Cluedo is a game of imperfect information. We can only compute the likelihood of the expectation of winning the game. Let us consider you as Player 1. In ordinary Cluedo game, if no one has a card to disprove a suggestion, that card may be in the case file or if you asked your own card, your opponents may confuse. In our game, a minor variation is that if no one has a card to disprove a suggestion and you have not this card, that card may be either in the case file or on the table.
Whatever original Cluedo or variation Cluedo, you can ask one or two of your own cards combined with unknown cards. In our version, this move can get the knowledge of the particular card, which is either on the table or in your opponent’s hand. If the particular card is not your opponent’s card or on the table, you may know this card is in the case file.
Alternatively, you may suggest all of three unknown cards and you may get at least one card’s information. In every turn, you should eliminate one impossible card that may not be in the case file.
If you ask all of your own cards, there is no advantage for you to get any information from your opponent even though you may mislead your opponent. However, in our Cluedo version, you may get a chance to swap out with one card on the table and you may know at least which card on the table.
To play wisely, you should observe that what cards your opponent suggested or showed in previous turns. Then you can use the knowledge of the cards in your opponent’s hands and deduce the next suggestion or make an accusation.
If you have more than one card of your opponent suggested cards, you should show one card that has been already shown in previous turn. In that way, your opponent could not get more information from your show.
Imagine the situation that you know the actual murderer, weapon and r1 or r3 may be the actual room card. How you decide whether you will make an accusation or you will wait the next turn? For multi player game, you should make accusation because the other players may make the correct accusation before your next turn. For our two-player version, it is better to sure that all cards you know are in the case file. To prevent your opponent’s correct accusation before your next turn, you may make mislead to your opponent.
In our game, Player 1 makes suggestions strategically to win during the less number of moves. First time, Player 1 makes a suggestion with unknown suspect and two of his own cards. Second time, he makes a suggestion with unknown weapon and two of his own cards. Third turn, he makes a suggestion with unknown room and two of his own cards. Then, he continues to ask one unknown card with two known cards. The unknown card must be the one that is not sure for the actual card in the case file and the one that is not in the impossible list.
Let P1 be Player 1, d be the function dealing, sure be the list of cards Player 1 knows that cards are in the case and imp be the list of cards that are impossible in the case file.
If d(s1)=P1, d(w3) = P1, and d(r2) = P1, then we can state P1’s suggestion as follows.
P1[suggest] : (¬sure ¬imp (s2 ˅ s3 ˅ s4) ˄ w3 ˄ r2) ˅ (s1 ˄ ¬sure ¬imp (w1 ˅ w2 ˅ w4) ˄ r2) ˅ (s1 ˄ w3 ˄ ¬sure ¬imp (r1 ˅ r3 ˅ r4)