What does the phrase "play the ... card" mean? For example:
"She played the victim card."
It's an unsubtle appeal for support if you belong to some kind of group that has been discriminated against. It's being used like a social trump card. The most common examples I have seen are these.
"playing the race card"
"playing the sexism card"
Have you ever played the game Monopoly? It involves moving pieces round a board, where most of the squares represent different streets, which can be bought by the first player to land on it. The owner of a street can then charge ‘rent’ to any other player to land on that square.
But there are two squares that are ‘CHANCE’ and two that are ‘Community Chest’. Each corresponds to a separate benefit, such as being allowed to claim a certain amount from other players, or a forfeit, such as paying a tax to the ‘bank’
There is one square that is ‘Jail’ and another that sends you to jail if you land on it. being in jail is a setback. You cannot charge rent or buy properties while there.
One of these cards says “Get out of Jail Free”. The player that picks up this card can keep it and play. it when needed. Not surprisingly, this card is known as ... yes,
THE GET OUT OF JAIL FREE CARD
This has become a common expression, particularly in connection with politics.
The Cambridge Dictionary has
something that allows you to avoid an unpleasant result of your actions, for example a punishment or duty: k quote
Naturally, though I have not substantiated this, this expression becomes extended to other ‘get-out’ behaviours. We hear of ‘playing the race (or gender) card’ and so on. But I do suspect it goes back to that Chance Card in the game of Monopoly!
to use a particular quality, argument etc in order to gain an advantage; to bring up a particular, typically contentious issue or idea in order to gain an advantage, as in an argument or political agenda
Politicians play the nationalist card in order to get votes.
play (or use) the — card
Exploit the specified issue or idea mentioned, especially for political advantage. https://en.oxforddictionaries.com/definition/card
It's an analogy to some card games where a lower card of the "Trump" suit can beat a higher card of another suit and it always carries an accusation that this argument or appeal is a weak one. The most common usage is to say that someone
played the race card by which one means that they used their race or accusations of racism illegitimately to win or derail a debate.
Note, that using this phrase is aggressive and accusatory and people will interpret it as a dismissal of the "card" that the person was playing. In your example of playing
the victim card, people will likely interpret that as dismissing the significance of whatever that person suffered.