I am trying to quantify the win probability of a game where two players have equal skill but one gets more attempts to achieve the best result. Can someone help me define a mathematical formula to solve a problem like this for example:
Two dart players have equal skill.
Player 1 gets 100 attempts to get closest to the bullseye.
Player 2 gets only 1 attempt.
What is the probability that player 2 wins?
For the sake of simplicity we will assume that darts are marked and removed after each throw, so there is no chance darts interfere with each other, and that no other outside forces impact the results. We will also assume that there is an infinite level of exactness to the measurement of who is closest, so there will be no ties.
Hint: Since the two players have equal skill, their collective 101 attempts can be lumped together into a single pool. You're then asking the probability that a particular distinguished one of those attempts (the one corresponding to Player 2) is the best one.
Can you see where to go from here?