The Josephus Problem

As the nation of Israel was moving closer towards crossing the Jordan, a number of tribes decided that they liked things right where they were on the eastern side of the Jordan River. The tribes of Reuben and Gad approached Moses and informed him of their desire to stay put. Moses was highly critical of the tribes. “Should your fellow Israelites go to war while you sit here?” Moses and the tribes made an agreement that the tribes of Reuben and Gad would help the other tribes conquer the land west of the Jordan River first, and only then could they return back to their territorial allotments east of the Jordan River.

This story highlights the importance of having a clear understanding about expectations in wartime, and ensuring the actions are completed before the reward is offered. Reuben and Gad must participate in the conquering of Canaan, and cannot return to their territories until the fighting is done. This lies in contrast to another event in Jewish history where the agreement was ignored.

When the First Jewish Revolt erupted in 66 CE, the Romans initially lost control of the course of events. Eventually they amassed the troops needed to suppress the revolt and began by marching north to south. In the Galilee, they captured to the town of Jotapata, Yodfat in Hebrew, in the Galilee.

Forty people, including the Jewish general Josephus, were hiding in a cave. The group wanted to commit suicide instead of surrendering the to the Romans. Josephus argued in favor of surrender, saying that it was an act against God. “Why do we set our soul and body, which are such dear companions, at such variance?” The group was intent on not falling into Roman hands, so Josephus convinced them to draw lots. The first person whose name was drawn would be killed by second, and so on, until the last two would kill each other. Josephus’ name fell into the last two, and he convinced the other man that they should surrender and not kill each other. The entire group was dead, save Josephus and the one other man. So while Josephus had seemingly agreed to not surrender, in the end he was able to work the system in his favor and survive.

This situation with Josephus inspired the game theory study of the ‘Josephus Problem.’ Game theory is a mathematical study of decision making in real life scenarios such as business and politics.

An example of the Josephus Problem in medieval Europe was the Turks and Christians example. 15 Turks and 15 Christians are on a ship which will sink unless half the passengers are thrown overboard. It is decided that the group will stand in a circle and every 9th person will be forced off the boat. As the order of the counting is known, the 15 of one group can decide where to stand so that they will survive the counting.

In the biblical account, Moses created an agreement that eventually was to lead to full tribal participation in the conquering of the land. Josephus skirted his agreement in a way that it remains a taint on his legacy that is memorialized in a way to cheat on an agreement.