Bob is playing a dice game in which he rolls a fair dice multiple times. If he rolls $n$ times under the number $4$ (not necessarily consecutively rolls) he loses the game, and consequently, if he manages to roll $4$ or more $n$ times he wins.
How could we calculate the chance that Bob loses? It is simple to determine the outcome of a single dice roll, and that, in the worst case scenario, he has to roll $2\cdot n-1$ times in order for the game to complete but I am not sure how to approach this problem?