# A Rule-Based AI Method for an Agent Playing Big Two
## 4 Experimental Results and Discussion
### Experiment 3: Rule-Based AI versus Human Players  
In the third experiment, two rule-based AI agents played 2000 games against two human players. We have gathered 4000 play logs from each set--4000 from the two rule-based AI agents and 4000 from the human players. Table 4 shows the statistics of play log data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistic** & **Rule-Based AI** & **Human Players** \\ \hline Win rate & 55.05\% (1101 games) & 44.95\% (899 games) \\ \hline \multicolumn{3}{c}{Scores in the positive zone} \\ \hline \(f\) & 1101 & 899 \\ Mean score & 18.25 & 16.10 \\ \(SD\) score & 7.24 & 7.71 \\ \hline \multicolumn{3}{c}{Scores in the negative zone} \\ \hline \(f\) & 2899 & 3101 \\ Mean score & \(-4.72\) & \(-5.31\) \\ \(SD\) score & 3.16 & 3.33 \\ \hline \multicolumn{3}{c}{Overall statistics concerning all scores} \\ \hline Total & 4000 scores & 4000 scores \\ \(p\)-value & \(2.5325\times 10^{-14}\) & \\ Effect size (\(r\)) & 0.1442 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of play log data from 2000 games of rule-based AI versus human players. Figure 7: The frequency distribution of scores for (**a**) rule-based AI, (**b**) conventional AI, (**c**) rule-based AI and conventional AI. The brown bars represent the intersection of purple bars and orange bars. The rule-based AI won 1101 games (55.05%) and lost 899 games (44.95%). Rule-based AI finished with a positive score 1101 times and a negative score 2899 times. Human players finished with a positive score 899 times and a negative score 3101 times. Rule-based AI's mean score when winning was 18.25 (\(SD\) = 7.24) and when losing it was \(-4.72\) (\(SD\) = 3.16). Human players' mean score when winning was 16.10 (\(SD\) = 7.71), and when losing it was \(-5.31\) (\(SD\) = 3.33). When testing the third hypothesis at a confidence level of 95%, we obtained a \(p\)-value of 2.5325 \(\times\) 10\({}^{-14}\). The statistics confirm that the results are statistically significant (\(p\)-value < 0.01). Thus, rule-based AI significantly outperforms human players. The effect size (\(r\)) was 0.1442, which is a small effect (0.10 < \(r\) < 0.30). Figure 8 shows the frequency distribution of rule-based AI agents and human players from 4000 scores. In Figure 8, rule-based AI finished with a positive score in 1101 games and with a negative score in 2899 games. In Figure 8, human players finished with a positive score in 899 games and with a negative score in 3101 games. We compared the frequency distribution of all game scores between rule-based AI and human players, as shown in Figure 8.  
In the positive zone, the percentage of rule-based AI was 55.05%, and the percentage of human players was 44.95%. The rule-based AI agents ended the game with a positive score (won) 10.10% more often than the human players. The rule-based AI agents tended to end a game with a positive score of 11 to 25, higher than the human players, which had positive scores of 8 to 22. The strategies to maximize the winning score worked because rule-based AI agents often achieved a high winning score. The rule-based AI agents outperformed the human players to end a game early and leave the human players with many cards. In the negative zone, the percentage of rule-based AI was 48.32%, and the percentage of human players was 51.68%. The human players lost with many cards left 3.36% more often than the rule-based AI agents. The rule-based AI agents tended to end a game with a negative score of \(-7\) to \(-1\), better than the human players, which had negative scores of \(-9\) to \(-1\). These results indicate that the strategies used to minimize losses in rule-based AI are effective. The rule-based AI agents could minimize the number of cards left when the chance of winning was low. We can conclude that rule-based AI significantly outperforms human players. Overall, the experimental results show that our AI agent played well in all the experiments that have been conducted.