Is it possible in UNO to run out of cards to draw?

The question Uno discard and draw pile empty? deals with what would happen according to the rules if a player has to draw one or more cards but is unable to do so because both the draw pile and the discard pile are empty. The author of the question assumed "I'm guessing this is impossible mathematically or they were missing cards".

But is it actually mathematically impossible for that to happen?

Assuming that:

• You are playing with a complete 108 card uno deck.
• You have between 2 and 10 players, as the rules say the game was designed for. Whatever number works best for achieving this game state.
• Players are playing according to the official rules and refrain from self-destructive behavior (like drawing cards even though they don't have to), but otherwise follow a strategy which provokes this situation.
• The cards happen to get shuffled in the ideal order necessary for this to happen.
• Does it even make sense that this could happen? Every card in Uno is doubled, so if there is a card on the top of the discard pile, there has to be at least one match in either a player's hand, in the draw pile, or in the discard pile. Commented Jan 27, 2020 at 22:02
• If there are fewer than 20 cards left in the deck+discard, then chain-playing "Draw 2" and "Wild Draw 4" can force a deckout. Still a high bar to reach, though. Commented Jan 27, 2020 at 22:33
• Does this answer your question? Uno discard and draw pile empty? Commented Jan 27, 2020 at 22:34
• @OlaStröm No, it doesn't. That question asks what happens in that situation. It does not ask if that situation can occur in the first place. Commented Jan 27, 2020 at 22:35
• @olaStröm did you even read the question?
– roel
Commented Jan 28, 2020 at 7:57

Yes. Here's how:

10-player game. Designate players 5 and 10 "lucky", meaning that these players monopolize the number that initially flops, and also monopolize the wilds, ensuring that they always manage to play, and the other eight "unlucky" players are never able to play. Assign two of the four colors to players 1-5, and the other two colors to players 6-10, ensuring that the current color is always inconvenient when an unlucky player's turn comes around.

Let's say players 1-5 got the colors blue+green, and the red 1 initially flopped. The "lucky" players proceed to play out the other 7 1's, with the unlucky players drawing (8*4=32) cards in the process, leaving only 5 cards in the discard pile. Player 10 plays a Wild, calling one of his own colors, and then the endgame begins:

• Player 1 draws a junk card
• Player 2 draws a Wild Draw 4 and plays it, calling one of player 10's colors
• Player 3 draws the last 3 cards from the deck, including a Wild Draw 4, then reshuffles the discard into the draw and also draws a Wild.
• Player 4 draws a previously played blue or green 1
• Player 5 plays a Wild, calling one of his own colors
• Player 6 draws a previously played red or yellow 1
• Player 7 draws a previously played red or yellow 1
• Player 8 draws a previously played red or yellow 1
• Player 9 draws a previously played red or yellow 1
• Player 10 plays a Wild Draw 4 that he has held since the start
• Player 1 draws draws the last three cards from the deck (all 1s), then reshuffles and draws a Wild
• Player 2 draws and plays a Wild Draw 4, calling one of player 10's colors
• Player 3 reshuffles that Wild Draw 4 into the draw pile and draws it, -there are no cards left to draw-
• Player 4 has nothing to play and no cards to draw

Here's a sample deck order for producing this result: https://pastebin.com/hzBiFQ0B

• While this may result in the scenario the OP described (and I have doubts that it would, since the discard pile would be shuffled as needed to allow the +4s to be resolved), I don't think there are enough cards in the deck to actually make this happen. Commented Jan 29, 2020 at 1:33
• @mmathis Not having enough cards in the deck is the whole point. Commented Jan 29, 2020 at 20:48
• I mean there aren't enough cards to set up the scenario which prevents players from playing, ergo the players can play and the draw/discard piles aren't run dry Commented Jan 29, 2020 at 20:51
• @mmathis Actually yeah, I've found it does work out that way with 5 lucky players; but 2 lucky players (that never miss a play) are able to suppress the other 8 no problem. I'll update the answer accordingly, with an example decklist. Commented Feb 4, 2020 at 23:38
• @IvoBeckers Crap, I forgot that rule. Hmm, I think there's enough flexibility there to work around it... I'll edit it again. Commented Feb 5, 2020 at 20:22