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And yet it does trigger Rat Trap, which, in context, makes no sense.
I got curious about this, so we tested it. Based on our testing, if your opponent has Rat Trap, and Masked Contender is the second card you play in a turn (which is the only way that the Secret it "plays" would activate the trap), it does not activate Rat Trap. You'd still need to play a third card to activate your opponent's Rat Trap.
Can you recall the circumstances under which you activated Rat Trap with Masked Contender's Secret? Maybe there was something else going on.
Edit: All that aside, we get why there might be some confusion about the text on this card.
What if you play masked contender and then a second card? Does this trigger rat trap? Maybe it counts for two cards, but doesn't activate it itself, for some reason?
Double-checked that too to be thorough, but no dice.