A milestone was set in modern machine learning history when AlphaGo Zero, based on reinforcement learning and with no training data from human players, became the undefeated Go champion against all machines and humans. Currently, Deepmind is building its next generation of protein folding prediction AI expected to surpass the famed AlphaFold that has already surpassed all human scientists, using the same mechanism of Zero, namely, reinforcement learning. In this work, we focus on using reinforcement learning and game theory to solve for the optimal strategies for the dice game Pig, in a novel simultaneous playing setting. First, we derived analytically the optimal strategy for the 2-player simultaneous game using dynamic programming, mixed-strategy Nash equilibrium. At the same time, we proposed a new Stackelberg value iteration framework to approximate the near-optimal pure strategy. Next, we developed the corresponding optimal strategy for the multiplayer independent strategy game numerically. Finally, we presented the Nash equilibrium for simultaneous Pig game with infinite number of players. To help promote the learning of and interest in reinforcement learning, game theory and statistics, we have further implemented a website where users can play both the sequential and simultaneous Pig game against the optimal strategies derived in this work.