Would it be accurate to say those 4 stones are about equivalent to one pawn in chess?
As a back-of-the-envelope calculation, one pawn is 1/43 of your starting material in chess if the king is included as a four-point fighting piece. Four stones in Go comes to 1/45 of your expected endgame material as half of a 19x19 board.
It's hard to make a comparison like that because Go and Chess operate on fundamentally different models. Chess is about capturing a specific piece and putting your opponent in a position where they have no options but to lose; to that end, it's a war of attrition where players slowly lose resources until the game is over (note that I do not play chess at any significant level).
In contrast, Go is about capturing territory by fencing it in. Placing four stones on the board is like placing four free fenceposts; you can't really call it a tangible resource like a pawn, but it gives you more of a structure and gives you some influence over the rest of the board.
It's possible to remove resources from your opponent in go, since you can surround pieces and capture them. But it's not really an attrition thing like in chess; it's more about territory and control.
Trying to make it a numbers game and saying "four stones is 1/45 of your expected endgame material" isn't really relevant to go, because the position of the stones matters so much more than the number. If you have four more pawns than your opponent in a game of chess, that's pretty clearly an advantage; if you have four stones in a totally useless area of the board, or four stones in a really useless configuration, then they're not helpful at all.
It's hard to make a comparison like that because Go and Chess operate on fundamentally different models
It is very easy. The nature of the game is completely irrelevant. The question is what expectation of winning rate a 4 stone advantage gives to a Go player. For middle ranks, one stone is about 100 ELO-equivalent, or 64% winning rate. (I think it's closer at top dan ranks, would have to look up the statistics). 4 Stones is about 92% chance of winning between equal players.
The equivalent in chess is slightly more than 4 pawns advantage, or about a minor piece.
I've read four different versions of the comparison you're describing as "very easy" (four pieces, four pawns, two bishops, a minor piece), so you'll forgive me if I don't find your statement very convincing given the lack of consensus?
My limited understanding of go is that the stone placement confers position and tempo, too, which would be undercounted looking at it purely from points.
Points (which are a game specific metric) have absolutely no relation to anything I posted. I didn't even mention them at all! It looks purely at game outcomes given the initial starting conditions.
Yes, you've got the right answer. Forget material and point comparisons which don't really port between the games. The winning percentage conferred by the handicap is what matters.
Four stones in Go sounds like a lot less than four pawns in chess, but if that's what the math says by each resulting in the same winning percentage, then the equivalency is true.
I'm around 2000 ELO in chess and I'd win every single game vs anyone with 4 pawns or a minor piece handicap. Being a single pawn up is usually decisive in chess. Having said that, this whole discussion is pointless, no one ever gives handicaps in chess, because it completely messes up the initial position. Even lacking one or two pawns at start will make it extremely hard to establish any kind of central presence.
I'm around 2000 ELO in chess and I'd win every single game vs anyone with 4 pawns or a minor piece handicap.
You'd only break even starting from opponents at around 2400 ELO, and would start losing about 2 out of 3 games when facing a top rank grandmaster.
Being a single pawn up is usually decisive in chess.
It only gives you slighly less than a 66% chance of winning (a bit more close to the endgame).
There's no point in arguing from your personal beliefs here. You're vastly and utterly overconfident in your own ability. The definition of the rating system and a few million games of evidence are against you.
More than a pawn: I think "two bishops" was about right.
The value of each stone (as an ability to stake out territory -- sometimes called the "temperature of the board" in game theory) decreases as the game goes on. A stone in each corner is huge, probably worth about 80pts of potential territory. In the middle game, the temperature might drop from 20pts to 10pts per move. So your averaging method doesn't quite work. :)
As a back-of-the-envelope calculation, one pawn is 1/43 of your starting material in chess if the king is included as a four-point fighting piece. Four stones in Go comes to 1/45 of your expected endgame material as half of a 19x19 board.