Socks are produced and replaced at a massive scale, yet their paired use makes them unusually vulnerable to waste, as the loss of a single sock can strand usable wear-capacity and trigger premature replacement. In this study, we quantify the economic and ecological value of pairing non-matching \say{orphan} socks, and the social cost that discourages this behaviour. We formalize sock ownership as a sequential decision problem under uncertainty in which socks wear out and disappear stochastically during laundering, while public exposure induces a person-specific mismatch penalty. We conducted an in-person study to estimate mismatch sensitivity and diversity preference, linking behavioural heterogeneity to optimal mixing strategies. Using these results and a computer simulation-based evaluation of interpretable pairing policies, we show that strict matching can appear resource-frugal largely because it generates many sockless days, whereas controlled tolerance for mismatch sustains service and reduces stranded capacity across loss regimes. This study establishes the feasibility of matching non-matching socks while outlining its limitations and challenges.

翻译：袜子的大规模生产与更换过程中，其成对使用的特性使其异常容易产生浪费：单只袜子的丢失可能导致可用穿着容量的闲置，并引发过早更换。本研究量化了配对非匹配"孤儿"袜子所产生的经济与生态价值，以及阻碍该行为的社会成本。我们将袜子所有权形式化为不确定性下的序贯决策问题：袜子在洗涤过程中会随机磨损和消失，而公开暴露则引发因人而异的错配惩罚。通过开展实地研究，我们估算了错配敏感度与多样性偏好，并将行为异质性与最优混合策略相关联。基于这些结果及对可解释配对策略的计算机模拟评估，我们发现严格匹配看似节约资源，主要是因其导致大量无袜可穿的日子；而受控的错配容忍度则能维持穿着服务，并在不同损耗机制下减少闲置容量。本研究证实了非匹配袜子配对的可行性，同时阐明了其局限性与挑战。