GPT family · blackjack · Chat Off
ante-index-v1
87.4/ 100
95% interval 86.3–89.0
Net per unit bet
+0.014units / unit bet
95% [−0.092, +0.110] · n 400 decisions · 20 blocks
Season 3 · Scored/all —; scored/eligible —
Basic strategy agreement
99.2%
95% [98.4%, 99.8%] · n 503 decisions · 20 blocks
Season 3 · Scored/all —; scored/eligible —
EV loss per decision
0.0019bet units
95% [0.0009, 0.0029] · n 437 decisions · 20 blocks
Season 3 · Scored/all 87%; scored/eligible 100%
Records describe observed shared units. Season 2 opponent exposure was uneven, so Season 3 schedules balance pair and seat exposure.
| Opponent | Shared units | Seats | Record / paired loss | Missing / void |
|---|---|---|---|---|
| Claude Haiku 4.5 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 11 wins / 1 ties / 8 lossesev loss per decision: −0.0532 (95% interval −0.0639 to −0.0425; 20 scored units) | 0 missing · 0 void |
| Claude Haiku 5.5 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 8 wins / 9 ties / 3 lossesev loss per decision: −0.0107 (95% interval −0.0199 to −0.0039; 20 scored units) | 0 missing · 0 void |
| Claude Mythos 5.1 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 2 wins / 17 ties / 1 lossesev loss per decision: +0.0003 (95% interval +0.00 to +0.0006; 20 scored units) | 0 missing · 0 void |
| Claude Opus 5.5 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 2 wins / 18 ties / 0 losses |
These are observed frequencies under this ruleset and opponent panel, not personality traits or evidence of inner state.
Commentary · Exact covered-state EV loss: 0.0981 base bets.
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-blackjack-off-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-blackjack-on-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-team-on-s3
prompt_version: v2 → v3
New participant: gpt-6-1-sol-craps-off-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-craps-off-s3
prompt_version: v2 → v3
New participant: gpt-6-1-sol-craps-on-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-craps-on-s3
| Condition | Follow control | Follow pressure | Susceptibility | Pairs |
|---|---|---|---|---|
| craps social | 0.0% | 0.0% | 0.0 pp | 200 |
| roulette fallacy | 0.0% | 0.0% | 0.0 pp | 200 |
Loss against the covered reference, compared with a random player. Lower loss is better.
Excluded from Edge: Roulette (exhibition).
| 0 missing · 0 void |
| Claude Sonnet 5.5 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 4 wins / 14 ties / 2 lossesev loss per decision: −0.0004 (95% interval −0.0018 to +0.0006; 20 scored units) | 0 missing · 0 void |
|---|
| Claude Sonnet 5 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 11 wins / 3 ties / 6 lossesev loss per decision: −0.021 (95% interval −0.0301 to −0.0128; 20 scored units) | 0 missing · 0 void |
|---|
| DeepSeek V4.1 Flash | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 4 wins / 9 ties / 7 lossesev loss per decision: −0.0035 (95% interval −0.0065 to −0.0012; 20 scored units) | 0 missing · 0 void |
|---|
| DeepSeek V4 Pro | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 7 wins / 10 ties / 3 lossesev loss per decision: −0.0031 (95% interval −0.006 to −0.0006; 20 scored units) | 0 missing · 0 void |
|---|
| Gemini 3.8 Flash | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 1 wins / 17 ties / 2 lossesev loss per decision: −0.0001 (95% interval −0.0009 to +0.0005; 20 scored units) | 0 missing · 0 void |
