Davriel, Rogue Shadowmage — ruling 1

If an opponent has two or more cards in their hand as their upkeep begins, Davriel's first ability won't trigger. No player may take any actions during a turn before the turn's upkeep begins. Because the upkeep step is before the draw step, that player won't have drawn a card for the turn yet.

Davriel, Rogue Shadowmage — ruling 2

If an opponent has one or fewer cards in hand as Davriel's first ability triggers but has two or more cards in hand as that ability resolves, Davriel doesn't deal damage to them.

Davriel, Rogue Shadowmage — ruling 3

In a Two-Headed Giant game, Davriel's first ability triggers for each opponent separately as appropriate during that player's team's upkeep.

Davriel, Rogue Shadowmage : règles, fonctionnement et interactions (MTG)

Davriel, Rogue Shadowmage is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

At the beginning of each opponent's upkeep, if that player has one or fewer cards in hand, Davriel deals 2 damage to them. −1: Target player discards a card.

How it works : Davriel, Rogue Shadowmage

Original English text — Wizards of the Coast / Scryfall

#1May 3, 2019· Wizards of the Coast
If an opponent has two or more cards in their hand as their upkeep begins, Davriel's first ability won't trigger. No player may take any actions during a turn before the turn's upkeep begins. Because the upkeep step is before the draw step, that player won't have drawn a card for the turn yet.
No other card is named in this ruling.
#2May 3, 2019· Wizards of the Coast
If an opponent has one or fewer cards in hand as Davriel's first ability triggers but has two or more cards in hand as that ability resolves, Davriel doesn't deal damage to them.
No other card is named in this ruling.
#3May 3, 2019· Wizards of the Coast
In a Two-Headed Giant game, Davriel's first ability triggers for each opponent separately as appropriate during that player's team's upkeep.
No other card is named in this ruling.