Abstract. Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m, M ]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum rate m. El-Yaniv et al presented the optimal worst-case threat-based strategy (WTB) for this game [4]. In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal algorithms for each of them. Remarkable differences in behavior are as follows: Unlike other algorithms, the average-case threat-based strategy (
Fujiwara et al. REF study the problem using average-case competitive analysis under the assumption that the distribution of the maximum exchange rate is known.