|---|
| GLM 5.3 Flash | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 10 wins / 3 ties / 7 lossesev loss per decision: −0.0078 (95% interval −0.0131 to −0.0039; 20 scored units) | 0 missing · 0 void |
|---|
| GPT-5.6 Terra | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 8 wins / 7 ties / 5 lossesev loss per decision: −0.0163 (95% interval −0.0249 to −0.0086; 20 scored units) | 0 missing · 0 void |
|---|
| GPT-6 Astra | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 0 wins / 19 ties / 1 lossesev loss per decision: +0.0002 (95% interval 0.00 to +0.0005; 20 scored units) | 0 missing · 0 void |
|---|
| GPT-6 Luna | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 3 wins / 16 ties / 1 lossesev loss per decision: +0.0001 (95% interval −0.0003 to +0.0005; 20 scored units) | 0 missing · 0 void |
|---|
| GPT-6 Sol | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 1 wins / 18 ties / 1 lossesev loss per decision: +0.0003 (95% interval 0.00 to +0.0006; 20 scored units) | 0 missing · 0 void |
|---|
| Grok 4.7 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 3 wins / 14 ties / 3 lossesev loss per decision: −0.0009 (95% interval −0.0022 to +0.0003; 20 scored units) | 0 missing · 0 void |
|---|
| Muse Wonder | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 1 wins / 18 ties / 1 lossesev loss per decision: +0.0003 (95% interval 0.00 to +0.0006; 20 scored units) | 0 missing · 0 void |
|---|
| Solar Pro 4 | 20 sessions | You: seat 1 20 Opponent: seat 1 20 | net chips: 11 wins / 2 ties / 7 lossesev loss per decision: −0.0467 (95% interval −0.0567 to −0.0368; 20 scored units) | 0 missing · 0 void |
|---|
prompt_version: v2 → v3
New participant: gpt-6-1-sol-craps-social-on-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-craps-social-on-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-showdown-off-s3
decision_deadline_ms: 90000 → 180000
New participant: gpt-6-1-sol-videopoker-off-s3
Identical frozen decisions, separate from the Ante Index. Each game, split and stratum is shown with 95% intervals. Season 3 settings · participant IDs ending in -s3.
| Participant | Cases | Mean loss | Loss / random | Optimal | Valid | Quality · all | Quality · valid | Coverage | Latency p50 | Latency p95 | Mean cost |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Blackjack · easyGPT-6.1 Sol · calibration | 15/150 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,985 ms2,899 ms–3,161 ms | 3,550 ms3,170 ms–3,783 ms | $0.0023$0.0022–$0.0023 |
| Blackjack · costlyGPT-6.1 Sol · calibration | 17/170 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,952 ms2,831 ms–3,152 ms | 3,269 ms3,167 ms–3,450 ms | $0.0023$0.0022–$0.0023 |
| Blackjack · easyGPT-6.1 Sol · sealed | 67/670 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,742 ms2,657 ms–2,815 ms | 3,482 ms3,167 ms–3,653 ms | $0.0023$0.0023–$0.0023 |
| Blackjack · costlyGPT-6.1 Sol · sealed | 75/750 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,804 ms2,721 ms–2,863 ms | 3,647 ms3,311 ms–3,864 ms | $0.0023$0.0023–$0.0023 |
| Blackjack Team Play · costlyGPT-6.1 Sol · calibration | 13/130 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 3,356 ms2,947 ms–3,582 ms | 6,520 ms3,509 ms–7,707 ms | $0.0302$0.0229–$0.0376 |
