I don't have the diamond membership, but from my experiences all opening explorers show next move based on position, not past sequence of moves, even if you access explorer from a game. URL contains the whole sequence because it gives necessary information to the game explorer. FEN has slashes / in it, which is a problem with URL.
Can the Game Explorer handle transpositions when accessed from a game?
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It seems like the Explorer is OK with transpositions when you enter the moves into the Explorer itself. For instance, I get exactly the same results at the end of either of these two move sequences:
1.e4 c5 2.Nf3 Nc6 3.Nc3
1.e4 c5 2.Nc3 Nc6 3.Nf3
However, what's more doubtful to me (and a bit harder to test) is whether linking to Explorer from an e-chess game works the same way.
(What makes me suspicious is that here, the URL to Explorer includes a move-list, not a FEN notation or something that would simply represent a position without regard to how it came to be.)
Does anyone know off-hand?
Cheers!