Count conditional probability of winning a game 
In a certain game of tennis, Alice has a 60% probability to win any
  given point against Bob. The player who gets to 4 points first wins
  the game, and points cannot end in a tie. What is Alice's probability
  to win the game?

When solving in terms of a random walk it gives a probability around 83%, but the actual solution for this particular problem is around 71%.
What's the difference between the methods used and how correctly solve such kind of problems?

Just as a generalization for the answer above, formula for getting N points in a game first
$\sum_{i=0}^{N-1}{N-1+i\choose i}\cdot p^N\cdot (1-p)^{i}$ 
So in our case we have N=4, p=0.6, q=1-p=0.4
$\sum_{i=0}^{3}{2+i\choose i}\cdot 0.6^4\cdot 0.4^{i}$ 
which gives us 0.71 as a result.