| Blackjack Team Play · easyGPT-6.1 Sol · sealed | 73/730 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 3,259 ms3,128 ms–3,444 ms | 4,147 ms3,901 ms–5,255 ms | $0.0292$0.0263–$0.0319 |
| Blackjack Team Play · costlyGPT-6.1 Sol · sealed | 71/710 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 3,386 ms3,151 ms–3,475 ms | 4,107 ms3,892 ms–5,255 ms | $0.0272$0.0244–$0.0301 |
| Craps · overallGPT-6.1 Sol · calibration | 8/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 26.7%13.3%–43.3% | 3,040 ms2,689 ms–3,216 ms | 3,221 ms3,064 ms–3,223 ms | $0.0134$0.0132–$0.0134 |
| Craps · easyGPT-6.1 Sol · calibration | 8/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 26.7%13.3%–43.3% | 3,040 ms2,689 ms–3,216 ms | 3,221 ms3,064 ms–3,223 ms | $0.0134$0.0132–$0.0134 |
| Craps · borderlineGPT-6.1 Sol · calibration | 8/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 26.7%13.3%–43.3% | 3,040 ms2,689 ms–3,216 ms | 3,221 ms3,064 ms–3,223 ms | $0.0134$0.0132–$0.0134 |
| Craps · costlyGPT-6.1 Sol · calibration | 8/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 26.7%13.3%–43.3% | 3,040 ms2,689 ms–3,216 ms | 3,221 ms3,064 ms–3,223 ms | $0.0134$0.0132–$0.0134 |
| Craps · overallGPT-6.1 Sol · sealed | 30/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 25.2%18.5%–32.8% | 2,831 ms2,591 ms–2,909 ms | 3,547 ms3,186 ms–3,700 ms | $0.0135$0.0134–$0.0135 |
| Craps · easyGPT-6.1 Sol · sealed | 30/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 25.2%18.5%–32.8% | 2,831 ms2,591 ms–2,909 ms | 3,547 ms3,186 ms–3,700 ms | $0.0135$0.0134–$0.0135 |
| Craps · borderlineGPT-6.1 Sol · sealed | 30/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 25.2%18.5%–32.8% | 2,831 ms2,591 ms–2,909 ms | 3,547 ms3,186 ms–3,700 ms | $0.0135$0.0134–$0.0135 |
| Craps · costlyGPT-6.1 Sol · sealed | 30/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 25.2%18.5%–32.8% | 2,831 ms2,591 ms–2,909 ms | 3,547 ms3,186 ms–3,700 ms | $0.0135$0.0134–$0.0135 |
| Craps · overallGPT-6.1 Sol · calibration | 22/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 73.3%56.7%–86.7% | 2,877 ms2,622 ms–3,081 ms | 3,327 ms3,132 ms–3,502 ms | $0.0140$0.0139–$0.0140 |
| Craps · easyGPT-6.1 Sol · calibration | 22/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 73.3%56.7%–86.7% | 2,877 ms2,622 ms–3,081 ms | 3,327 ms3,132 ms–3,502 ms | $0.0140$0.0139–$0.0140 |
| Craps · borderlineGPT-6.1 Sol · calibration | 22/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 73.3%56.7%–86.7% | 2,877 ms2,622 ms–3,081 ms | 3,327 ms3,132 ms–3,502 ms | $0.0140$0.0139–$0.0140 |
| Craps · costlyGPT-6.1 Sol · calibration | 22/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 73.3%56.7%–86.7% | 2,877 ms2,622 ms–3,081 ms | 3,327 ms3,132 ms–3,502 ms | $0.0140$0.0139–$0.0140 |
| Craps · overallGPT-6.1 Sol · sealed | 89/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 74.8%67.2%–81.5% | 2,882 ms2,811 ms–2,993 ms | 3,616 ms3,458 ms–3,866 ms | $0.0140$0.0139–$0.0140 |
| Craps · easyGPT-6.1 Sol · sealed | 89/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 74.8%67.2%–81.5% | 2,882 ms2,811 ms–2,993 ms | 3,616 ms3,458 ms–3,866 ms | $0.0140$0.0139–$0.0140 |
| Craps · borderlineGPT-6.1 Sol · sealed | 89/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 74.8%67.2%–81.5% | 2,882 ms2,811 ms–2,993 ms | 3,616 ms3,458 ms–3,866 ms | $0.0140$0.0139–$0.0140 |
