Ship collision avoidance involves helping ships find routes that will best enable them to avoid a collision. When more than two ships encounter each other, the procedure becomes more complex since a slight change in course by one ship might affect the future decisions of the other ships. Two distributed algorithms have been developed in response to this problem: Distributed Local Search Algorithm (DLSA) and Distributed Tabu Search Algorithm (DTSA). Their common drawback is that it takes a relatively large number of messages for the ships to coordinate their actions. This could be fatal, especially in cases of emergency, where quick decisions should be made. In this paper, we introduce Distributed Stochastic Search Algorithm (DSSA), which allows each ship to change her intention in a stochastic manner immediately after receiving all of the intentions from the target ships. We also suggest a new cost function that considers both safety and efficiency in these distributed algorithms. We empirically show that DSSA requires many fewer messages for the benchmarks with four and 12 ships, and works properly for real data from the Automatic Identification System (AIS) in the Strait of Dover.