I play a game (you can think of it as a coin tossing game) where the probability of winning a round is equal to $p$ for each round (so you can think of if you get a head $H$, you win, probability of getting a head is $p$). The game ends when I lose two rounds in a row ( so you lose if you get two subsequent tails $T$, probability of getting a seat is $(1-p)$). The question is, what is the expected number of rounds I play this game, or on average, how many matches do I play until I lose the game? Thank you for your help in finding the answer! Can we solve this using Markov chain idea?
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See this duplicate – lulu Oct 21 '22 at 13:08
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Thanks, Can we solve this using idea from the Markov chain? – Myshkin Oct 21 '22 at 13:15
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Sure. States, other than Start and End, are determined by the prior roll. Easy to write out the transitions. – lulu Oct 21 '22 at 13:32
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can you write in details please? – Myshkin Oct 21 '22 at 13:33
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One of the posted solutions to the linked duplicate uses a Markov approach to solve it for a fair coin. Just modify that. – lulu Oct 21 '22 at 13:33