We might not have captured the complete extent in which epistemic logic influences the games by just looking at the amount of turns a game takes. It is quite possible that during a single game epistemic logic causes a great difference in the amount of possible worlds for the agents, but that this gets evened out as the game progresses, having the game end in the same amount of turns anyway.
There is also a small difference in the amount of winners between the magic and no-magic games. In the games where epistemic logic is used it is possible to have three winners at once, because all three players gain information when it is clear that the others do not know the answer yet. While in the no-magic games only the two other players than the one answering the question get new information, so there can be at most two winners at once. We can conclude from this that the game is not completely a logicians game and is still based somewhat on luck with regard to which information you will get and if it will be enough for you to draw the right conclusion before the others.
With Kooi's Choice enabled "What's My Number?" becomes more of a logician's game. When we use Kooi's Choice in a game without epistemic logic we see that the game gets stalled to such an extent that there are a lot less games that end in someone winning. This is because Kooi's Choice makes agents give out as little information as possible while they do not use all information possible to infer the true state. With epistemic logic we still see some stalling but to a much lesser extent than without the logic step. As with the standard game using infinite epistemagic makes games last a little bit shorter.
Using Kooi's Choice while looking at the full model instead of just the possible worlds in the model slightly decreases the stalling effect of Kooi's Choice. While the amount of worlds disproven in the total model by answering a question might be very large, this does not mean that the amount of worlds disproven for the other agents is also very large. A question disproving less worlds in the total model might have a greater effect on the agents possible worlds than a question which disproves a lot of worlds in the total model. Since using the full model in KC prioritizes the epistemic step over the simple deduction step, this result seems to indicate that the simple deduction step is more important in winning the game.
In conclusion, the use of epistemic reasoning affects the course of the game in at least two ways. Games take less turns on average before there is a winner, an effect which is especially strong under the Kooi's choice condition. In addition to that, the use of epistemic reasoning also dramatically alters the distribution of win probabilities under the KC condition. Since that distribution becomes more uniform, epistemic reasoning has the interesting effect of making the game fairer.
Future work could be done in implementing different player styles in the same game and researching how that influences the game. Another interesting feature when implementing different player styles would be to implement a lying player. This player answers questions randomly or always wrong but nobody knows who the liar is. Players will need to have the possibility to add possible worlds to the model and not only remove them. A wrong answer could remove the wrong world but then somebody elses answer might make that world a possibility again. It would also be interesting if we could build on this game towards the rules of the real Code 777, so we can draw conclusions if epistemic logic is actually useful for winning a commercial game like that. By counting the information gain per question we can also say wether the questions are fair or not. Qua implementation it might be more efficient to explicitly keep track of the states players consider possible in a certain set by a set-like data structure, instead of coding for all states whether they are considered possible or not.
