We present an analysis of the optimal development of natural gas infrastructure in Europe based on the scenario studies of Holz and von Hirschhausen (2013). We use a stochastic mixed integer quadratic model to analyze the impact of uncertainty about future natural gas consumption in Europe on optimal investments in pipelines. Our data is based on results from the PRIMES model of natural gas demand and technology scenarios discussed in Knopf et al. (2013). We present a comparison between the results from the stochastic model and the expected value model, as well as an analysis of the individual scenarios. We also performed sensitivity analyses on the probabilities of the future scenarios. Comparison of the results from the stochastic model to those of a deterministic expected value model reveals a negligible Value of the Stochastic Solution. We do, however, find structurally different infrastructure solutions in the stochastic and the deterministic models. Regarding infrastructure expansions, we find that 1) the largest pipeline investments will be towards Asia, 2) there is a trend towards a larger gas supply from Africa to Europe, and 3) within Europe, eastward connections will be strengthened. Our main finding using the stochastic approach is that there is limited option value in delaying investments in natural gas infrastructure, until more information is available regarding policy and technology in 2020, due to the low costs of overcapacity.