# Card Game Spades Strategy - by Example

### by Holger @ World of Card Games

# Spades rankings at World of Card Games

### by Holger @ World of Card Games April 21 2016 [Edited Dec 25 2017]

**Table of Contents**

### Elo ratings and Skill

Ranked tables were added to the Spades game at World of Card Games on April 10, 2016. They are similar to Hearts rankings. In Spades, however, there are **teams**, so the rankings have to be computed differently.

To review: A ranked game is similar to a regular game, except that your "Elo rating" and "skill rating" are recorded upon finishing the game. Also, the rules are more strict. If you are eligible to play in ranked games, you will see one in the list of tables, under "spades" - it shows up as being "ranked" in the description and is colored purple. You can also get to ranked games by clicking on the Menu button next to the Spades game panel.

The "Elo rating" is described at Wikipedia, and is used by many online games to rank players. I use this system because almost everyone else does!

There are many skills needed to play Spades well. When I was learning to play, the thing that I found most difficult was setting an opponent's nil bid. It can really throw you off your game when you see a nil bid. So to encourage people, especially non-experts, to try to set nil bids, I've added a "skill rating" to ranked games. The skill ratio is the number of times you set an opponent's nil bid divided by the number of times your opponent bid nil. I should point out here that in unusual cases, prioritizing setting a nil bid over making your own bid can be against your best wishes. Remember that the main goal is to 1) have fun and 2) win.

### Rules

These are the rules about **who** can play a ranked game:

- Only Registered players can participate.
- You must be "experienced" at the site to participate. You just need to play a few regular games before you are "experienced". It gives you a chance to become familiar with the site before you play a more serious ranked game.
- You must have the "Rank Me" player setting checked - all eligible players have this checked by default.
- Robots are not allowed at ranked tables to start, but can be invited if someone drops out. (I'd like to make robots forbidden altogether, but at this point, it's just too difficult to get players to sit at a no-robots table, even if the game has barely started. I may revert this rule later.)

**how**you play a ranked game:

- If you quit a ranked table before the game has finished, you will be banned from participating in ranked games for
**2 hours**. - If you uncheck the "Rank Me" player setting, you will be banned from ranked games for
**1 week**. Your current Elo rating will also be reset to the default value (1500).

If a player quits a ranked table, other players can join as "substitutes". Substitutes do not participate in the rankings, however - so it will just look like an ordinary game to them. If you quit a ranked table, it counts as a forfeit for you. Your teammate is unaffected, and may even go on to win. Note: it can sometimes happen that a player drops out unintentionally, perhaps due to a computer problem. If you drop out, but return to the site within 3 minutes, you will be reconnected to your ranked game automatically.

You can view your Elo rating and skill rating by clicking the "stats" link in the upper right corner, and checking the "Spades" radio button.

When you hover your mouse over a player in the "list of tables", you will be shown the player's Elo rating, provided they have been ranked.

### How Elo Ratings are Computed

Wikipedia does a pretty good job of explaining how Elo ratings are computed.. There, an example is given of someone playing in a 5-round tournament:

Suppose Player A has a rating of 1613, and plays in a five-round tournament. He or she loses to a player rated 1609, draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. The player's actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. The expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore the player's new rating is (1613 + 32 * (2.5 - 2.867)) = 1601, assuming that a K-factor of 32 is used.At World of Card Games, the process is very similar. The performance of each player against their opponents at the table is treated as a "round" in the tournament described above. Here's an example for a game of Spades.

Suppose there are 4 players: A, B, C, and D, with ratings 1512, 1562, 1484, and 1417, respectively. A and C are teammates, while B and D are their opposing teammates. The "expected" score for player A competing against player B is computed as 1 / ( 1 + 10^{(Rbavg-Raavg)/400} ). As of Dec 24, 2017, Rb_{avg} is the average Elo rating for team B and D, (Rb + Rd)/2, and Ra_{avg} is the average Elo for team A and C, (Ra + Rc)/2. Using the average Elo rating helps to distribute the performance of the team more evenly, especially when a team is composed of players with widely mismatched skills. In this example, Rb_{avg} is 1489.5 and Ra_{avg} is 1498. Prior to this change, the expected score was computed as 1 / ( 1 + 10^{(Rb-Ra)/400} ), where Rb was just the Elo rating for player B (1562), and Ra was the rating for player A (1512).

