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2026-08-12

Maybe a maximally stressful tennis match will make it easy to gain an advantage but hard to actually win

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• personal
• target audience - friends and potential friends

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• Link to relevant SE question. Also quoted below in case link breaks.
• Title should be self-explanatory
• I now have ideas for a potential solution:
  • Whenever both players are at approximately equal points, it should be easy for either player to score a few points and get a big advantage. Once a player has gotten a big advantage, it should be hard for that player to lose that advantage but also hard for them to win the match completely.
  • Example 1 of such a points system:
    • A Match is composed of a series of Rounds. Each Round is composed of a series of atomic Points.
    • Each Round has a Lead that is required to be obtained, for the round to end. For instance, if the Lead is 3, then scoring 5-2 ends the round, as does 4-1 or 6-3. Once the Lead is obtained, the Round immediately ends.
    • Every Round also has a player designated the Leader and the other is the Follower. If the Leader wins the Round, then they continue to be Leader, however the Lead required next Round is incremented by 1. If the Follower wins the Round and the Lead is 2 or more, then they typically continue to be the Follower, however the Lead required is decremented by 1. If the Follower wins the Round and the Lead is 1, then the Follower becomes the Leader, the Leader becomes the Follower and the Lead remains.
    • For Round 1, the Lead is just 1. Whoever gets a point advanced to next round.
    • If the Lead hits 10, then the Leader wins the Match.
    • Example of a playthrough:
      • A (1-0, Lead=1, Leader is A) A B A B A A (4-2, Lead=2) B B A B B (1-4, Lead=3) B B (0-2, Lead=2) A (1-0, Lead=1) B (0-1, Lead=1, Leader switches to B) A B A B B A B B (3-5, Lead=2) B B B (0-3, Lead=3) A A A B A A (5-1, Lead=4) B A B A B B B (2-5, Lead=3) A B B B A B B B (2-6, Lead=4) B B B B A B B (1-6, Lead=5)
      • B now has a Lead of 5. (If 5 was the Lead required to win the match, then B would win the match here.)
    • Obviously the Rounds with small Leads are the highest stress, but even Rounds with larger Leads can ideally have decent Stress in this points system.
    • I haven't written a program to actually compute the Stress generated by this points system. I am not sure if this solution works or not.
  • Example 2 of such a points system:
    • Use the same rules as Example 1 but with a major exception. All Rounds must play a minimum of 10 Points, even if a player has scored the required Lead for that Round. Round ends when either a) 10 Points have been played and one player has obtained the required Lead or b) 10 Points have not yet been played but one player is sufficiently many Points ahead that it is mathematically guaranteed they will be ahead by atleast by Lead once the 10 Points are played.
    • Example of a playthrough:
      • A B A A B B B B B (3-6, Lead=1, Round ended before 10 Points, Leader is B) A B A B A A B A B B B B (4-6, Lead=2) A B A B A B B A A A B A A (8-5, Lead=3) B B B B B B (0-6, Lead=2, Round ended before 10 Points) B B A B B A B B A B (3-7, Lead=3) B B A B B B B A B (2-7, Lead=4, Round ended before 10 Points)
      • Leader never switched in this particular playthrough. B now has a Lead of 4. (If 4 was the Lead required to win the match, then B would win the match here.)

Asked by ghosts_in_the_code in 2015-02

Some sports, such as tennis, use a complicated points system (point, game, set, match; with deuces and tie-breaks) for what would otherwise be an extremely simple and monotonous sport. The main reason, I suppose, is to make the sport more stressful, by making some parts of the match more crucial than others. It should be possible to make it a lot more 'stressful' mathematically.

Mathematical scenario: There is an event, played by 2 players, worth 1 point. The probability of winning the entire match, if they (a) win (b) lose the next point is calculated. The difference between these values is the 'stress' value of that point. The sum of all the stress values is called the 'total stress' value of the match, and this number divided by the number of points played is the 'average stress'. For players of equal skill, and stress-handling, the probability of either player winning any given point is 12 . The 'skill' of a player is a randomly generated number from 0% to 100% , and the probability of a player winning a point is given by Skill(own) / ( Skill(own) + Skill(opponent) )

Your job is to create a points system, however simple or complicated, using any kind of conditions, limits, etc, that produces the maximum possible: (a) Total stress (b) Average stress for a match. You are allowed to create your own definitions of 'point', 'set' and so on, however, the 'points' I am referring to is a single valid serve (double faults to be ignored) with a single winner.

The only constraint is that the total number of points played should be between 1000 and 1500 for at least 90% of the scenarios (9 in every 10 matches should not have the players play less than 1000 or more than 1500 points).

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