In this paper, we propose a new analysis for randomized 2-SAT and 3-SAT algorithms, and show that we could determine more precise boundaries for transition probability of Markov chain using Karnaugh map. In our analysis we will show the probability that the selected literal has been flipped correctly is so close to 2 3 and 4 7 , respectively for 2-SAT and 3-SAT with large number of variables. Then we will extend our result to k-SAT and show that both transition probability of Markov chain in randomized algorithm for kSAT approaches to 0.5. Finally we use this result to determine the probability and complexity of finding the satisfying assignment for randomized k-SAT algorithm. It will be shown that the probability of finding satisfying assignment and its complexity respectively are within a polynomial factor of (0.9272 ) n and (1.0785 ) n for satisfiable 3-SAT with n variables (for n   ).