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Just started playing Uno. What are the most important strategies that might improve my game? Of course luck is important, but I'm trying to do better than crossing my fingers.

For example, before and after a player announces "Uno", should my play be different? While there's a "wild" card, how should I decide which color to switch to?

@paul-marshall thanks for the reply. I understand that normally i shall change color to the one that i have most cards -- but is there any occasion that i shouldn't do so?

For the wild card, let's say now i have one blue, one yellow, and one wild card, and the table is playing red. shall i use wild card to change color (to blue or yellow), or, just hold the card and hope i could discard yellow and blue later? is there some thumb rule when shall use wild card and when not?

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I have a possible second answer (might just delete the first), but I need some direction. What sort of strategies are you interested in? It looks like you are specifically interested in how strategy should changed based upon if one or more opponents have one card left (are you also interested in 2,3 or other late game decisions based on player hand size?), what call color you should choose when you have 2 colors and at least one wild, when the best time to use a wild (did you mean any wild?). important strategy, are you measuring that strategies increased odds at winning? –  user1873 Aug 30 '13 at 3:18
    
Or is Important Strategy a measure of improved odds at winning by difficulty to implement that strategy. For example, card counting all played card colors and ranks (0-9 and Special cards) is quite difficult to do, but probably increases your odds of winning by a substantial amount. (Counting colors only also probably increases your odds by almost the same amount, but is much easier to do.) Does color&rank counting rate higher as an important strategy than color counting alone? (Then there is the difficulty of measuring just how difficult a strategy is to pull off.) –  user1873 Aug 30 '13 at 3:23
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3 Answers

You're trying to run out of cards, and the opportunities to change colors are somewhat limited. Your goal, therefore, should be to play the last card of one of your colors, then be able to switch to another color you have on the next play. This doesn't always work, of course.

When changing colors (via wild or matching the card), you should switch to the color that you have the most of. Switching to the color that you have the most cards in gives you the best chance to "even out" your hand; if you're stuck with 7 cards in your hand, it will be easier to play when you have 2 yellows, 2 reds, and 3 greens than to play when you have 5 yellows and 2 reds. Note that it will be easy to play one card when you have a four-card hand consisting of one of each color, but it will be hard to go out with such a hand: changing colors is somewhat difficult, and you can't count on it happening when you want it to.

When somebody calls "Uno," it's best to assume that their last card is the same color as the previous card they played; otherwise, the player going out is hoping against hope for a lucky play. Therefore, you change the color in play after somebody calls "Uno," by whatever means is handy. (Or inflict a Draw Two or Draw Four Wild against them.)

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I disagree on your theory about a player who called Uno being more likely to have the same colour card as the one he/she just played. I consider myself above average at calculating statistics during game play and have found that this is more often not the case than you might expect from the play style that you'd expect players to play (eliminate cards by colour). In my experience keeping the colour the same is the better choice, the player with just one card is more likely NOT to have the same colour. Just my opinion and on-the-fly statistics. –  Bazzz Aug 27 '13 at 13:21
    
@Bazzz, what do you mean by "more often than not"? 10% chance of same color? 30%? 60%? If they have a 34% chance of matching the current color (or higher), then you should definitely change colors; if you change, and they don't have the current color, then you still have a 67% chance of stymieing them. –  Paul Marshall Aug 27 '13 at 17:13
    
I have a feeling (based on my own experiences with the game) that if you were to keep track of the times players calls Uno and the last card is the same colour as the one they just played, and you were to keep track of the times players call Uno and the last card is of a different colour than the one they just played, that the "different colour" track will end up having a higher number. –  Bazzz Aug 27 '13 at 19:26
    
That's a problem: you'd need to know how much more often they have a different color. If they have the same color just 34% of the time or more (it's different less than twice as often as it's the same), you need to switch, because the odds of switching to the wrong color are pretty low. –  Paul Marshall Aug 27 '13 at 22:08
    
@Bazzz and PaulMarshall, I am working on modifications to an UNO simulator. I am very interested in this question of how often the 2nd to last card (UNO!) is the same color as their very last card when they go out (all possible scenarios;Wild&Wild, Wild&Color, 2CardsSamecolor, 2CardsDifferentColors). My problem is that I am not certain exactly how to model players "normal" behavior. What colors a player has left will vary greatly based upon their strategy. The best strategy I have found so far is to always play the highest Point card in the color with the most cards. –  user1873 Sep 21 '13 at 2:53
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A couple of pointers from the rules.

  • Keep your score low: The winner is determined by whomever scores 500 points first, or in the variation Running Player Totals, by whomever has the lowest total points when someone reaches 500. A good strategy is always try to play your highest value card if you can (other than a Wild/Wild-Draw-4, since at least one of those can be played when a player calls UNO), or to switch to a color that has the most points in that color in your hand. (I.e. if the top card of the discard is a red 5, and you have a red-6, red-0, blue-5, blue-7, the best play to keep your score lowest is probably the blue-5. Although it is one point higher than the red-6, "blue" has more total points in that color that you need to get rid of.)

Scoring - When a player goes out, all other players card values are added that players total. First player to 500 points wins. Wild, Wild Draw4: 50 pts, Draw2, Skip, Reverse: 20 pts, All number cards (0-9): Face Value. Variation: Running totals for each player can be kept instead. When one player's total reaches 500 (or some other value), the game is over and the player with the least points wins.

  • Maximize playable cards - While Paul Marshall points out that you should try to even out colors, you should also try to even out numbers and word cards (numbers/names are a lot less probable with 25 cards of each color, and only 8 of each name/number other than 0). Each extra differently named/numbered card reduces unplayable discards (I.e. With only two cards left, if they are differently numbered and colored, there are only 42/100 unplayable cards (not counting Wilds). If the two cards are different colors, but are the same number/name then there are 46/100 unplayable cards). Additionally, if you have lots of a particular named/numbered card, then there are fewer of those in the deck or players hands, which also reduces the likelihood that you can play them.

  • Play Draw cards when going out - If you can manage to go out on a Wild Draw-4 or a Draw 2, those cards are added to an opponents hand before scores are calculated. These additional card draws add on average 11.48 points/card to your score.

  • Attack the leader - This is only easy if you sit adjacent to them. You can choose to play Wild Draw-4 cards, even if you have a playable color. If you aren't caught, the person about to win just drew 4 cards. If you are caught though, you draw 4 and likely added 46 points to their score. If not adjacent to a player, you can choose to change colors if the leader called UNO and chose the color themselves (makes it less likely to have the right color).

  • Reneg instead of using Wilds If you have 3-4 cards left, in different colors, with a Wild, it might make sense to Reneg and draw a card instead of giving up the wild. When you Reneg, you can only play the card you draw, but you have approximately (24+8+7)/108=35% chance of drawing a playable card (24 other cards of that color, 7 other wilds, 7 other cards of that number/name.

Some of these strategies conflict with others, so the state of the game will determine what the proper action to take is. For example, if you have many more cards than an opponent who is sitting on 3 cards, you should probably start getting rid of your high point Wild-Draw 4 card (50 points instead of the average 46). Draw 2 actually has a worse average payout for an opponent than making another player draw two cards.

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Change colour as much as you can, most players want to maintain the colour as long as they still have cards of that colour and want to change otherwise. A nice way to approach this game is to always change the colour when you can (by number on number or by wild), even if you still have cards of the previous colour. The theory behind this is that on average you'll receive an equal number of cards of every colour. If you deplete yourself of a certain colour you will end up drawing cards when that colour is the current one. Changing colour often results in you having a multi-coloured hand that enables you to always have a playable card, and depend less on luck. Subsequently it minimizes the number of draws that you need to make. And, it annoys the other players which is a good thing.

As mentioned in my comment I disagree with Paul on his theory that the player who calls "Uno" is most likely to have a card of the colour that they just played. Expecially if the card that they just played is a low number. Players tend to get rid of the higher numbers earlier (for obvious reasons). If the Uno caller just played a red "2", I will most certainly attempt to keep the colour red as I strongly believe that the chance that they have another red card and it being lower than 2 (as players tend to play 2s before they play 1s and 0s) is smaller than the chance that they have any card of another colour.

Generally speaking what I'm saying here is that if you want to be less dependent on luck you should likely get yourself familiar with some quick on-the-fly basic statistics that you can apply whilst playing. How many cards of a certain colour have been played already? Is it therefore more likely that the Uno caller has that colour, or not? Etc.

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