This paper deals with a two-person zero-sum timing game 
with the following structure: Player I  
has a gun with one bullet and player II has 
a gun with two bullets and they fight a duel.  
Player I's gun is noisy and player 
II's gun is silent, and hence player II hears the shot of 
player I as soon as player I fires, whereas player I does not 
hear the shot of player II. 
Player I is at the place 0 at the beginning of the duel 
and he can move as he likes and player II is always at the place 1. 
The accuracy functions, which denote the probability of hitting the 
opponent when a player fires his bullet, are arbitrary.
If player I hits player II without being hit himself first, then the 
payoff is +1; if player I is hit by player II without 
hitting player II first, the payoff is -1; if they hit each other at
the same time or both survive, the payoff is 0.  

The objective of this paper is to obtain the game value 
and the optimal strategies for this timing game.  
In the final section, some examples are given.