Murderous Compulsion

A card with madness that's discarded counts as having been discarded even though it's put into exile rather than a graveyard. If it was discarded to pay a cost, that cost is still paid. Abilities that trigger when a card is discarded will still trigger.

If you choose not to cast a card with madness when the madness triggered ability resolves, it's put into your graveyard. Madness doesn't give you another chance to cast it later.

Casting a spell with madness ignores the timing rules based on the card's card type. For example, you can cast a sorcery with madness if you discard it during an opponent's turn.