What is the simplest Go scoring system? It's this:
- Stone Scoring: just count the stones on the board
At the end of the game, both players will want to fill in as much of their own territory as they can, while allowing two eyes per group (so they aren't captured). Then the winner is just the player with more stones on the board. Note that prisoners are not counted.
But nobody wants to play all these extra stones at the end. So we can instead use:
- Naive Area Scoring: count stones on the board, plus territory totally surrounded
Now, at the end of the game, players need to capture enemy stones inside their territory (because territory is not surrounded -- in a mathematical sense -- until only one colour is present), but after that, the game is ready to be scored. Note that prisoners still aren't counted.
In practice, players with some experience can tell whether a group is alive or dead. Actually playing moves to capture dead stones is a waste of time. Hence we may prefer:
- Fast Area Scoring: the players agree which groups are dead, remove them, then count as above
This is how modern Chinese rules work, at least online (in real life there's a certain physical method to it). Note that prisoners still aren't counted. I would argue this is the best system for beginners. In particular, if there's any uncertainty about whether a group is alive, you can just play it out at the end without losing anything. Playing inside your own territory does not lose points, except for wasting a move, but at the end of the game, there is no such concern.
However, counting stones is tedious in real life. Which leads us to:
- Territory Scoring: as above, but count prisoners instead of counting stones
In a normal game, both players play the same number of stones [note 1]. Any difference in the number of stones on the board is caused by captures. Therefore, we can dispense with counting stones on the board and just count prisoners. This is how modern Japanese rules work.
The problem with Japanese rules comes when a beginner, unsure about life and death, plays moves inside his territory (losing 1 point) while his opponent is passing (losing nothing). For this reason, I prefer Chinese rules for beginners.
Aside from that, all the rules described should be more-or-less mathematically equivalent [note 2] when the players know what they're doing.
1: Black might get 1 more move in if White passes first.
2: Stone Scoring doesn't count territory at all. When you fill your territory with stones, you must leave 2 eyes per group. If you have more groups than your opponent, you are worse off in this ruleset, because the eyes, which would be counted in any other ruleset, aren't counted here. Incidentally, throughout history some rulesets explicitly penalised each living group with a 2-point eye tax, for the sake of maintaining mathematical equivalence with Stone Scoring.