I have got a problem. The dice is thrown until 1 has been rolled twice. The two 1´s do not need to be rolled consecutively. Whenever the counter of the 1´s is one and if a 6 is rolled, then the counter of the 1´s is reset to zero, i.e. at least two more 1´s have to be rolled in order to end the game. Questions: What is the average number of dice throws ? How often is the counter of the 1´s reset to zero on average in the whole game?