If you have no cards in your hand at the end of your opponent's End Phase, draw 1 card from your Deck during your next Standby Phase.
Rulings for The Agent of Wisdom - MercuryYu-gi-oh! Card
When it is the END of your opponent's End Phase and you have no hand, then "The Agent of Wisdom - Mercury"'s effect activates. So if you activate "Dust Tornado" during your opponent's End Phase, and Set your last card in your hand, and have no cards at the end of the End Phase, "The Agent of Wisdom - Mercury"'s effect activates.
If your hand was increased during the End Phase by activating "Jar of Greed", and you have a card in your hand at the end of the End Phase, then "The Agent of Wisdom - Mercury"'s effect does not activate.
If your Standby Phase is skipped then "The Agent of Wisdom - Mercury"'s effect disappears.
If you have multiple "The Agent of Wisdom - Mercury" you can draw multiple times.
When the effect of "The Agent of Wisdom - Mercury" is negated by "Skill Drain", and you have no hand at the end of your opponent's End Phase, and you destroy "Skill Drain" before your "Standby Phase" (such as with "Mystical Space Typhoon" during your Draw Phase), you CAN draw because "Skill Drain" was destroyed. This is because the "when you have no cards in your hand during your opponent's End Phase" is a condition, not an effect, so it is not negated by "Skill Drain". As long as you can make it so that "Skill Drain" is not negating "The Agent of Wisdom - Mercury"'s card-drawing effect by the time the Standby Phase begins, you can draw.
When you have "The Agent of Wisdom - Mercury" on your side of the field and you have no cards in your hand at the end of your opponent's End Phase, but it is destroyed before your Standby Phase (such as with "Ring of Destruction" during your Draw Phase), then you do NOT draw during your Standby Phase because "The Agent of Wisdom - Mercury" is no longer on the field.
