Introduction:

I saw there was only one other badminton related challenge right now. Since I play badminton myself (for the past 13 years now), I figured I'd add some badminton-related challenges. Here the first one:

Challenge:

Input: Two integers
Output: One of three distinct and unique outputs of your own choice. One indicating that the input is a valid badminton score AND the set has ended with a winner; one indicating that the input is a valid badminton score AND the set is still in play; one indicating the input is not a valid badminton score.

With badminton, both (pairs of) players start with 0 points, and you stop when one of the two (pairs of) players has reached a score of 21, with at least 2 points difference, up to a maximum of 30-29.

So these are all possible input-pairs (in either order) indicating it's a valid badminton score AND the set has ended:

[[0,21],[1,21],[2,21],[3,21],[4,21],[5,21],[6,21],[7,21],[8,21],[9,21],[10,21],[11,21],[12,21],[13,21],[14,21],[15,21],[16,21],[17,21],[18,21],[19,21],[20,22],[21,23],[22,24],[23,25],[24,26],[25,27],[26,28],[27,29],[28,30],[29,30]]

And these are all possible input-pairs (in either order) indicating it's a valid badminton score BUT the set is still in play:

[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[0,15],[0,16],[0,17],[0,18],[0,19],[0,20],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[1,9],[1,10],[1,11],[1,12],[1,13],[1,14],[1,15],[1,16],[1,17],[1,18],[1,19],[1,20],[2,2],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[2,10],[2,11],[2,12],[2,13],[2,14],[2,15],[2,16],[2,17],[2,18],[2,19],[2,20],[3,3],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[3,10],[3,11],[3,12],[3,13],[3,14],[3,15],[3,16],[3,17],[3,18],[3,19],[3,20],[4,4],[4,5],[4,6],[4,7],[4,8],[4,9],[4,10],[4,11],[4,12],[4,13],[4,14],[4,15],[4,16],[4,17],[4,18],[4,19],[4,20],[5,5],[5,6],[5,7],[5,8],[5,9],[5,10],[5,11],[5,12],[5,13],[5,14],[5,15],[5,16],[5,17],[5,18],[5,19],[5,20],[6,6],[6,7],[6,8],[6,9],[6,10],[6,11],[6,12],[6,13],[6,14],[6,15],[6,16],[6,17],[6,18],[6,19],[6,20],[7,7],[7,8],[7,9],[7,10],[7,11],[7,12],[7,13],[7,14],[7,15],[7,16],[7,17],[7,18],[7,19],[7,20],[8,8],[8,9],[8,10],[8,11],[8,12],[8,13],[8,14],[8,15],[8,16],[8,17],[8,18],[8,19],[8,20],[9,9],[9,10],[9,11],[9,12],[9,13],[9,14],[9,15],[9,16],[9,17],[9,18],[9,19],[9,20],[10,10],[10,11],[10,12],[10,13],[10,14],[10,15],[10,16],[10,17],[10,18],[10,19],[10,20],[11,11],[11,12],[11,13],[11,14],[11,15],[11,16],[11,17],[11,18],[11,19],[11,20],[12,12],[12,13],[12,14],[12,15],[12,16],[12,17],[12,18],[12,19],[12,20],[13,13],[13,14],[13,15],[13,16],[13,17],[13,18],[13,19],[13,20],[14,14],[14,15],[14,16],[14,17],[14,18],[14,19],[14,20],[15,15],[15,16],[15,17],[15,18],[15,19],[15,20],[16,16],[16,17],[16,18],[16,19],[16,20],[17,17],[17,18],[17,19],[17,20],[18,18],[18,19],[18,20],[19,19],[19,20],[20,20],[20,21],[21,21],[21,22],[22,22],[22,23],[23,23],[23,24],[24,24],[24,25],[25,25],[25,26],[26,26],[26,27],[27,27],[27,28],[28,28],[28,29],[29,29]]

Any other pair of integer would be an invalid badminton score.

Challenge rules:

• I/O is flexible, so:
  
  
  • You can take the input as a list of two numbers; two separated numbers through STDIN or function parameters; two strings; etc.
  
  
  • Output will be three distinct and unique values of your own choice. Can be integers (i.e. [0,1,2], [1,2,3], [-1,0,1], etc.); can be Booleans (i.e. [true,false,undefined/null/empty]); can be characters/strings (i.e. ["valid & ended","valid","invalid"]); etc.
  
  
  • Please specify the I/O you've used in your answer!
  
  


• You are allowed to take the input-integers pre-ordered from lowest to highest or vice-versa.


• The input integers can be negative, in which case they are of course invalid.

General rules:

• This is code-golf, so shortest answer in bytes wins.
  
  Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language.


• 
  Standard rules apply for your answer with default I/O rules, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs. Your call.


