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?

Define $p_n$ as the probability of the sum reaching exactly $n$. Try to find a reccurence relation for $p_n$.
The starting conditions are $p_2 = \frac{1}{6}$, $p_3=\frac{1}{6}$, you will have to first work out $p_4, p_5$ and $p_6$ as they are slighly special, but from then on, it should be simpler. The probability of reaching $n>6$ is the probability of reaching $n-2$ and rolling $2$ or reacing $n-3$ and rolling $3$ and so on.
Once you have $p_n$ for general $n$, just calculate $p_{100}+p_{101}+\dots + p_{104}$
