While scoring go uses area you control + number of stones you capture right?

Somewhere I read about go it makes no sense to put stones on the area your opponent control because they will be captured. however

  wwwww
  w   w
  w b w
  w   w
  wwwww

in this case white has to put 4 stones (thus reduce area by 4) just to get 1 point. am I missing something

This is why I much prefer Chinese (and similar) rules with area scoring. In area scoring you get one point for each space you surround, and one point for each stone on the board. It's immediately obvious and simple.

In Japanese rules you lose points for playing in your own territory. The black stone in your example is dead, and a reasonable player would allow it to be removed, but there's nothing stopping them from claiming it to be alive and forcing white to play to capture it. At this point the only option is for white to dispute its life status, and to duplicate the game board and make a hypothetical sequence of plays to prove it to be dead without actually playing the moves. There's a lot of added complexity for no real benefit, because the end result is usually identical.

I still prefer Japanese counting since it takes a lot less time to count (at least for me) a full 19x19 board. The only way white loses points (relative to black) by being forced to "play it out" is if black passes -- but the AGA resolves that by requiring you to give up a pass stone as a prisoner when you pass, and if the game has ended and you have to play it out, passes aren't allowed.

The next AI challenge is to have the AI make an argument that will convince everyone to adopt the One True Most Elegant Ruleset for Go. (http://warp.povusers.org/go/RulesElegance/ is an interesting page, along with his proposal: http://warp.povusers.org/go/MyRulesProposal/)

Chinese counting is just as fast once you're used to it. Remember that you only need to count one player under Chinese rules. And the AGA rules are a nice hack to Japanese rules to make them always give the same result as Chinese rules and avoid trolling/unreasonable plays, but it's still more complicated to explain to beginners than Chinese rules.

Yes, I always teach novices with area scoring, because all of the "if I played it out, I'd kill you, but I don't have to actually play it out" stuff is incredibly confusing to someone learning the rules for the first time. It's much nicer to have no penalty (other than opportunity cost) for playing these sequences out.

The AGA system of pass stones, bringing area and territory scoring into alignment, is very nice, but I think it's still a bit abstract for someone who's just starting out.

But in practice there usually ends up being no difference in score under either ruleset, or by at most 1 point difference.

A computer will correctly score that b as a dead stone, since it can't possibly make life, and white can kill it. That insurmountable threat makes the territory white's.

If a human tries to argue that b is alive, then either (a) that human is a novice, you can teach them, or (b) that human is a poor sport, and you shouldn't play with them.

Japanese counting is like Chinese counting, but assumes your opponent is not a jerk without explicitly handling cases when that's not true.

If a group is dead, it will be automatically captured at the end of the game.

So, in this case, the black stone is auto-captured, and you get the territory within as well.

So, yes, playing white stones to capture is actually detrimental to yourself. But also imagine if black keeps playing. They would be giving away free captures since black can never create eyes. And once the space is almost filled white can play 1 stone to capture all of the black stones.

Edit: Another way to imagine it is if neither player could pass. While yes White would lose territory as it played stones, it would be compensated by Black playing stones that will be captured in the end. Thus it becomes a wash, and thus why dead groups are auto-captured.

That thinking does help, I did read that on one of the sites as well but in some cases the capture appears to mean the loss of territory itself in addition to the actual pieces and it's hard to weigh up the value of each territory.

Another reason the computer might ignore a direct capture is because the stones are already "dead", it doesn't need to waste a move to actually capture them unless you futilely try to save them. Solving tsumego might help you see those cases better when it's not as simple a case of leaving your stones in atari. But yeah, even if you can "save" them next move it might still ignore the capture if there's a bigger (in terms of gaining / securing territory) move on the board, especially if your save actually isn't making them alive yet.

I think scoring and score estimating is one of the hardest things to understand (for full games I still often use a $5 android app where I just upload a picture of the board game, help it convert to an SGF, and then it auto-scores it, though sometimes it's faster to just count by hand), especially since there's multiple ways of doing it. With simple territory scoring when the game ends the dead stones that haven't actually been captured yet still get removed and added to the prisoners pile and the prisoners fill in your other territory so it might feel extra painful to lose stones... With area/stone scoring you still remove the dead stones but prisoners don't (directly) matter for the score, since you're just counting stones on the board plus uncontested area. But if a game was X moves with black having X/2 stones but white only having (X/2 - 10) stones on the board, clearly (assuming X is even and no passes, or if passes then giving up pass stones) 10 white stones were captured at some point, so there's already that relative difference in score before counting anything else. With some qualifications, the results (and the relative scores themselves) from each counting system will be the same. Thinking more about your relative score instead of giving each player actual numbers might help; I feel slightly better if I lost by 10 than if I had a negative score, say -5 to 5...