• 
  Default Loopholes are forbidden.


• If possible, please add a link with a test for your code (i.e. TIO).


• Also, adding an explanation for your answer is highly recommended.

Test cases:

These test cases are valid, and the set has ended:

0 21
12 21
21 23
28 30
29 30

These test cases are valid, but the set is still in play:

0 0
0 20
12 12
21 21
21 22

These test cases are invalid:

-21 19
-19 21
-1 1
12 22
29 31
30 30
42 43
1021 1021

Python 2, 47 bytes

lambda a,b:[61>60-a>b<3+max(19,a)for b in-~b,b]

Try it online!

Outputs a list of two Booleans. Thanks to TFeld for writing a test suite in their answer that made it easy to check my solution.

ended: [False, True]
going: [True, True]
invalid: [False, False]

The key insight is that a valid score ends the game exactly if increasing the higher value b makes the score invalid. So, we just code up the validity condition, and check it for (a,b+1) in addition to (a,b) to see if the game has ended.

Validity is checked via three conditions that are chained together:

• 
  b<3+max(19,a): Checks that the higher score b isn't past winning, with either b<=21 or b<=a+2 (win by two)


• 
  60-a>b: Equivalent to a+b<=59, ensuring the score isn't above (29,30)
  


• 
  61>60-a: Equivalent to a>=0, ensures the lower score is non-negative

Python 2, 44 bytes

lambda a,b:[b-61<~a<a>b/22*b-3for b in-~b,b]

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An improved validity check by TFeld saves 3 bytes. The main idea is to branch on "overtime" b>21 with b/22*b which effectively sets below-21 scores to zero, whereas I'd branched on a>19 with the longer max(19,a).

Python 2, 43 bytes

lambda a,b:a>>99|cmp(2+max(19,a)%30-a/29,b)

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Outputs:

ended: 0
going: -1
invalid: 1

Assumes that the inputs are not below $-2^99$.

Python 2, 97 95 75 72 71 70 69 64 55 54 52 51 50 48 bytes

lambda a,b:(b-61<~a<a>b/22*b-3)*~(19<b-(b<30)>a)

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Takes input as pre-ordered a,b.

Returns -2, -1, 0 for ended, in play, invalid.

_{-1 byte, thanks to Kevin Cruijssen}

Left part (b-61<~a<a>b/22*b-3) is a validity-check, and right part (19<b-(b<30)>a) is a check for game ended.

JavaScript (ES6),  55 53  48 bytes

^{Thanks to @KevinCruijssen for noticing that I was not fully assuming $ale b$ (saving 5 bytes)}

Takes input as (a)(b) with $ale b$. Returns $0$ (valid), $1$ (ended) or $2$ (invalid).

a=>b=>a<0|a>29|b>30|b>21&b-a>2?2:b>20&b-a>1|b>29

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C# (Visual C# Interactive Compiler), 53 52 bytes

a=>b=>b<0|a-b>2&a>21|b>29|a>30?3:a>20&a-b>1|a>29?1:2

Called as f(max)(min). Returns 3 for invalid, 1 for finished, 2 for ongoing.

Saved 1 byte thanks to Kevin Cruijjsen

Try it online!

Jelly, 25 bytes

»19«28‘<‘×+2>ɗʋ⁹×,%Ƒ“œþ‘ɗ

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Left argument: minimum. Right argument: maximum.

Invalid: 0. Ongoing: 1. Ended: 2.

Mathematically, this works as below (the left argument is $x$, the right is $y$):

$$[a]=casesacolon1\lnot acolon0\otimes(a,b)=(abmod30,bbmod31)\x,yinmathbb Z\X:=min(max(x+1,20),29)\p:=(x,y)\([X<y]+1)[X+2>y][p=otimes p]$$

Explanation:

»19«28‘<‘×+2>ɗʋ⁹×,%Ƒ“œþ‘ɗ Left argument: x, Right argument: y
»19«28‘ X := Bound x + 1 in [20, 29]:
»19 X := max(x, 19).
 «28 X := min(X, 28).
 ‘ X := X + 1.
 <‘×+2>ɗʋ⁹ X := If X + 2 <= y, then 0, else if X < y, then 2, else 1:
 < t := If X < y, then 1, else 0.
 ‘ t := t + 1.
 +2>ɗ u := Check if X + 2 > y:
 +2 u := X + 2.
 > u := If u > y, then 1, else 0.
 × X := t * u.
 ,%Ƒ“œþ‘ɗ z := If x mod 30 = x and y mod 31 = y, then 1, else 0:
 , z := (x, y).
 % “œþ‘ m := z mod (30, 31) = (x mod 30, y mod 31).
 Ƒ z := If z = m, then 1, else 0.
 × X * z.