Cash-out products offered by bookmakers allow a bettor to liquidate, for a small fee, an existing bet prior to “game end”. Previous research has found that bettors are likely to hold preferences consistent with cumulative prospect theory (CPT). We obtain analytic expressions for the ‘optimal’ proportion of the bet to cash-out for bettors with CPT preferences. Diminishing sensitivity or marginal utility leads bettors to prefer to cash-out likely winning bets, but not likely losing bets. Any preference to liquidate bets early is exacerbated by probability weighting and loss aversion. We demonstrate that partial liquidation (cashing-out a fraction of the bet) may be optimal under CPT in well-defined situations. Some potential solutions are presented for reducing the tendency for bettors to cash-out in the gain domain.

博彩公司提供的现钞产品使投注者可以在“游戏结束”之前以少量费用清算现有的投注。先前的研究发现，投注者可能会持有与累积前景理论（CPT）一致的偏好。对于具有CPT偏好的投注者，我们获得投注与兑现的“最佳”比例的解析表达式。敏感性降低或边际效用降低，导致投注者倾向于兑现可能获胜的赌注，但不太可能输掉赌注。概率加权和损失规避会加剧任何提早清算赌注的偏好。我们证明在明确定义的情况下，在CPT下进行部分清算（兑现赌注的一小部分）可能是最佳的。提出了一些潜在的解决方案，以减少投注者在收益域中兑现的趋势。