Results

In this section we present the results of our experiments. We simulated 7560 games for each of the conditions, using each possible distribution of cards once. The following tables show the average number it takes until at least one player knows her cards. In the Kooi's Choice condition, not all games have a winner after 60 turns. To be able to sensibly compare the average number of turns under the different conditions, we only took those games into account which had a "winner" under all conditons. This was the case in 78.21 percent of the games. The table also shows the percentage of games which had a winner under each separate condition. In addition to the average number of turns, the standard deviation of the number of turns is shown as well (after the ±-sign).

Standard games

	No epistemagic	Epistemagic once	Epistemagic infinite
Average number of turns	8.29 ± 4.74	6.98 ± 3.53	6.82 ± 3.46
Games finished (%)	100.00	100.00	100.00

Kooi's Choice

	No magic, possible	No magic, full
Average number of turns	22.83 ± 10.64	16.55 ± 5.43
Games finished (%)	79.39	99.39

	Epistemagic once, possible	Epistemagic once, full	Epistemagic infinite, possible	Epistemagic infinite, full
Average number of turns	17.67 ± 3.58	15.39 ± 3.82	17.40 ± 3.98	15.06 ± 3.81
Games Finished (%)	99.07	98.97	99.02	98.85

Distribution of winners

In addition to the number of turns games last on average, we also kept track of the number of times each player wins. The following plot shows the distribution of winners in 6 of the 9 conditions (recall that a game can have multiple winners):

Note that in the plot only Kooi's choice games in which player's choices are based on the information gain in states considered true are shown, because we know that is the most effective way to stall the game. From the plot it is clear that the third player is most likely to be a winner. This should not come as a surprise: She will always hear information from the other two players before having to give information herself. For the Kooi's choice condition, using epistemagic has a dramatic effect on the shape of the distribution. We believe we can explain this in the following way: When players can choose their own questions and a game takes at least twenty turns, the second player is forced to answer the twentieth question. This question was not chosen before because it has a very large information gain. That is why the second player has a disadvantage when players choose their own questions. Using epistemic reasoning shortens the length of the game, making it less likely that the twentieth turn is reached and thereby removing the second player's disadvantage to a certain extent.

These results are analyzed thoroughly in our conclusion.