Bowling: Improved clarity of scoring system

bowling.md

@@ -4,23 +4,33 @@ of a game of bowling.
 
 ## Scoring Bowling
 
-The game consists of 10 frames. In each frame the player has two
-opportunities to knock down 10 pins.  The score for the frame is the
-total number of pins knocked down, plus bonuses for strikes and spares.
-
-A spare is when the player knocks down all 10 pins in two tries.  The
-bonus for that frame is the number of pins knocked down by the next
-roll. For example a player rolls in the first three frames respectively
-4+2, 3+7 and 5+1. For frame 2, the score is 10 (the total number knocked
-down) plus a bonus of 5 (the number of pins knocked down on the next roll.)
-
-A strike is when the player knocks down all 10 pins on his first try.
-The bonus for that frame is the value of the next two balls rolled
-(the value of the next frame, not counting the bonus).
-
-In the tenth frame a player who rolls a spare or strike is allowed to
-roll the extra balls to complete the frame.  However no more than three
-balls can be rolled in tenth frame.
+The game consists of 10 frames. A frame is composed of one or two ball throws with 10 pins standing at frame initialization. There are three cases for the tabulation of a frame.
+
+* An open frame is where a score of less than 10 is recorded for the frame. In this case the score for the frame is the number of pins knocked down.
+
+* A spare is where all ten pins are knocked down after the second throw. The total value of a spare is 10 plus the number of pins knocked down in their next throw.
+
+* A strike is where all ten pins are knocked down after the first throw. The total value of a strike is 10 plus the number of pins knocked down in their next two throws. If a strike is immediately followed by a second strike, then we can not total the value of first strike until they throw the ball one more time.
+
+Here is a three frame example:
+
+| Frame 1         | Frame 2       | Frame 3                |
+| :-------------: |:-------------:| :---------------------:|
+| X (strike)      | 5/ (spare)    | 9 0 (open frame)       |
+
+Frame 1 is (10 + 5 + 5) = 20
+
+Frame 2 is (5 + 5 + 9) = 19
+
+Frame 3 is (9 + 0) = 9
+
+This means the current running total is 48.
+
+The tenth frame in the game is a special case. If someone throws a strike or a spare then they get a fill ball. Fill balls exist to calculate the total of the 10th frame. Scoring a strike or spare on the fill ball does not give the player more fill balls. The total value of the 10th frame is the total number of pins knocked down.
+
+For a tenth frame of X1/ (strike and a spare), the total value is 20.
+
+For a tenth frame of XXX (three strikes), the total value is 30.
 
 ## Requirements