I played a game over the weekend in which players are required to roll a single fair die in independent trials. The objective was to roll a specific number 5 times before another specific number was rolled. If you rolled specific number X, you would get a point, but if you rolled specific number Y, your points would reset to 0. Non-X or Y numbers would not affect your score.
For example, say you had to roll five 3s before rolling a single 6. You may roll as many 1s, 2s, 4s, and 5s as you please without consequence; the only way to end the sequence is five cumulative 3s OR a single 6.
I don't know where to begin calculating the odds of this so any help is appreciated. Thanks in advance!