What specific strategies have the highest win:loss ratio in Uno?

Question

I decided to delve deeper into this question to discover exactly how effective certain strategies would have on your win percentage. This led me to this Stanford Computer Science project that pits students' individual UNO strategies against each other.

This particular UNO simulator has some issues that I have corrected:

• A proper pseudo-random number generator (PRNG-Mersenne Twister)

• Support for 2-15 players

• Scoring for wins instead of points

• Proper rules implementation of initial special cards

• Hhandling of draw cards when going out.

I opted not to add a "catch"/bluff mechanic when playing Wild-Draw4, so those can only be played when you don't have a matching color.

I have implemented some basic strategies that you will be playing against:

• Play random legal

• Play most color

• Play most point

• Play highest rank in most color

• Call random

• Call color I have

• Call color most

• Call points most

These strategies will face off in 100,000+ games multiple times to get a Confidence Interval (CI) for how effective the strategy is. (I am open on direction of how to accomplish this best. Should it be a 4-player game, with 2 copies of the strategy seated non-adjacent to each other (ABAB)?)

So: what is your Uno strategy? Be specific: I'm going to write a program to execute your strategy, and since computers are dumb like me, instructions need to be specific. (If they are not, I will post comments for you to clarify)

Things to think about in your answer:

• What card do you play next? Do you try to get down to one color or number, or always keep as much variety as possible in your hand? If you have a pair of 0's and a 9, do you play the 9 to reduce your point count, or play a 0 to keep up some variety in your hand? Do you play Skip, Reverse, Draw Two, Wild, and Wild Draw Four early or late, or does it depend on how many cards other people have?
• What do you do if you must change color? Do you call a color with the most cards, most points, least variety in ranks? Do you think about what opponents might have, or only consider your own hand?
• Does your strategy change if someone is very close to winning the entire match, i.e. somebody's close to 500 points? How close to 500 do they have to be for you to change how you play?
• Does your strategy change if you're losing the hand? How do you decide if you're losing? (Do you start ditching the high-point cards like Wild and Draw Two?)

Don't worry about answering all of those questions, but if you change your play depending on circumstances around the table, please mention it in your answer. Being precise helps me program a strategy that matches what you do, but if you cannot, just give me a general idea and I will post pseudo code of what the computer will do.

Don't worry about having the absolute best answer. I will program your strategy, and edit your answer to show its actual win-rate against other strategies.

Answer 1

I play the largest number I can and save my draws, skips, and reverses for when they can be used against a winning opponent. I really don't worry about number variety. However, I try to keep a low number of high value cards in my hand, namely reverses, wilds, and skips, in that order, so if someone manages to win I don't give them too many points.

call color: No Strategy (color i have?)

play: 
if hand has X or more Special Cards (SC), 
    play SC(if possible): priority Reverse, Wild, Skip, (Wild Draw-4, Draw-2), 9-0
else if opponent has Y or fewer cards
    if opponent next and hand has Draw-2 or Skip (or Wild Draw-4)
        play Draw-2, Skip, (or Wild Draw-4)
    else if opponent last and hand has Reverse and (Draw-2 or Wild Draw-4)
        play Reverse
    else
        play 9-0, Draw-2, Skip, Reverse, (Wild, Wild Draw-4)
else
    play 9-0, Draw-2, Skip, Reverse, (Wild, Wild Draw-4)

Answer 2

Getting the excuses out of the way early: I don't play much Uno at all, and when we do play we typically aim to win a hand, rather than keeping score over several hands. My strategy doesn't take any account of how near to 500 a player is, but presumably you should, as in the optimal Pig strategy.

I aim to get rid of high value cards, but keep a wild card for the end. I also included a 'panic' strategy for when I've been hit with a Wild Draw-4.

One interesting feature is that I occasionally choose to draw a card rather than play a wild card. I'm not sure whether you're allowed to do this according to the official rules, but we allow it.

Notation:
P - Previous opponent
N - Next opponent
O - Opposite opponent
M - Me
C(X) - The number of cards in player X's hand
min(C) - The number of cards in the leading player's hand

Call:
If I don't only have black cards left:
    Filter out colours I don't have
# Vaguely try to annoy other people
Name the one I have seen the most of so far (including my current hand)
Tie break by colour I have most of, then most recently played
If this is the first turn and I've only been dealt black cards, then pick red because it's my favourite.

Play:
If min(C) <= C(M) / 2 and min(C) < C(M) - 3:
    # I'm about to be trounced - throw away high points
    Play +4, change colour, +2
    If C(P) > C(O):
        Play change direction, skip a turn, 9-0
    Else:
        Play skip a turn, change direction, 9-0
Else if I have more than one black card left:
    # Try to save a black card for the end
    Play +4, change colour
Else if I have more than one +2 or C(N) < 3:
    # Very occasionally try to save a +2 in case there's one left over on top of the deck
    Play +2
Play skip turn, +2, change direction, 9-0, +4
If min(C) > 2 and min(C) > C(M) - 1:
    # I've got a wild card, and there's not much chance I won't get to play it
    Choose to draw a card
Play change colour

Additional 'strategies' that presumably aren't relevant in the AI tester:
If I play my second to last card call "Uno".
If an opponent fails to do this then point it out at the appropriate moment.

Answer 3

I don't know whether you're still running your experiment, but lately I've been trying various strategies for the phone-based version of Uno that I have and one that I've been doing is, when the color is C and I have X cards of C and Y cards of another color, D, if Y is greater than X, I go ahead and switch. It seems like it increases my opportunity of a string of cards being played versus staying in the same color and getting stuck earlier, assuming the color doesn't change on its own.