Is expiation obligatory upon one who swore to play a game for some time before studying, then discovered the game was not working, so he began to study?

A Muslim must revere an oath sworn by Allah Almighty and should not swear except in important matters. Scholars have differed concerning one who swore to do something but was unable to do it due to an impediment beyond their will: do they break their oath or not? The more preponderant opinion is that they do not break their oath, because fulfilling and breaking an oath are analogous to obedience and disobedience in commands and prohibitions. Just as a person is not considered disobedient for a reason beyond their will, similarly, they are not considered to have broken their oath if they did not fulfill it for the same reason. The one who swore an oath only bound their oath to do what is within their power, and what is not within their ability, such as forgetfulness or compulsion, is not covered by their oath. Based on this, since you did not do what you swore to do due to a reason beyond your control, there is no breaking of the oath upon you.