy 1.34 of 4.91 bits (27% of uniform)
per-model favourite:
  claude-fable-5.1          17  20/20
  claude-opus-5             17  20/20
  claude-sonnet-5           17  20/20
  deepseek-v4-flash-0731    17  11/20
  deepseek-v4-pro-0813      25   5/20
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  19/20
  qwen3.8-flash             17  11/15
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  14/20
  glm-5.3                   17  18/20
  glm-5.3-flash             17  15/20

--- 1-50  (n=233 of 233 answers parsed) ---
top three: 37 (107, 45.9%)   27 (73, 31.3%)   23 (21, 9.0%)     uniform would be 2.0% each
spread: 12 distinct values of 50 possible; entropy 2.11 of 5.64 bits (37% of uniform)
per-model favourite:
  claude-fable-5.1          27  15/20
  claude-opus-5             37  20/20
  claude-sonnet-5           27  20/20
  deepseek-v4-flash-0731    37   8/20
  deepseek-v4-pro-0813      42   5/20
  gemini-3.8-flash          37  11/20
  gpt-6-astra               37  19/20
  qwen3.8-flash             37   9/13
  qwen3.8-max-0902          37  18/20
  grok-4.6                  27  11/20
  glm-5.3                   23   7/20
  glm-5.3-flash             23   6/20

--- 1-100  (n=236 of 236 answers parsed) ---
top three: 47 (93, 39.4%)   42 (50, 21.2%)   73 (42, 17.8%)     uniform would be 1.0% each
spread: 17 distinct values of 100 possible; entropy 2.51 of 6.64 bits (38% of uniform)
per-model favourite:
  claude-fable-5.1          47  16/20
  claude-opus-5             73  19/20
  claude-sonnet-5           47  20/20
  deepseek-v4-flash-0731    42   8/20
  deepseek-v4-pro-0813      57   7/20
  gemini-3.8-flash          42  14/20
  gpt-6-astra               47  14/20
  qwen3.8-flash             42  12/16
  qwen3.8-max-0902          47  12/20
  grok-4.6                  73   8/20
  glm-5.3                   47  13/20
  glm-5.3-flash             47   8/20

==============================================================================
LANGUAGES: the same 1-30 question asked five ways
==============================================================================

--- english  (n=237 of 237 answers parsed) ---
top three: 17 (206, 86.9%)   7 (5, 2.1%)   14 (4, 1.7%)     uniform would be 3.3% each
spread: 18 distinct values of 30 possible; entropy 1.05 of 4.91 bits (21% of uniform)
per-model favourite:
  claude-fable-5.1          17  20/20
  claude-opus-5             17  20/20
  claude-sonnet-5           17  20/20
  deepseek-v4-flash-0731    17   9/20
  deepseek-v4-pro-0813      17   4/20
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  20/20
  qwen3.8-flash             17  16/17
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  18/20
  glm-5.3                   17  20/20
  glm-5.3-flash             17  19/20

--- spanish  (n=238 of 238 answers parsed) ---
top three: 17 (194, 81.5%)   7 (10, 4.2%)   14 (9, 3.8%)     uniform would be 3.3% each
spread: 15 distinct values of 30 possible; entropy 1.30 of 4.91 bits (26% of uniform)
per-model favourite:
  claude-fable-5.1          17  20/20
  claude-opus-5             17  20/20
  claude-sonnet-5           17  20/20
  deepseek-v4-flash-0731     7   6/20
  deepseek-v4-pro-0813      14   7/20
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  20/20
  qwen3.8-flash             17  14/18
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  17/20
  glm-5.3                   17  19/20
  glm-5.3-flash             17  19/20

--- mandarin  (n=239 of 239 answers parsed) ---
top three: 17 (196, 82.0%)   7 (9, 3.8%)   8 (6, 2.5%)     uniform would be 3.3% each
spread: 20 distinct values of 30 possible; entropy 1.36 of 4.91 bits (28% of uniform)
per-model favourite:
  claude-fable-5.1          17  20/20
  claude-opus-5             17  20/20
  claude-sonnet-5           17  20/20
  deepseek-v4-flash-0731     7   7/20
  deepseek-v4-pro-0813       5   4/20
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  19/20
  qwen3.8-flash             17  18/19
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  16/20
  glm-5.3                   17  20/20
  glm-5.3-flash             17  20/20

--- arabic  (n=240 of 240 answers parsed) ---
top three: 17 (186, 77.5%)   7 (17, 7.1%)   14 (14, 5.8%)     uniform would be 3.3% each
spread: 11 distinct values of 30 possible; entropy 1.39 of 4.91 bits (28% of uniform)
per-model favourite:
  claude-fable-5.1          17  20/20
  claude-opus-5             17  20/20
  claude-sonnet-5           17  20/20
  deepseek-v4-flash-0731     7  12/20
  deepseek-v4-pro-0813      14   8/20
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  20/20
  qwen3.8-flash             17  13/20
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  15/20
  glm-5.3                   17  16/20
  glm-5.3-flash             17  19/20

--- hindi  (n=241 of 246 answers parsed) ---
top three: 17 (200, 83.0%)   14 (6, 2.5%)   15 (6, 2.5%)     uniform would be 3.3% each
spread: 16 distinct values of 30 possible; entropy 1.25 of 4.91 bits (25% of uniform)
per-model favourite:
  claude-fable-5.1          17  28/28
  claude-opus-5             17  20/20
  claude-sonnet-5           17  18/19
  deepseek-v4-flash-0731    17   6/20
  deepseek-v4-pro-0813      15   5/16
  gemini-3.8-flash          17  20/20
  gpt-6-astra               17  20/20
  qwen3.8-flash             17  11/18
  qwen3.8-max-0902          17  20/20
  grok-4.6                  17  19/20
  glm-5.3                   17  18/20
  glm-5.3-flash             17  19/20

==============================================================================
COIN FLIPS: ten flips, models against an exact fair-coin baseline
==============================================================================

parsed 200 valid ten-flip sequences of 211 answers

                                   models        fair coin
run of 4 or more the same:        1.0%   46.5%
mean longest run:                 2.23   3.66
mean switches (of 9):             6.21   4.50
mean heads (of 10):               5.02   5.00
exactly 5 heads:                 86.0%   24.609375%

per model:
  model                     n   run>=4   mean run   switches   heads
  claude-fable-5.1          5    0.0%       2.20       5.80    5.00
  claude-opus-5            18    0.0%       2.00       6.50    5.00
  claude-sonnet-5          19    0.0%       2.00       6.95    5.00
  deepseek-v4-flash-0731   20    0.0%       2.00       6.65    5.00
  deepseek-v4-pro-0813     11    0.0%       2.18       5.91    5.00
  gemini-3.8-flash         20    0.0%       2.35       5.90    4.65
  gpt-6-astra               8    0.0%       2.38       5.75    4.63
  qwen3.8-flash            20    5.0%       2.50       5.90    5.45
  qwen3.8-max-0902         20    0.0%       2.00       6.45    5.05
  grok-4.6                 20    0.0%       2.05       6.55    5.00
  glm-5.3                  19    0.0%       2.58       5.74    5.21
  glm-5.3-flash            20    5.0%       2.50       5.70    5.00

a fair coin would give 93.0 sequences with a run of 4+; the models gave 2. z = -12.9
