对决审查下对手利用的安全观测容量
Safe Observation Capacity for Opponent Exploitation under Showdown Censoring
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中文总结 AI 辅助
该研究针对类扑克游戏中对决数据非随机缺失的问题，提出安全观测容量κ_ρ(I)及安全主动去审查（SAD）方法，通过实验验证其在恢复被审查弃牌质量、认证安全可利用差距等方面的有效性。
中文摘要 AI 辅助
在类扑克游戏中，弃牌会隐藏私有牌，因此对决数据并非随机缺失。常规的单牌估计量会收敛到选定的分布，且其置信集会随样本量增大而失去覆盖率。安全底线探测会改变监测过程：它推动选定的行动路线进入对决，揭示所有非弃牌的延续情况，并使用序列形式的流来恢复经揭示认证历史上被审查的弃牌质量。我们通过安全观测容量κ_ρ(I)来量化这种修复，它是安全预算ρ下最大的安全底线可达率。其前沿是凹的分段线性函数，原点斜率等于底线的影子价格。当单手揭示质量分解为安全可达性和对手延续性时，匹配边界给出局部被审查纤维方向的条件单目标成本N=Θ~(1/(κ_ρ(I)π ε²))。安全主动去审查（SAD）将容量与公共异常路由及稳健部署相结合；跨目标路由仍为启发式方法。实验证据涵盖分桶的转牌-河牌终局、受控实例，以及固定棋盘的未分桶河牌子博弈。在后一情况中，构建的公共孪生体允许安全底线响应，其价值V=0.815；经审计的公共通道仅认证蓝图底线，而总体揭示证据认证至少V的96%。在更广泛的合成对手群体中，公共和已求解的分组揭示纤维分别认证安全可利用差距的中位数份额为73%和91%。独立的底线审计覆盖所有评估的探测和响应。研究结果将无条件安全性与主动揭示的条件统计价值区分开来。
英文摘要
In poker-like games, folds hide private cards, so showdown data are missing not at random: per-card estimates converge to behavior conditional on reveal, and shrinking confidence sets can lose coverage. A floor-safe probe carries a line to showdown; sequence-form flow then recovers censored fold mass on reveal-certified histories. We price acquisition through safe observation capacity, the largest target reach attainable by a floor-safe plan at a given value slack. Its frontier is concave and piecewise linear, with initial slope given by the floor's shadow price. When that reach converts fully to reveal and parent flow is non-bottleneck, matching local bounds make the hands required for conditional-probability half-width $\varepsilon$ inversely proportional, up to logarithms, to capacity, opponent continuation mass, and $\varepsilon^2$. Safe Active De-censoring (SAD) combines public screening, an independent reveal batch, and robust deployment; a max-min safe audit gives positive joint reveal rate to every coordinate in a finite library-covered target set, including public-null deviations. With $10^6$ hands, SAD raises the river over-fold certified gain from $0.485$ to $0.692$ and improves both gains over public-only collection on all three deviations (Holm-adjusted paired $p\le0.012$), while selecting no control target. On a fixed-board public twin, a disjoint audit-refit-deploy loop detects all $30$ simulation seeds and no control seed, certifying absolute value $0.655$ (95% confidence-interval half-width $0.008$). Every floor-constrained probe and response passes a floor audit.
