It has been brought to my attention that there exist people in this universe who do not know how to keep score in bowling. Most online resources suck for this so I'll give it a go myself. Also, I'll explain what No-Tap means.
Part 1: Scoring in Bowling
Overview
As you hopefully know, bowling is a game where you throw a ball at pins and attempt to knock them down. The more you knock down, the more points you get. I am focused only on 10-pin bowling; the type with 10 pins in a triangular formation. Each frame (there are 10 frames in a game) you have two chances to knock the pins down. If you knock down all 10 on the first throw it is a strike. If you knock some down on the first throw and the rest on the second throw it is a spare.
Ex 1) You knock down 7 pins on your first throw, and 2 pins on your second throw for a total of 9 pins* every single frame. Result: You scored a 9 for the first frame, a 9 for the second frame, etc, up to 10 frames, so you total score is 9 * 10 = 90.
*Any time you get neither a spare or a strike for a frame, it is called an open and is bad to get.
Spares
Getting a spare entitles you to a bonus. Suppose your first throw of frame 1 is an 8, and the second throw is a 2. This is called "8 spare" or "8/". In addition to the 10 pins you earned for this frame, you can get additional pins equal to the value of the next throw. So, if your first throw in the second frame is a 9, then the total points that you earned for your first frame are 10 pins plus 9 pins = 19.
Ex 2) In your first frame you throw a 7/. In your second frame you score a 8/. In your third frame you throw a 6 and then a 3 for a total of 9. How many pins have you earned so far? Result: You initially earned 10 pins in the first frame, however, that spare entitled you to more pins. Since your first throw in your second frame was 8, you get 10+8 = 18 pins for the first frame. In the second frame you initially scored 10 pins, however, you also get to add 6 pins since you had a spare in the second frame. The second frame earns you 16 pins. So after the second frame you have 18 pins from the first frame plus 16 pins from the second frame for a total score of 34. Then in the third frame it was an open and you only scored 9 pins. So, after the third frame you had 34 pins plus 9 pins = 43.
Strikes
The best thing you can do in a given frame is knock down all 10 pins on the first throw. When you get a strike you are entitled to even more bonus pins than a spare entitles you to. Recall that a spare lets you add the value of the first throw from the NEXT frame to your current frame's total score. A strike lets you add the value of the next TWO throws to your current frame. This gets a bit more complicated so one example won't quite be enough.
Ex 3) In your first frame you get a strike. In your second frame you get a 6/. What is your score? Results: You initially earned 10 pins for the first frame. However, you get to add bonus points depending on your result in the second frame. You are allowed to add the total value of the next two throws to your first frame score. Since you rolled a 6 and then a 4 in the second frame, you can add each of these to your first frame score. So your first frame score is 10+6+4=20. Your 6/ entitles you to a bonus also, but since we haven't bowled the third frame yet, we don't know what it is. Thus, our current score is 20+10=30.
Ex 4) You bowl a strike in the first, a strike in the second, a 7 and then a 2 in the third. What's the score? Result: You earn 10 points initially in the first plus two throws of bonus points. Since your second throw was a 10 (strike) and your third throw was a 7, you can add 17 bonus points to your first frame score. Thus, your score after the first frame is 10+10+7 = 27. In the second frame you initially earned 10, but also got a bonus of 7+2. Thus, you earned 19 points in the second frame. Your total score after 3 frames will be 27+19+9=55. As you can see, chaining together multiple strikes gets your score high very quickly!
10th frame
The 10th and final frame is scored a little differently than the other frames if you manage to get a strike or a spare. The concept of 'bonus points' can be thought of as not existing anymore, but you are entitled to make more throws. If you get an 8/ in the 10th, then you can throw one more time for a chance to get up to 10 additional pins. These pins from the third throw will not get added to the value of the 8/ and will just count normally. After all, you are getting a bonus (third) throw already anyway. If you get a strike at the beginning of the 10th, then you are entitled to two additional throws. As with spares, strikes in the 10th don't entitled you to bonus points, but do give you a chance to throw the ball more times. So, if you get a strike as your first throw in the tenth, and a strike for the second throw, then you can make a third throw with a chance to earn another 10 pins for a frame total of 30 pins. These rules my seem strange/arbitrary but they should make sense if you stop to think about how many pins maximum you can get in a normal frame, and how many pins maximum you can get in the 10th frame using these modified rules.
Ex 5) In the 10th frame you throw 6/ X. Result: you earned 10 points for the 6/ and 10 points for the X for a total of 20.
Ex 6) In the 10th frame you throw X X 7. Result: 10+10+7 = 27.
Ex 7) In the 8th frame you throw a X, in the 9th frame you throw a X, in the 10th frame you throw a XXX. How many pins did you earn from frames 8-10? Result: In the 8th you earned 10 initially, plus 10 from the first bonus throw, plus 10 from the second bonus throw for a total of 30. From the 9th you earned 10 initially plus 10 for the first bonus throw plus 10 for the second bonus throw for a total of 30. In the tenth you knocked down 30 pins for a total of 90 points earned for the last 3 frames.
Ex 8) In the 10th you throw a 5 and then a 3. Are you entitled to a third throw? Result: No.
Review
You get two chances to knock down all the pins. If you knock them all down on the first throw it is called a strike and you are entitled to add the value of your next two throws to the score of the current frame, esentially making your next two throws count double or triple what they normally would (very good). If you knock the pins down on your second throw it is a spare and entitles you to add the value of your next single throw to the score of the current frame. Essentially, your next throw counts double towards your score (good). In the 10th frame you don't get bonus throws added to your score, but get a third throw within that frame if you get a strike or a spare, thus making the total number of pins you can earn in the 10th 30 just like any other frame.
Problems
Here are a few problems I put together with answers to make sure you know how to keep score.
Problem 1: You throw nothing but strikes for the entire game.
a) How many throws did you do?
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You threw the ball once for frames 1-9, and then 3 times in the 10th for a total of 12 throws.
b) What was your score?
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You earned 30 in the first, 30 in the second, etc, 30 in the 10th, for a total of 30*10 = 300. 300 is the max score you can get in a game of bowling without handicaps.
Problem 2: Convert the following score diagram into the final score:
9/ X X 62 X X X 3/ 9/ 8/X
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I will place how many points earned from each frame, in order:
20, 26, 18, 8, 30, 23, 20, 19, 18, 20
Thus, the total score is the sum of these, or 202.
20, 26, 18, 8, 30, 23, 20, 19, 18, 20
Thus, the total score is the sum of these, or 202.
Part 2: No-Tap Scoring
Yesterday I played in a 'no-tap' tournament. It is the same as normal bowling except any time you get a 9 on your first throw in a frame it counts as a strike. Essentially, 9 or 10 pins both count as a strike. As you might have guessed, this makes it much easier to bowl a very high score. I've actually had a 300 with no-tap rules during a tournament (they are pretty common).
I don't remember my games exactly yesterday, but I'll make one up that's similar to one I played:
9/ 9/ 72 X X 9/ 63 X X XX9
By conventional scoring I got a 208. However according to No-Tap all of those 9's were really strikes:
X X 72 X X X 63 X X XXX
By No-Tap scoring I got a 229. This game doesn't have a huge difference in score between regular scoring and no tap scoring due to the small number of 9's and placement of open frames. However, I leave it as an exercise to the reader to determine how big of a difference no tap scoring would make for the following game:
9/ X 9/ 8/ 9/ X 9/ X X 9/9