Try it online: https://dotnetfiddle.net/Q32WcF

bowling.cs

using System;
using System.Linq;
using System.Collections.Generic;

public class Program
{
	// https://bowlingguidance.com/all-about-strikes-and-spares-in-bowling/
	static int Score(IList<int> pins)
	{
		bool startsWithStrike(IList<int> list) => list[0] == 10;
		bool startsWithSpare(IList<int> list) => list[0] + list[1] == 10;
		int Loop(int accumulator, int turn, IList<int> list)
		{
			//Console.WriteLine($"{turn}: {accumulator}");
			if (turn == 0)
			{
				return accumulator;
			}

			if (startsWithStrike(list))
			{
				return Loop(10 + list[1] + list[2] + accumulator, turn - 1, list.SkipList(1));
			}

			if (startsWithSpare(list))
			{
				return Loop(10 + list[2] + accumulator, turn - 1, list.SkipList(2));
			}

			return Loop(list[0] + list[1] + accumulator, turn - 1, list.SkipList(2));
		}

		return Loop(0, 10, pins);
	}

	public static void Main()
	{
		var zeros = Enumerable.Repeat(0, 20).ToList();
		Console.WriteLine(Score(zeros) == 0);
		
		var zerosAndOne = Enumerable.Repeat(0, 19).Prepend(1).ToList();
		Console.WriteLine(Score(zerosAndOne) == 1);
		
		var zerosAndStrike = Enumerable.Repeat(0, 19).Prepend(10).ToList();
		Console.WriteLine(Score(zerosAndStrike) == 10);
		
		var strikes = Enumerable.Repeat(10, 12).ToList();
		Console.WriteLine(Score(strikes) == 300);
		
		var zerosAndSpare = Enumerable.Repeat(0, 18).Prepend(9).Prepend(1).ToList();
		Console.WriteLine(Score(zerosAndSpare) == 10);
		
		var spares = Enumerable.Repeat(new []{9, 1}, 10).SelectMany(x => x).Append(9).ToList();
		Console.WriteLine(Score(spares) == 190);
	}
}

public static class Extensions
{
	public static IList<T> SkipList<T>(this IList<T> list, int n) => list.Skip(n).ToList();
}

True. Smaller problem is easier to reason with