============================================================================== 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