In order to obtain the scores in the figure above, we need to determine the rules of scoring certain components. The following will explain how to score a strike, spare, open, and the 10th frame.

The most basic algorithm or rule is: The total running score is the sum of the current frame plus the previous frame. The total running score is shown underneath what the bowler got on each roll. In the example above, the running total goes: 9,29,55,74,83,89,109,124,133, and 163. It is assumed that the previous frame score for the first frame is 0.

Special Rules for calculating individual frame scores:
The strike is worth 10 plus the next two throws, not the next two frames. Unless the next two throws are strikes. Then that would be the next two frames.

The Spare is worth 10 plus the next throw.

An Open is just worth the total number of pins knocked down in the frame.

The 10th Frame's individual score is just the total number of pins knocked down. The spare and strike rules do not apply.