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, handling 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.