In Uno, can you quickly finish a two player game by skipping your opponent's final turn and without saying Uno?

Question

So me and my friend are playing Uno.
It's a 2 player game and we play where you can stack draw 2’s or draw 4’s.

My friend (player 1) has 2 cards left.
I (player 2) have 2 cards left.
It is player 1’s turn.

Player 1 plays a blank wild Card and says “red, draw 2”
Player 1 immediately lays next card down not saying Uno or giving player 2 time to draw two cards or if they wanted to stack another draw 2 card on top. Player 1 laid both cards down back to back.

Player 2 calls out that player 1 did not say Uno or give you time to draw two cards or stack a draw 2 card.

Player 1 says it doesn’t matter because they are out of cards and the game is over and that they are not obligated to give you time to:
A) draw two cards; or
B) call them out for not saying Uno

Did or did not player 1 win?

Answer 1

Player 1 hasn't won yet at all. They broke the rules.

Uno says when it's your turn, you play a card. Then it's the next player's turn. That player might have to do something with their turn (like draw cards) but if they have a draw 2 in their hand, they have an opportunity to respond instead.

Player 1 says [...] they are not obligated to give you time to:
A) draw 2 cards; or
B) call them out for not saying Uno.

Actually, that's exactly what player 2 has time to do now. Player 1 played their card. Now it's player 2's turn, and they can choose whether to respond with a draw 2 in hand or not. Players are obviously obliged to give their opponents time to take their turns, and player 1 is given no allowance to just unilaterally decide to skip player 2's turn.

Let's address that bit I skipped over with the “[...]” though:

Player 1 says it doesn’t matter because they are out of cards and the game is over

Imagine this: at the start of the game immediately after we're given our hand of cards, I just put all mine down face-up in the discard pile and say I've won. You object and say I can't do that. I say it doesn't matter because I'm already out of cards and the game's over and I won.

That doesn't work, does it? I broke the rules, and I definitely haven't won at all. Winning has to occur within the bounds of the game—if I broke the rules, I'm essentially not playing the game, and at that point me winning or losing is neither here nor there.

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At the point you reached, you've got some options:

1. Back up to player 2 having their turn. Player 1 probably draws, on account of being rightly called out for not saying Uno.
2. End the game (nobody won), shuffle up and play another properly.

Answer 2

You cannot play a "Wild Card" and say "Red, draw 2" because you are only allowed to pick a colour (and not a specific card of that colour) to change the top of the discard pile to.

From the rules (pdf) on Mattel's website:

Wild Card - When you play this card, you may change the color being played to any color (including the current color) to continue play. [...]

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Assuming you did actually play a "Red, Draw 2" card (rather than a "Wild Card" or you have a specific house rule that lets wild cards be treated as any other card) then the rules for Draw 2 cards state that the next person forfeits their turn:

Draw 2 Card - When you play this card, the next person to play must draw 2 cards and forfeit his/her turn. [...]

But the two-player rules explicitly state that play does not return to you until they have drawn their cards:

Rules for Two Players - The following special rules apply to two-player UNO:

[...]

3. After playing a Draw 2 card or a Wild Draw 4 card, your opponent draws the number of cards indicated, and play is back to you.

So you need to pause and wait. The rules also tell you when your opponent is allowed to catch you out for not saying "UNO":

LET'S PLAY!

[...] Before playing your next to last card, you must say "UNO". If you don't say UNO and another player catches you with just one card before the next player begins their turn you must pick FOUR more cards from the DRAW pile. If you are not caught before the next player either draws a card from the DRAW pile or draws a card from their hand to play, you do not have to draw the extra cards. Once a player plays their last card, the hand is over. Points are tallied (see Scoring section) and you start over again.

GOING OUT

If you forget to say "UNO" before your card touches the DISCARD pile, but you "catch" yourself before any other player catches you, you are safe and not subject to the 4 card penalty.

You may not catch a player for failure to say "UNO" until his/her second-to-last card touches the DISCARD pile. Also, you may not catch a player for failure to say it after the next player begins his/her turn. "Beginning a turn" is defined as either drawing a card from the DRAW pile or drawing a card from your hand to play.

[...]

If your opponent has started drawing their 2 cards then the time has passed for you to be caught out and you don't need to draw any more cards as a forfeit for not saying "UNO"; but if your opponent hasn't drawn cards then they can call you on having not said "UNO" and you will need to draw FOUR cards. But either way, you need to wait for them to draw their two cards first.

Answer 3

In a two-player game, someone who plays a skip card would get to play another card, but I would say that other card is played by the "same" player, rather than the "next" player. I thus think the intention of the rules is that a player whose penultimate card has touched the pile should be eligible to be caught out until the next action by some other player; additionally, the person's turn wouldn't really be over while they are eligible to be caught out.

As such, I would argue that if someone with two cards plays a SKIP and then plays the other card without saying "UNO", the opponent should be able to challenge unless or until they table and score their hand or take some other meaningful action besides challenging. If the opponent challenges, the last turn by the person who didn't say "UNO" should be voided, with the person taking back any cards discarded in the revoked play, and that person would then draw the penalty cards. After drawing the penalty cards, they would then be entitled to either play the same card as they had before, or one of the cards they just drew, whichever they regarded as a more useful play.

In the scenario where a player with two cards played a skip, but then had to draw a card, which they then proceeded to play (getting down to Uno again), I would rule that a person "challenging" should be entitled to specify whether they wish to challenge the first play (in which case the drawn card would become the player's first penalty card) or the second (in which case the second card would remain played, and the player would draw all new penalty cards).

For a player to deliberately put down the last two cards without saying "Uno" between would strike me as poor sportsmanship. Anyone who could plan on doing that could just as well say "Uno", and if the opponent wouldn't be getting a chance to play there could be no strategic advantage to not saying it. The only "sensible" reason for not saying Uno would be if one forgot, and if one forgets to say it one would deserve to get caught out.