Simulations

Stats

Four strategies are implemented (available in Game2048.game.Main.Game_2048).

For each one we simulate n=300.000 games and plot the score obtained over this number of simulation.

Let \(s\) the score fonction of a given strategy game. Using the following functions :

\[\mu = \mathbb{E}(s(strategy)) = \frac{1}{300000} * \sum_{i=1}^{300000} s_{i}(strategy)\]

\[\sigma^{2} = \mathbb{V}(strategy) = \frac{1}{300000} * \sum_{i=1}^{300000}(s_{i}(strategy) - \mathbb{E}(s(strategy)))^{2},\]

a 95% confidence interval of the mean score, given by,

\[[\mu - 1.96 * \sqrt{\frac{\sigma^{2}}{n}} \; , \; \mu + 1.96 * \sqrt{\frac{\sigma^{2}}{n}}] \; ,\]

is also provided on the graphs.

Note

Python scripts of confidence intervals builder and their plot are available for consultation in the submodule Stats of Game2048 in the github repository.