A cumulative prospect theory explanation of gamblers cashing-out

Abstract

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.