Balancing Games

I think one reason I don't like that sort of thing is there's more ambiguity in "what it took to win the game"

It's hard to know whether an artificial advantage is proportional to the skill gap. If I win, I won't know the extent to which I should attribute that win to good play (that I ought to be proud of, and that will impress others), VS attributing the win to a potentially greater than 1/N chance of winning(that I came by artificially).

If the greater skill is the absolute advantage that leads me to a win , I will discount the achievement on account of having an absolute advantage, but I'll still feel satisfied that I have achieved a relatively higher skill level.

If an improperly calibrated handicap is the absolute advantage that leads me to a win, it's a win I'd discount on account of there being an absolute advantage, but in this case I'd garner no satisfaction from having an (artificial) absolute advantage.

Morestill the win might feel insulting or condescending if I was given a disproportionately large advantage due to my friends/competitors underestimation of my expected quality of play.

My win will also not necessarily give my competitors an update as to whether they underestimated my expected quality of play.

If the expectation is that I will win 1/N times, they won't update on my skill level if I win. (Maybe very slightly, and eventually as you play more games)

If I win when the odds are against me, people update significantly on my expected quality of play.

It feels good to know people are updating favourably on my expected quality of play.

In chess, I think there are a few reasons why handicaps are not more broadly used:

1. Chess in its modern form is a game of European origin, and it is my impression that European cultures have valued "equal starting conditions for everyone" always higher than "similar chances for everyone to get their desired outcome". This might have made use of handicaps less appealing, because with handicaps, the game starts from a position that is essentially known to be lost for one side.
2. There is no good way to combine handicaps in chess with Elo ratings, making it impossible to have rated handicap games. It is also not easy to use handicap results informally to predict optimal handicap between players who haven't met (if John can give me a knight, and I can give f7 pawn and move to James, it is not at all clear what the appropriate handicap for John against James would be). This is different in Go. 
3. Material handicaps significantly change the flow of the game (the stronger side can try to just trade down into a winning endgame, and for larger handicaps, this becomes easy to execute), and completely invalidate opening theory. This is different in Go and also in more chess-like games such as Shogi, where I understand handicaps are more popular.
4. Professional players (grandmasters and above) are probably strong enough to convert even a small material handicap like pawn and move fairly reliably into a win against any human (computers, at a few hundred elo points above the best humans, can give probably about pawn to top players and win, at tournament time controls). This implies any handicap system would use only very few handicaps in games between players strong enough that their games are of public interest (Go professionals I understand have probably 3-4 handicap stones between weak and best professional, and maybe two stones vs the best computers). I think that would have been different in the 19th century, when material handicaps in chess were more popular than today.

That said, chess does use handicaps in some settings, but they are not material handicaps. In informal blitz play, time handicaps are sometimes used, often in a format where players start at five minutes for the game and lose a minute if they win, until one of the players arrives at zero minutes. Simultaneous exhibitions and blindfold play are also handicaps that are practiced relatively widely. Judging just by the number of games played in each handicap mode, I'd say though that time handicap is by far the most popular variant at the club player level.

In Drawback Chess, each player gets a hidden random drawback, and the drawbacks themselves have ELOs (just like the players). As players' ratings converge, they'll end up winning about half the time, since they'll get a less stringent drawback than their opponent's. 

The game is pretty different from ordinary chess, and has a heavy dose of hidden information, but it's a modern example of fluid handicaps in the context of chess.

• Win about 1/N of the time

Morphie's law does this.  

https://store.steampowered.com/app/948960/Morphies_Law_Remorphed/

Doesn't seem to be a particularly successful implementation, but it's an FPS game where players with more kills grow bigger (and are easier to hit), while players with more deaths grow smaller (and are harder to hit and can hide in places the larger players cannot access)

This algorithm is supposed to make the KDR 1/1 over infinite time.

In multiplayer games, one balancing factor is that other players can gang up on the person who is ahead. Depending on the game dynamic, this can even things out a lot. In some games, this even creates the dynamic where you don't want to look too strong, so that others don't focus their attention on you.

Playing games against my kids when they were young, rather than just slack off and let them win, it was more fun for me to figure out the best way to handicap myself: What algorithm for sub-optimal play would keep the game close? Solving that puzzle effectively became my victory condition, rather than the game's victory condition, and I was effectively competing against myself, a more balanced opponent.

Small edges are why there's so much money gambled in poker. 

It's hard to reach a skill level where you make money 50% of the night, but it's not that hard to reach a point where you're "only" losing 60% of the time. (That's still significantly worse than playing roulette, but compared to chess competitions where hobbyists never win any sort of prize, you've at least got chances.) 

In a game where you play a higher number of shorter games, you can ideally have a handicap that adjusts after every game.  For example, in Super Smash Bros, if you turn handicap to "auto" then the stronger player starts with damage, which (in two player) goes up 10% every time they win, and down 10% every time they lose. It gets a little more complicated in 3+ player games, and I'm not sure the exact algorithm, but it works reasonably well. Maybe something to emulate in a game where handicaps can be reasonably granular?

When I play an N-player game I want everyone to both: 

• Try to win
• Win about 1/N of the time

This may be besides the point of your post, but: you can do even better than that, and without a need for handicapping, by playing co-op board games instead. Versus-style board games are just one type of game, and while you can modify their rules to come closer to equality of outcomes, that seems like a rather convoluted way of getting there. Like, in this situation, why play a zero-sum game when you could play a positive-sum game instead?^[1]

Or if entirely co-op games don't seem appealing, another option along this axis is to play team-based games; then you can balance team strengths by which and how many people you assign to each team.

Some co-op board game recommendations suitable even for groups of widely disparate skill levels: Letter Jam, Just One.

A co-op game for groups that want a challenge: Hanabi.

Some team-based board game recommendations: Codenames, Decrypto. I wrote about these two games here [LW(p) · GW(p)].

1. ^{^}

   Speaking from my own experience, when I grew up I only knew versus board games, stuff like Monopoly or Settlers of Catan. But once I discovered co-op board games, I eventually realized that I had a lot more fun playing those with my siblings.

I don't play golf, but the idea of "handicap" is a part of at least pop-culture renditions of the game.  In my boardgame and videogame groups, explicit in-game support for varying player skill levels is pretty well absent and not really considered.  Competitive sports tend to have "divisions" rather than individual compensations.

It's pretty obvious why it's not common in money games like poker or betting pools.  

In my experience for casual games, the expectation of equality of outcome just isn't there, and isn't all that important.  People still have fun in the optimization and game decisions, even when some of us are really known to be more likely to win.  Having a formal handicap system would BOTH be too much effort, AND make some players have less fun because it feels like they're not "really" playing the same game.  Maybe.  Maybe it's just the effort thing.  

Also, for many multiplayer games, there are social dynamics that make current leaders have a bit of a disadvantage in trading or interactions.   

Bridge is a slightly odd choice of example in your opening section. A single hand of Bridge has very high randomness; it's quite likely the weaker partnership will "win", assuming they have at least basic competence in the game. The advantage of a stronger pair only really becomes apparent over a large number of hands. 

The same is true is Poker, even more so. In fact stronger players may not "win" very many more hands than weaker players at all; it's just that when they win they win more and when they lose they lose less. 

This isn't true at all in Chess, of course.

mostly of historical interest in chess

Aren't time handicaps still common in chess?