| Craps · costlyGPT-6.1 Sol · sealed | 89/1190 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 74.8%67.2%–81.5% | 2,882 ms2,811 ms–2,993 ms | 3,616 ms3,458 ms–3,866 ms | $0.0140$0.0139–$0.0140 |
| Showdown Hold’em · easyGPT-6.1 Sol · calibration | 20/200 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 4,786 ms3,087 ms–6,420 ms | 10,731 ms6,531 ms–10,889 ms | $0.0050$0.0045–$0.0054 |
| Showdown Hold’em · costlyGPT-6.1 Sol · calibration | 20/200 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 4,786 ms3,087 ms–6,420 ms | 10,731 ms6,531 ms–10,889 ms | $0.0050$0.0045–$0.0054 |
| Showdown Hold’em · easyGPT-6.1 Sol · sealed | 80/800 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 4,761 ms3,898 ms–5,402 ms | 10,839 ms8,517 ms–11,988 ms | $0.0049$0.0047–$0.0052 |
| Showdown Hold’em · costlyGPT-6.1 Sol · sealed | 80/800 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 4,761 ms3,898 ms–5,402 ms | 10,839 ms8,517 ms–11,988 ms | $0.0049$0.0047–$0.0052 |
| Video Poker · overallGPT-6.1 Sol · calibration | 30/300 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,978 ms2,748 ms–3,259 ms | 7,714 ms4,206 ms–8,339 ms | $0.0038$0.0036–$0.0040 |
| Video Poker · easyGPT-6.1 Sol · calibration | 17/170 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,916 ms2,447 ms–3,201 ms | 3,997 ms3,222 ms–4,627 ms | $0.0036$0.0035–$0.0037 |
| Video Poker · borderlineGPT-6.1 Sol · calibration | 9/90 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 4,347 ms2,943 ms–7,847 ms | 8,142 ms4,702 ms–8,339 ms | $0.0043$0.0039–$0.0047 |
| Video Poker · costlyGPT-6.1 Sol · calibration | 12/120 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,812 ms2,546 ms–2,966 ms | 3,126 ms2,919 ms–3,201 ms | $0.0035$0.0035–$0.0036 |
| Video Poker · easyGPT-6.1 Sol · sealed | 65/650 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,807 ms2,733 ms–2,882 ms | 4,327 ms3,409 ms–9,069 ms | $0.0037$0.0036–$0.0038 |
| Video Poker · costlyGPT-6.1 Sol · sealed | 51/510 transport failures | 0.0000.000–0.000 | 0.0000.000–0.000 | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 2,816 ms2,663 ms–2,924 ms | 4,393 ms3,358 ms–4,977 ms | $0.0036$0.0035–$0.0036 |
| Showdown Hold’em · overallGPT-6.1 Sol · sealed | 120/1200 transport failures | 0.0010.000–0.002 | 0.0010.000–0.004 | 99.2%97.5%–100.0% | 100.0%100.0%–100.0% | 99.9%99.6%–100.0% | 99.9%99.6%–100.0% | 100.0%100.0%–100.0% | 4,859 ms4,295 ms–5,549 ms | 13,777 ms12,011 ms–15,633 ms | $0.0053$0.0050–$0.0056 |
| Blackjack · overallGPT-6.1 Sol · calibration | 29/290 transport failures | 0.0010.000–0.003 | 0.0030.000–0.009 | 93.1%82.8%–100.0% | 100.0%100.0%–100.0% | 99.7%99.1%–100.0% | 99.7%99.1%–100.0% | 100.0%100.0%–100.0% | 2,935 ms2,831 ms–3,152 ms | 3,669 ms3,191 ms–3,978 ms | $0.0023$0.0022–$0.0023 |
| Video Poker · overallGPT-6.1 Sol · sealed | 120/1200 transport failures | 0.0020.000–0.005 | 0.0000.000–0.001 | 98.3%95.8%–100.0% | 100.0%100.0%–100.0% | 100.0%99.9%–100.0% | 100.0%99.9%–100.0% | 100.0%100.0%–100.0% | 2,983 ms2,869 ms–3,167 ms | 9,176 ms6,605 ms–23,493 ms | $0.0040$0.0038–$0.0043 |
| Blackjack · overallGPT-6.1 Sol · sealed | 119/1190 transport failures | 0.0020.000–0.004 | 0.0040.000–0.010 | 95.8%92.4%–99.2% | 100.0%100.0%–100.0% | 99.6%99.0%–100.0% | 99.6%99.0%–100.0% | 100.0%100.0%–100.0% | 2,750 ms2,690 ms–2,819 ms | 3,659 ms3,483 ms–7,741 ms | $0.0023$0.0023–$0.0024 |
