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Tennis Scoring: Relationship b/w Points Won + Games Won
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| class Game: | |
| def __init__(self): | |
| self.p1_points = 0 | |
| self.p2_points = 0 | |
| def who_won(self): | |
| ''' | |
| 0, 1, 2, 3, 4 | |
| 0, 15, 30, 40, win (need 4 points to win, and to win by 2) | |
| ''' | |
| if self.p1_points >= 4 and self.p1_points - self.p2_points >= 2: | |
| return 'p1' | |
| if self.p2_points >= 4 and self.p2_points - self.p1_points >= 2: | |
| return 'p2' | |
| import random | |
| P1_CHANCES = range(50, 100, 1) | |
| def p1_wins(percent): | |
| return random.randrange(100) < percent | |
| from collections import Counter | |
| ROUNDS = 10_000 | |
| p1_results = [] | |
| for p1_chance in P1_CHANCES: | |
| wins = Counter() | |
| for _ in range(ROUNDS): | |
| game = Game() | |
| while not game.who_won(): | |
| if p1_wins(p1_chance): | |
| game.p1_points += 1 | |
| else: | |
| game.p2_points += 1 | |
| wins[game.who_won()] += 1 | |
| p1_result = (wins["p1"]/ROUNDS) * 100 | |
| p1_results.append(p1_result) | |
| print(f'when p1 has a {p1_chance}% chance to win each point, p1 wins {p1_result}% of games\n') | |
| relationships = [rel for rel in zip(P1_CHANCES, p1_results)] | |
| print(f'relationships:\n {relationships}') |
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output from local run shows a non-linear relationship b/w the odds of winning a point and the odds of winning a game, with the odds of winning a game increasing faster as the odds of winning a point increase until an inflection point when the chance to win each point is ~70%: