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John and Shane are playing a game, where after each round you get 1 point if you win and lose 1 point if you lose the game. The winner is the one who first reaches 4 points. In how many ways can any one of the players win?

I had this question in the exam yesterday and I was trying to solve it by taking either of the two possibilities game after game and add them all, but I thought it wouldn't work if in general if we have $n$ points for winning.

So can anyone help me show how to solve it?

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    Maybe the answer is that there is only one way: $4$to -4. Or maybe two ways, one for each player. It sounds silly, but as user38034 shows, there is no useful answer if you count different orders of win/loss as different ways.2012-08-24

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If player a is awarded a point then player b loses a point and also the other way around. Therefore the final score is always going to be 4,-4 or -4,4. However there are infinite number of ways this can happen. The game can last 4 turns, 6 turns, 8 turns, any even number of turns. Therefore there are infinite ways it can happen but only two possible outcomes.