Chess on an Infinite Plane (hitthepin - captaintugwash)

Yep, I'm afraid so. At least you dodged checkmate by not playing K(5,0)

16... Qx(6,1)+

I do think the two chancellors are probably better than a queen, but you're seeing my queen win a piece from (4,24). The queen poses very serious threats that are very hard to anticipate. Certainly she is a great deal stronger than a queen bound by edges.

I'm discussing the value of the queen vs 2 chancellors in general.

I'll discuss the power of the queen in more detail after the game.

17... H(6,-2)+

Figured you might. It's getting harder to visualise. That said, my next two moves are already made.

Unfortunately, this next combo is because you put the hawk on a bad square.

So many threats to watch out for with an enemy queen on the board.

Thanks. Although I'm not won yet, I can still blunder this!

16.K(7,1)...Qx(6,1)+
17.K(8,0)...H(6,-2)+

18... Hx(4,0)

Thanks for that, some solid thoughts there. I assume archbishop is another name for the chancellor?

I suspect in an endgame, the two chancellors will easily match the queen. However, you're right about the long range attacking potential of the queen, and it's this potential that makes the queen an extremely powerful supporting piece. In this game, when my queen was sat on (4,24), she was silently controlling the fifth rank (sadly nothing was happening there). That control shifted to the fourth rank when he moved his king out of the first check. I'll explain how that was the case after, although you might be able to figure it out. It's why I allowed him to grab the pawn. It's this ability to dominate from afar that makes the queen so powerful. From that same square (4,24), the queen was able to win a piece, with the hawk's support. I think his best defence was to abandon the guard with 14. R(-1,-1) to protect the king's rear, saving bishop, so from (4,24) the queen was silently attacking the guard, while also silently controlling a central rank.

The chancellors will be useful in the centre, with their leaping action, however, their power is their downfall to a degree... knights will be better in the opening because they aren't so valuable. A bishop attacks a knight, you can ignore it if it's protected already, but you have to move your chancellor. So perhaps their power in closed positions is limited by their endgame value.

We know a queen alone is not going to be enough to checkmate the king, so in that respect it's easy to see the chancellor pair will outperform a queen in endgame. But the queen will rule the middlegame, and this is where most games will be won or lost.

I must say I have a very high opinion of the queen's power because I'm currently using it to brutal effect, while my chancellors sit there undeveloped. I might be raving about those pieces when I finally get to use them.

18.K(9,0)...Hx(4,0)