The player who knows the sequence for liberties as a function of eye size (1, 2, 3, 5, 8, 12, 17) has an advantage over a player who has to read the capturing race. The general formula is
L(n) = (n^2-3n)/2 + 3
for 2 <= eye size n <= 7. Subtract the enemy stones inside to determine the number of eye liberties remaining.
Instead of using that formula it might be easier for some players to remember: '3is3, 4is5, 5is8, 6is12'. The first number is the size of the eye in question the second number is the amount of liberties it is worth before(!) an enemy stone is placed inside. To memorize this read it out loud repeatedly.
Another perhaps easier way to remember the number of eye liberties in an empty big eye is the following.
The smallest big eye (four points) has 1 extra liberty.
The next big eye (five points) has 1+2 extra liberties.
The next big eye (six points) has 1+2+3 extra liberties.
The largest big eye (seven points) has 1+2+3+4 extra liberties.