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What happens if both players have only 3 cards in their library and I cast Wheel of Fortune (Each player discards his/her hand and draws seven cards) ?

Is it any different if one player has 1 card and the other player has 3 ?

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The active player performs all his draws before the next player performs his. (But it doesn't matter here.) –  ikegami Feb 17 at 20:03
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up vote 12 down vote accepted

Here are the relevant Comprehensive Rules:

104.3c If a player is required to draw more cards than are left in his or her library, he or she draws the remaining cards, and then loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)

Nothing happens until a player would get priority, so the order in which the players drew the cards doesn't matter.

704.4. Unlike triggered abilities, state-based actions pay no attention to what happens during the resolution of a spell or ability.

All the SBAs are performed simultaneously.

704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. [...]

All the players would lose simultaneously if it were not for the following exception:

104.4a If all the players remaining in a game lose simultaneously, the game is a draw

In both cases, the game ends in a draw. Because the rules pay no attention to what's happening during the spell's resolution, having more cards doesn't protect you in this case. As soon as state-based actions are checked (i.e. after the spell resolves) you both lose the game at the same time and it's therefore a draw.

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