What is the probability to win? Die game You have a die. If you get one pip at any point in the game you lose. If you get two,..., six pips you start adding the number of pips to a sum. To win the sum must get greater or equal to 100. What is the probability to win the game?

An alternative approach, which still requires numerical calculation is to define a system state as the cumulative score. The system starts in state $0$ and there are a couple of absorbing states $L$ (lost) and $W$ (won). This yields 102 possible system states ${0,1,2,...,99,L,W}$. Each roll of the dice transforms the system state and it is straightforward to create the 102$\times$102 state transition matrix, $T = (p_{ij})$ where $p_{ij}$ is the probability of moving from state $i$ to state $j$. 
Multiplying $T$ by itself $n$ times, yields a matrix of the state transitions resulting from $n$ rolls of the dice and the row of this matrix corresponding to state $0$ yields the distribution of possible outcome states after these $n$ rolls. Taking $n\ge50$ ensures that for such outcomes only $L$ and $W$ have non-zero probabilities. (Note that whilst it is possible to lose from the first roll onwards, the definition of $L$ as an absorbing state with a corresponding transition $L \to L$ having a probability of 1 in $T$ means that it is legitimate to include rolls beyond the losing one. Similarly, defining $W$ as an absorbing state means we can consider rolls after the game is won.)
In my calculation procedure, I constructed $T$ and from this derived $T^2,T^4,T^8,...,T^{64}$. From the latter my results indicate that the probability of winning is 0.010197(to 6 decimal places).
