Let \(X_ 1,X_ 2,X_ 3,..\). be a discrete stochastic process with a stopping time N. Our goal is to compute \(E[p(X_ 1,X_ 2,...,X_ N)]\) for some payoff function p by computational methods more efficient than exhaustive search. The author introduces dynamic exchangeable programming as an approach which is applicable over a process of exchangeable random variables, when we wish to compute the expected value of a symmetric payoff function upon an exchangeable stopping time. This technique is exponentially faster than exhaustive search. One instance of an exchangeable stopping time is where a stopping time is defined by a threshold on the sequential sum of the process. Another instance is where a stopping time is defined by the occurrence of given patterns in observed values of the process. This new computation technique has applications in bin packing, casino blackjack and random drawing for patterns.