Let's say 2 players play a game where 2 players will keep uttering one sentence out of some random given sentences. Rules of game are either "A" or "B" needs to pick of one sentences in random from their own lot (player A has N , player B as M) and utter that sentence. The opponent has the capacity to remember only last "2" sentences uttered by other one (he wont remember his own).If one is taking other can't talk, he just listens and records.If the one playing repeats the same sentence uttered by him in recent past (last 2 sentences only) since the 2nd one who has record of his opponents last 2 sentences ,cross verify and says he won and player who is playing loses.
eg: Player A --> sentences --> phone , milk , stone ( "N") Player B --> sentences --> apple , tv , pc,laptop ( "M" ) Lets say A starts game and B continues like as shown below
A-> phone (now B records this in his memory ) B-> tv (now A records this in his memory ) A -> stone (now B records this in his memory --> phone ,stone ) B -> pc (now A records this in his memory --> tv,pc) A -> milk (now B records this in his memory --> stone,milk removes phone as he can store only recent 2 ) B -> pc (since A has this in his memory so A wins)
How many number of minimum iterations are required for completing the game and chances of one's winning?