4. Two students, A and B, play chess. Winning a game earns 2 points, drawing a game earns 1 point each, and losing a game earns 0 points. They play three consecutive games, and the one with more points wins. What is the probability that A wins?
4. $\frac{10}{27}$.

Each game has three possible outcomes: win, draw, or lose. For three games, there are $3 \times 3 \times 3=27$ possible outcomes. The scenarios where Player A wins are: winning all three games for 6 points, which has 1 scenario; winning two games and drawing one for 5 points, which has 3 scenarios; winning two games and losing one for 4 points, which has 3 scenarios; winning one game and drawing two for 4 points, which has 3 scenarios. In total, there are 10 scenarios. Therefore, the probability of Player A winning is $\frac{10}{27}$.