First, we start with the total number of tickets Delon has, which is 37. He uses 4 tickets for the carousel, so we need to subtract that from his total:
\[ 37 - 4 = 33 \]
Now, Delon has 33 tickets remaining to use for the roller coaster. Each ride on the roller coaster uses 3 tickets. To find out how many times he can ride the roller coaster, we divide the remaining tickets by the number of tickets per ride:
\[ \frac{33}{3} = 11 \]
Therefore, Delon can ride the roller coaster 11 times.
The answer is 11.