I have a basic question in probability theory. The question is about a Russian roulette where we spin the chambers before each turn. 

The question asks "what is the probability that the player who started will be killed, in the long run?", and similarly for the second player.

The thing that confuses me a little bit is the meaning of "in the long run". The probability of staying alive after a long period of time is quite low (distributed geometrically). But how do I get the probability from that? 

Thank you.