Yes, you can still make Conditional Moves on the website. It has to be your opponent's turn to move and one of the buttons will change and look like f forking arrow. Clicking that will allow you to make the conditional moves.
What happened to contingent moves?
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When I joined in 2010, you could make a contingent move (if you were a paid member). So if you anticipated or forced a move, you could make your responding move in advance. Is this still possible? If so, how?