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[ackack]

Technically, I was first, but his 4-cost buy came before mine making it relevant to a "2nd player advantage" discussion.

I find this unconvincing. A very healthy chunk of the first player advantage on some of the strongest boards is in effect having an extra turn and has nothing to do with informational advantages at the beginning. edit: That's phrased poorly. What I mean is that in essence you have the informational advantage and potentially the extra turn advantage, and so trying to compare this to true 2nd player status seems way off to me. This is so even if the extra turn aspect didn't come into play (I'm not in the mood to comb the log at the moment.)

[ftl]

Well, he won by 9 points, which is a province and a half.  He did have the extra turn. They were playing different strategies; by my estimate, the bishopping player could have gotten at best 6 points next turn. 

It would have been a lot closer of a game if the number of turns had been equal, but the result would have stayed the same, I think.

[DG]

If my memory serves me correctly, someone once set a challenge to design a kingdom where the second player had a clear advantage. It was never fully answered.


The first logical consideration is that the first player can possibly either (1) buy nothing or (2) buy a silver just to pass any "first player penalty" onto the next player. Any solution kingdom needs to prevent this by making every available supply card a game losing purchase but still not as bad as buying nothing at all. While this might seem like a minor point, it may restrict the solution kingdoms to such a degree that any second player advantage has negligable effect.

[Buggz]

The second player can do the exact same move to pass the hypothetical "first player penalty" back to the first player.

[DStu]

The first logical consideration is that the first player can possibly either (1) buy nothing or (2) buy a silver just to pass any "first player penalty" onto the next player. Any solution kingdom needs to prevent this by making every available supply card a game losing purchase but still not as bad as buying nothing at all. While this might seem like a minor point, it may restrict the solution kingdoms to such a degree that any second player advantage has negligable effect.

I don't think it's a minor point, it greatly limits the search space...
Assume for simplicity that we would reshuffle after each turn and the winning condition would be symmetric (i.e. not differntiate if you where first or second player), which are I think the only things that prefend this from being a proof.
Then buying nothing at all would just swap the positions. By buying nothing the second player is in exactly the same position as you where before. By assumption every move he can make is a winning move for you (including, by assumption, doing nothing), which contradicts the assumption.

So under the simplifications such a board can not exist, that means that, if such a board exists the second player advantage must either involve the shuffling or is limited by the "second player compensation".

[WanderingWinder]

The first logical consideration is that the first player can possibly either (1) buy nothing or (2) buy a silver just to pass any "first player penalty" onto the next player. Any solution kingdom needs to prevent this by making every available supply card a game losing purchase but still not as bad as buying nothing at all. While this might seem like a minor point, it may restrict the solution kingdoms to such a degree that any second player advantage has negligable effect.

I don't think it's a minor point, it greatly limits the search space...
Assume for simplicity that we would reshuffle after each turn and the winning condition would be symmetric (i.e. not differntiate if you where first or second player), which are I think the only things that prefend this from being a proof.
Then buying nothing at all would just swap the positions. By buying nothing the second player is in exactly the same position as you where before. By assumption every move he can make is a winning move for you (including, by assumption, doing nothing), which contradicts the assumption.

So under the simplifications such a board can not exist, that means that, if such a board exists the second player advantage must either involve the shuffling or is limited by the "second player compensation".

Yes, except that those are two big exceptions, particularly on the shuffling aspect. Throwing away a 5 in a 5/2 split is big tempo loss. Then you need an RPS of 5s that's so bad that one missing tempo on any end is killing. I actually think this is out there, given that 2nd player wins ties where 1st turn is important, which comes up more importantly in a situation where making a move gives something like a 51% chance to tie and a 49% chance to lose. 1st player moving loses 49% of the time, ties 51%, 2nd player moving first wins 51%, loses 49%. Obviously these numbers are ridiculous, but in principle this is possible.