According to Elo, a player's actual score is given by 1 for a win, 0.5 for a draw, and 0 for a loss. If player A won against player B, then the actual score for player A would be 1.

In a Spades game, performance for an individual player is evaluated against 2 opposing players. If players A and C won over B and D, then player A's "actual" score is Sa = 1 + 1 = 2. The expected score for player A is the sum of [1 / ( 1 + 10^{(Rbavg-Raavg)/400})], evaluated for each player on the opposing team: Ea = 1 / ( 1 + 10^{(1489.5-1498)/400} ) + 1 / ( 1 + 10^{(1489.5-1498)/400} ). Note that it is not a mistake to add the same number twice; the computation is done once for each "match" against your two opponents. The total amounts to 1.024 approximately (previously, without using the average Elo, it was 1.06). You can plug the formula into Google, which can calculate this for you.

Player A's new Elo rating is computed according to the formula given in Wikipedia: Ra' = Ra + K * (Sa - Ea), where Ra is their current rating, 1512. At World of Card Games, I have used an Elo K factor similar to those found at other game sites ~~30 for experienced players (who have played more than 50 games) and 50 for inexperienced ones~~ [Edit: In 2017, the Elo K was changed to 25 for all players.] Then Ra' = 1512 + 25 * (2 - 1.02). Google's handy calculator function says that is 1536, the player's new rating.

A similar computation is made for players B, C, and D. Each player's Elo rating is computed using their own Elo rating and the Elo rating of their two opponents.

Please check out the Wikipedia article for more details if you are curious. Obviously, there are flaws to applying a rating system that was developed for chess to a card game like Spades. Most game sites use this system, and I have followed suit.

You may want to try the Elo rating calculator for team games, to get a feel for how points are traded off between players during a Spades match.

#### Why aren't quitters penalized extra?

In Hearts, your Elo rating suffers more if you quit a game because you automatically lose to all remaining players. In Spades this is not done. For one, rating a player against their teammate when they quit seems just too bizarre. It would put the player in a match against three other players, while the opponents would be matched against just two, and that would lead to a skewing of the ratings. Also, I've had a few protests about the way that a player's Elo is affected when quitting a Hearts game. Some people say that it is enough that they lose the game automatically, and they should not take a loss to all remaining players. So the Elo ratings in Spades do not place an additional penalty on a quitter. It's an experiment to see if a heavier penalty is needed for quitting or not.

#### Example when a player quits

Suppose 4 players with an Elo rating of 1500 start a ranked Spades game. Mary and Sue are teamed up against John and Peter. Halfway through the game, Peter realizes he must rush off to pick up his kids from school, so he apologizes and quits the game by clicking the "leave table" link. His Elo rating is immediately changed from 1500 to 1475, and he is banned from ranked play for 2 hours. The new Elo rating is computed from the formula Ra' = Ra + K * (Sa - Ea) = 1500 + 25 * (0 - 1) = 1475.

The Elo ratings of all remaining players are unaffected until the game is finished. Now suppose that John, whose partner quit, goes on to win the game. The resulting Elo ratings of the remaining players are computed with Mary and Sue winning against Peter, but losing to John, so their Elo ratings actually remain at 1500. As an example, Mary "won" over Peter (because he quit), and lost to John, so Mary's Sa = 1 + 0 = 1. Mary's Ea is also 1. So the formula Ra' = Ra + K * (Sa - Ea) = 1500 + 25 * (1 - 1) = 1500.

Finally, John wins his 2 matches against Sue and Mary. His Sa = 1 + 1 = 2, and his Elo rating becomes Ra + K * (Sa - Ea) = 1500 + 25 * (2 - 1) = 1525.