Case 1: Suppose that Ram has A amount of money and Shyam has infinite amount of money and they play this gamble using an unbiased coin. In that case the transition probability matrix looks as given below

Case 2: Suppose that Ram has A amount of money and Shyam has B amount of money and they play this gamble using an biased coin, such that the probability of Ram winning one unit of money is  and losing one unit of money is . In that case the transition probability matrix looks as given below

Case 3: Suppose that Ram has A amount of money and Shyam has B amount of money and they play this gamble using an biased die, such that the probability of Ram winning one unit of money is when numbers 1 or 2 come, losing one unit of money is when numbers 5 or 6 come, and the outcome of the game being a draw when numbers 3 and 4 come. In that case the transition probability matrix looks as given below