hex 5x5 opening move puzzle

I've been working through the 5x5 openings. Here's one which is presumably well-known/easy for experts (I should say that I am just learning this stuff and I'm putting up puzzles which I have to think about myself -- it could well be the case that for experienced players these are all easy). Black has just played their opening move in a game of 5x5 hex. Should white swap?

Link to game on trmph [www.trmph.com]

I’ve been working through the 5x5 openings. Here’s one which is presumably well-known/easy for experts (I should say that I am just learning this stuff and I’m putting up puzzles which I have to think about myself — it could well be the case that for experienced players these are all easy). Black has just played their opening move in a game of 5x5 hex. Should white swap?

link to trmph [trmph.com]

This site is always so broken :-/ I can't figure out how to remove my first post, which has an incorrect link in it. There's an "x" to remove it, but it doesn't seem to work. I am now remembering why I left this site in the first place :-/

The random striking out in my above post just adds to the confusion.

I think White wins with the center move.

So after 1.a2 you don't swap and play 2.c3. Then what about 3.a4?

1.c3 2.a4 3.c2

I go the numbers wrong ;)

a2 c3 a4 c2

Well done yper, it's all too easy for you :-) c3 is the only winning move after 1.a2.

What if black had played 1.a3 instead?

It is the only move but it could be delayed (and played after black tries to break the ladder at d4 or e4), eg.:

a2 c3  a4 a5  b4 b5  d4 c2

I'm not sure about 1.a3, I think it wins and should be swapped. I think there are results published (and gathered somewhere, all in one place) about which starting moves are winning (and should be swapped) and which are losing. There was a link posted in this forum, if memory doesn't betray me.

But I don't think it had winning moves for White (for the losing first Black moves)

Or 1.a3 2.b4 wins for White.

Yes! After 1.a3, 2.b4 is white's only winning response. The winning and losing moves for boards up to 9x9 are here:

Hexwiki Small Boards [hexwiki.amecy.com]

The reason I was playing a2 and a3 was that they were the only losing moves which were not obviously-losing.