I always used to think that white is half a tempo up, in the opening position.
You were right. The arithmetic works that way. It doesn't with the usual claim that white is one tempo up (unless a "tempo" is half a ply, which is not what anyone thinks ).
Thankyou. I believe I used an arithmetical approach at the time: but it was decades ago and I can't remember exactly what the thought processes were. Maybe that tempo is logically half a ply, when applied to white's opening advantage of the move.
For instance, in the giving of odds, I believe the odds "pawn and move" was ambiguous; referring possibly to two different things.
@5950
"Therefore, we don't have to consider this position in the proof that chess is a draw."
++ You misrepresent my arguments.
1. Chess is a draw because:
a) Expert opinions of all World Champions
b) TCEC: needs 50 imposed slightly unbalanced openings to prevent all draws
c) ICCF: 136 draws, 6 white wins, 3 black wins
d) AlphaZero self play 97.7% draws, more with more time/move, even if stalemate = draw
e) Human top matches and tournaments: more draws with time and with higher ratings
f) White is up 1 tempo = 1/3 pawn, not enough to win. A pawn can queen, but a tempo cannot.
2. Thus weakly solving chess is hopping from the initial drawn position to other drawn positions until a drawn 7-men endgame table base position or a prior 3-fold repetition.
3. Therefore a position where one side is winning cannot be reached from the initial position by optimal play from both sides and thus is not relevant in weakly solving chess.
That isn't a deductive argument and you're employing different criteria from Elroch's. I'm not saying that you're wrong that chess is a draw but you have not proven it to Elroch's satisfaction because what you have given is not a deductive proof and there's nothing that can make it so.
Your 1a) is fully reasonable but still opinion.
1b) is incorrect, so far as proof goes. One reason is that "50" is clearly an arbitary number but again, it's opinion and is much weaker than 1a). It may be a corollary of 1a).
1c) is corroborative evidence but in no way conclusive if it stands alone.
1d) A computer playing itself isn't a proper test, AT ALL. In fact I think that could be held as evidence that chess is a win.
1e) strongly confirms the assumption that chess is a draw but it remains an assumption.
1f)) I agree with that. It's evidence that chess ought to be drawn from a theoretical point of view but it's still opinion.
2. "Thus" here is therefore not so in the deductive sense.
3. Well, that's my opinion too but it's your opinion and also my opinion. Therefore, your use of "therefore" cannot be part of a deductive argument. It merely reflects the conclusion we draw from our opinions, which is that chess is definitely drawn with best play. It still isn't the proof which Elroch demands. I personally think he's mistaken to demand it, if such a proof is impossible, which I believe it is. But it's still his prerogative to remain agnostic.