How to make a game where match duration is determined only by skill disparity between the best player and the second best player?

Question

I want to create a real-time multiplayer game (with a variable number of players, potentially 2-20+, per match) where the match duration is determined only by how much better the best player is compared to the second best player. Thus, 2 properties are required:

1. Game duration is independent of the number of players. Racing games have this property in that the time it takes for a match to end (which is how long it takes the best player to finish) is independent of how many players are playing. However they don't have the 2nd property.

2. Game duration is inversely proportional to the skill disparity between the best and second best players - we want close games to last longer than complete stomps. I'm not aware of any game where there is such a strong correlation between match duration and skill disparity that one could say it's the rule. I mean, in Chess, if one is really bad, one could be mated in a few moves, and if two players are close in skill, then games might last really long, but this is not certain. In any case, these games tend to not have the first property.

How might one design a game that has both properties?

Answer 1

Im not quite sure if this example really fits your two requirements, but Micro Machine games have an elimination mode that basically does that.

1. The Game duration is idependent of the number of players, as its only important, when the second best player gets eliminated.
2. Game duration is inversely proportional to the skill disparity between the best and second best players - the better the best player, the sooner everyone else gets eliminated.

Only problem would be, that you could argue at 1. that more players could interact more and thus disturb the other players, like the first and the second best player. The alternative would be to disable player interaction at all.

Answer 2

Here's a solution I thought up (but consider to be imperfect):

Racing game except when the top player pulls ahead of the second player by a certain distance, the race ends instantly. This way, if two players are roughly equal in speed, the race can go on really long, but if the top player is much faster than everyone else, then the game ends pretty quickly.

The problem with this game is that there has to be no personalized interaction between players, and if there's no player-player interaction then the game will feel boring.

The problem with having player-player interaction is that the minimal total duration will inherently depend on the number of players (assuming there is a minimal amount of time that a player-player interaction will take and that we want all players to interact with the best player). I suppose one way to minimize the problem here would be to make the interactions really short and repeat them a lot over time (so that the worst players only interact with the best player once each whereas the second best player might interact with the best player hundreds of times). But I'm not sure how such a game might be constructed.