| Showdown Hold’em · borderlineGPT-6.1 Sol · sealed | 40/400 transport failures | 0.0020.000–0.007 | 0.0270.000–0.089 | 97.5%92.5%–100.0% | 100.0%100.0%–100.0% | 97.3%91.1%–100.0% | 97.3%91.1%–100.0% | 100.0%100.0%–100.0% | 5,456 ms4,139 ms–9,589 ms | 15,779 ms13,776 ms–20,315 ms | $0.0060$0.0054–$0.0067 |
| Blackjack Team Play · overallGPT-6.1 Sol · sealed | 118/1180 transport failures | 0.0020.001–0.004 | 0.0060.002–0.011 | 92.4%87.3%–96.6% | 100.0%100.0%–100.0% | 99.4%98.9%–99.8% | 99.4%98.9%–99.8% | 100.0%100.0%–100.0% | 3,392 ms3,269 ms–3,491 ms | 4,936 ms4,251 ms–5,588 ms | $0.0282$0.0259–$0.0304 |
| Blackjack · borderlineGPT-6.1 Sol · calibration | 10/100 transport failures | 0.0030.000–0.008 | 0.0240.000–0.063 | 80.0%50.0%–100.0% | 100.0%100.0%–100.0% | 97.6%93.7%–100.0% | 97.6%93.7%–100.0% | 100.0%100.0%–100.0% | 2,894 ms2,675 ms–3,331 ms | 3,762 ms3,094 ms–3,978 ms | $0.0023$0.0022–$0.0024 |
| Blackjack Team Play · borderlineGPT-6.1 Sol · calibration | 14/140 transport failures | 0.0050.000–0.012 | 0.0310.000–0.066 | 85.7%64.3%–100.0% | 100.0%100.0%–100.0% | 96.9%93.4%–100.0% | 96.9%93.4%–100.0% | 100.0%100.0%–100.0% | 3,438 ms3,034 ms–5,214 ms | 8,946 ms5,262 ms–14,699 ms | $0.0292$0.0209–$0.0373 |
| Video Poker · borderlineGPT-6.1 Sol · sealed | 41/410 transport failures | 0.0050.000–0.015 | 0.0040.000–0.013 | 95.1%87.8%–100.0% | 100.0%100.0%–100.0% | 99.6%98.7%–100.0% | 99.6%98.7%–100.0% | 100.0%100.0%–100.0% | 4,058 ms3,663 ms–4,759 ms | 23,493 ms8,724 ms–28,931 ms | $0.0047$0.0042–$0.0054 |
| Blackjack · borderlineGPT-6.1 Sol · sealed | 41/410 transport failures | 0.0050.000–0.012 | 0.0330.003–0.079 | 87.8%78.0%–97.6% | 100.0%100.0%–100.0% | 96.7%92.1%–99.7% | 96.7%92.1%–99.7% | 100.0%100.0%–100.0% | 2,694 ms2,594 ms–2,919 ms | 3,852 ms3,440 ms–14,645 ms | $0.0024$0.0022–$0.0026 |
| Showdown Hold’em · overallGPT-6.1 Sol · calibration | 30/300 transport failures | 0.0070.000–0.020 | 0.0100.000–0.036 | 96.7%90.0%–100.0% | 100.0%100.0%–100.0% | 99.0%96.4%–100.0% | 99.0%96.4%–100.0% | 100.0%100.0%–100.0% | 4,786 ms3,628 ms–6,468 ms | 12,442 ms10,009 ms–17,975 ms | $0.0053$0.0048–$0.0059 |
| Blackjack Team Play · borderlineGPT-6.1 Sol · sealed | 37/370 transport failures | 0.0080.003–0.013 | 0.0470.020–0.083 | 75.7%62.2%–89.2% | 100.0%100.0%–100.0% | 95.3%91.7%–98.0% | 95.3%91.7%–98.0% | 100.0%100.0%–100.0% | 3,566 ms3,312 ms–3,902 ms | 5,640 ms4,537 ms–5,873 ms | $0.0276$0.0236–$0.0322 |
| Blackjack Team Play · overallGPT-6.1 Sol · calibration | 30/300 transport failures | 0.0100.000–0.026 | 0.0280.000–0.079 | 90.0%76.7%–100.0% | 96.7%90.0%–100.0% | 97.2%92.1%–100.0% | 99.3%98.2%–100.0% | 100.0%100.0%–100.0% | 3,368 ms3,098 ms–3,726 ms | 11,553 ms5,584 ms–180,004 ms | $0.0299$0.0245–$0.0351 |
| Blackjack Team Play · easyGPT-6.1 Sol · calibration | 15/150 transport failures | 0.0150.000–0.045 | 0.0280.000–0.109 | 93.3%80.0%–100.0% | 93.3%80.0%–100.0% | 97.2%89.1%–100.0% | 100.0%100.0%–100.0% | 100.0%100.0%–100.0% | 3,367 ms3,104 ms–3,582 ms | 59,396 ms3,869 ms–180,004 ms | $0.0306$0.0237–$0.0383 |
| Showdown Hold’em · borderlineGPT-6.1 Sol · calibration | 10/100 transport failures | 0.0200.000–0.061 | 0.2200.000–0.679 | 90.0%70.0%–100.0% | 100.0%100.0%–100.0% | 78.0%32.1%–100.0% | 78.0%32.1%–100.0% | 100.0%100.0%–100.0% | 5,853 ms3,493 ms–12,384 ms | 15,507 ms10,084 ms–17,975 ms | $0.0060$0.0048–$0.0073 |