# whats the probability of winning the following game and how many trails are required for it

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?

• This requires some clarifications. 1) Do the players speak alternatingly? If not, how is it determined who speaks when? 2) Are you using "words" and "sentences" interchangeably, or are you making a distinction between the two? 3) It's not clear (to me) exactly which utterances must not be repeated. Is it a) one's own last two utterances, b) the opponent's last two utterances, or c) the last two utterances in the game (i.e. the opponent's last utterance and one's own last utterance)? 4) Why does memory play a role if the players are anyway required to pick the utterances at random? – joriki Sep 14 '15 at 16:25
• You seem to use sentence and word as synonyms for each other. Are the sentences single worded? – karmanaut Sep 14 '15 at 16:26
• 1)Yes players speak alternatingly.Choice of selecting the first speaker is random.In simple case lets say Player A starts the game.2)corrected the question both words and sentences mean the same.3)Both of players will have N random sentences , he will pick one to utter.Other player records in memory last 2 sentences of the opponent (no one will record his own sentences) 4) Because the one playing wont remember his own sentences uttered ,opponent needs to have memory to remember last two sentences of the one playing so,he will check if the present sentence is already present in memory,he wins – bharadwaj yadati Sep 16 '15 at 9:21