The probability is one-half. If you look at the picture of the Push Penny board, you'll notice that the shaded strips are one diameter wide, and the unshaded strips are also one diameter wide:
This means that, if the game is random, it is just as likely for the coin to land on a shaded strip as on an unshaded strip. This makes the probability of hitting a line (and landing on a shaded strip) equal to one-half, or 50%.
Let's use a probability table to compare the experimental probability for this player to the probabilities for a random player:
This player seems to have improved. In particular, this player's experimental probability of getting four hits in four tries is more than three times larger than the expected probability for a random player. This suggests that this player has developed skill in playing Push Penny.