Hearts rankings at World of Card Games

by Marya @ World of Card Games Oct 2 2015

Table of Contents

Elo ratings and Skill

Ranked tables have been added to the Hearts game at World of Card Games.

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 "hearts" - it shows up as being "ranked" in the description.

The "Elo rating" is described at Wikipedia, and is used by many online games to rank players. The reason that I'm using this system is that almost everyone else does. :) I think some people will enjoy seeing how well they do in the ranks.

It takes skill to play a game of Hearts well... so I've added a "skill rating" to ranked games as well.

There are several skills required to win a game of Hearts. As you grow in Hearts wisdom, you will find that if you are dealt the Queen of Spades, you won't always want to pass it to another player. Rather, you will want to hold onto it, and as you play your cards, look to drop it on the player with the lowest score. It takes a lot of skill to know when you should pass the Queen or hold it, and when you should play it rather than dumping it on anyone at the earliest opportunity...

So the site now records when you hold the Queen, and when you drop it expertly on the low-scoring player. Your skill ratio is the number of times you drop the Queen on the "low man" divided by the number of times you hold the Queen. Some adjustments are made: for example, during the first hand, there is no "low-scoring" player (you all start out at zero), so holding or dropping the Queen is not recorded in this case. Also, if you are the player with the lowest score, and you drop the Queen on yourself, this does not count towards your skill rating (but at least it doesn't subtract from it!).


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

There are also rules about how you play a ranked game:

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. Since ranked tables carry penalties for dropping out, it might be hoped that players will be less inclined to quit midway... so there is an incentive to playing as a substitute.

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

hearts Elo rating in stats

When you hover your mouse over a player in the "list of tables", you will be shown the player's Elo rating:

hearts Elo rating in list of tables

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 the other players at the table is treated as a "round" in the tournament described above. Here's an example for a game of Hearts (gory details are here only for those who are intensely interested).

Suppose there are 4 players: A, B, C, and D, with ratings 1512, 1562, 1484, and 1417, respectively. The "expected" score for player A competing against player B is computed as 1 / ( 1 + 10(Rb-Ra)/400 ), where Rb is the rating for player B (1562), and Ra is 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.

But in a Hearts game, performance has to be evaluated against 3 players. So if player A came in 1st, they won against players B, C, and D. So their "actual" score is Sa = (1 + 1 + 1) = 3. The expected score for player A is the sum of [1 / ( 1 + 10(Rb-Ra)/400)], evaluated for each player: Ea =1 / ( 1 + 10^((1562-1512)/400)) ) +1 / ( 1 + 10^((1484-1512)/400)) ) +1 / ( 1 + 10^((1417-1512)/400)) ). This amounts approximately 1.6 (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. Suppose player A is experienced. Then Ra' = 1512 + 30 * (3 - 1.6). Google's handy calculator function says that is 1554, the player's new rating.

A similar computation is made for players B, C, and D. If player B came in 2nd, they "lost" to player A, but "tied" with players C and D. This determines their actual and expected scores. If player C is 3rd, they also lost to player A, but tied with players B and D. [Editor's note: As of November 11, 2015, Elo ratings are computed with only 1 winner. The Elo ratings of players who come in 2nd, 3rd, and 4th are computed as if they lost to the 1st place finisher, and tied with each other. This change was made due to popular demand.]

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 Hearts. Most game sites use this system, and I have followed suit.

Why Don't Second and Third Place Count?

Some people find it intuitive that a person coming in 2nd place did better than a person in 3rd and 4th place. I've had people tell me that they want 2nd place to count, since it shows that they are at least doing better than coming in last. I've also had people tell me that it should not count. They say that only 1st place matters in Hearts, and that giving credit to 2nd place winners for a "win" over 3rd and 4th placers gives them an incentive to play poorly, by striving for 2nd place instead of going all out for 1st. (FWIW if you are frequently coming in 2nd, you will probably want to change your strategy.)

There is one advantage to giving people credit for placing ahead of dead last. If 2nd and 3rd placers are given no credit at all, they have less incentive to finish the game.

As of November 11, 2015, I changed the Elo ratings so that only 1st place is rewarded, due to popular demand. Players who come in 2nd, 3rd, and 4th all get Elo ratings computed with a loss to the 1st place finisher, as mentioned in the previous section. Their Elo rating is computed as a tie in the "matches" against each other. So in fact, everyone still has a good reason not to quit, even when they are losing. If they quit the game early, they will be penalized by getting an Elo rating that is computed as a loss to all remaining players in the game. This Elo rating is worse than if they stay and accept a tie with the other non-winning players.

comments? email me marya@worldofcardgames.com


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