World of Card Games

Here's another post for the Euchre fans! Have you ever heard about the "reverse next" strategy? Recently, I've explored some statistics about how often "reverse next" can be used, and whether it works. Click that link to get the full scoop!

my partner, the dealer, is going to pass on this up card, a jack...

I'll call clubs with only the king and nine of clubs, using "reverse next" strategy. Will it work??

I've collected some statistics about the "consider" phase in Euchre, as played at World of Card Games. If you like Euchre, you might enjoy reading this! Click the link above to see more.

what are your chances of calling trump if you're the dealer?

[Edit: I added a second page of stats - check out part II.]

Today, we have a guest blog from DevilDoc about the nil bid in Spades. I have added some links to definitions of "jargon" terms to help beginners. There's also an intro to nil bidding at the World of Card Games website. - Marya

The nil bid in Spades is the strongest of all the bids one can make. Worth 100 points, it represents 20% of the total game score if your partnership makes it. It also costs your partnership 100 points if you get set plus the penalty for your partner’s bid.

How to bid a nil: The ideal hand should be rich in distribution; i.e., singletons, doubletons, and voids. Ideally, you don’t want any honor [face] cards but if you have any, they should be protected by at least two low cards. The maximum number of spades should not exceed three, with no higher card than the Jack (25% probability of being set). While some will use the Queen of Spades, your probability of being set rises to 50%.

How to defend a nil: The bidding player needs to focus on his loser cards. You want to discard your highest cards as soon as safely possible. If your partner is running a long suit or you have a good distribution, that is the easiest way to get rid of your riskiest cards. The bidder’s partner needs to lead out with the highest card of his longest suit and keep running that suit, from high to low cards if possible. If the bidder’s partner’s hand is weak, he should focus on what the opponents are leading to see if they can cover your cards.

- DevilDoc

stats info panel

I've had a number of people tell me that they accidentally click their avatar when playing a card, and it causes the "stats info" panel to pop up, unintentionally.

I've had it happen a few times myself. Since it was bothering some people, I've changed this feature so that you must click your own name to get the "stats info" panel to pop up. See the screenshot above for how it works. If you click another player's avatar, the stats will still pop up that way. It just works differently for you, and will not appear if you click your own avatar.

You can view a few player statistics while you are at a table, after this morning's update. Just click any player's avatar, and a "mini stats panel" will pop up for each player [Edit July 24 2016 - click your name to get the stats panel to appear; click any other player's avatar for the same effect]:

mini stats panel

The first number is their Elo rating. This only appears in games that have rankings (currently Hearts and Spades). If all that you see is a dash, then the player is not yet ranked.

The 2nd number is how many games the player has "completed". This is the same as the number shown as "Finished" in your own stats panel.

The 3rd number tells you how much the person tends to quit games. You should not expect this to be a perfect 0%, since people sometimes get kicked from games accidentally, or have to leave due to unforeseen circumstances. Only the last 16 games are tracked, so it's pretty easy to improve this score with just a few games. Note: it is not counted as quitting if

• you leave a table that has not yet started
• you leave a bots-only table before the game finishes
• you leave a private table before the game finishes

This score is supplied to give you an idea about how reliable the player is. The higher the percent, the more likely it is that the person might skip out on your game.

The update this morning also fixed a long-standing issue that players were able to sign in from a table. It's convenient to be able to do this if you forget to log in from the home page, but some people were using it to manipulate their stats by logging in just before a win at a table. It's no longer allowed, and there's an obvious reminder at the top of the home page letting you know when you're not logged in.

sign in from the home page only!

Other changes: The cards are now fanned wider by default in the Twenty-Nine game, and chat lobbies now hang around for 24 hours at least. Also, bot strategies have been slightly improved in Spades and Double Deck Pinochle.

You can now play ranked Hearts card games at World of Card Games. There are more details at that link, so take a look there if you are interested.

I've added two different rankings - an "Elo rating" and a "Skill rating" -

Elo rating and Skill rating

If you are eligible to play at a ranked table, you'll see the "ranked" table in the list of tables panel. Click on a seat to be taken to the table.

a ranked table in the list of tables with 3 seats available, note purple color

Bots are unavailable at ranked tables until near the end of the game, so I expect that it may be difficult to get a ranked game going, especially for players outside the US time zone [Edit: as of Oct 3 2015, bots may be invited as soon as someone drops out]. I don't think it makes a lot of sense to rank individuals against bots, though, since they don't have expert levels of skill.

There are several advantages to playing at a ranked table: because quitting a table has a more serious penalty than simply taking a loss, it can be hoped that players will be less likely to quit. In addition to your Elo rating taking a hit, quitting gets you banned from ranked tables for 4 hours. This means that you should find more reliable players at the ranked tables, on average.

I'll be playing at the ranked Hearts tables on and off during the day, and look forward to hearing from people about their experiences with it.

If you experience any problems or bugs after this update, please let me know. There were some major changes!

Some Euchre players may be interested to know where they stand in their win/loss statistics at World of Card Games. If you don't want to know, stop reading now! ☺

In September of 2015, I computed the win ratio for Euchre players who had completed at least 100 games. I used the numbers that produce the "Absolute win/loss ratio" shown under your "stats" link. Below you will see the distribution of players by win percents. There's one player who has managed to attain a win ratio of > 70%. There are 15 with win ratios between 60-70%... most players come in around 40-50%, which I still think is really very good (especially because that's where my stats stand!).

distribution of players by win percent

Personally, I don't care about my statistics at all. Well, maybe a tiny bit, because I do look at them once in a blue moon. But when I'm playing, it is just for fun. This is what matters to me most.

There is some speculation about just how good you can get with your statistics; how much of Euchre is a matter of luck, and how much is skill. Some people think the best you can do is somewhere around 66%... and these statistics support that idea.

The server at World of Card Games was down for a short period this morning, to apply some bug fixes and updates - sorry for the interruption in service!

There's a new category in your "stats" area: "absolute" wins and losses.

The rules for a game counting as an "absolute" win or loss are as follows:

1. There is only 1 winner per game.
2. If you leave a game before it ends, you forfeit that game, and it counts as a loss for you.
1. Exception: If you are seated at a table for less than 30 seconds, it will not be counted as a forfeit if you leave. This is done to be fair to someone who takes a losing seat directly at the end of a game.
3. Only human players are counted as winning or losing; if a bot wins or loses, it does not show up in the global statistics for absolute wins and losses.

new "absolute" statistics

This is in contrast to your "Games Played" number. That includes all games that you have been in, even if you left after 1 second! If you stay with the game until the end, that is counted in your "Games Finished" number. If you quit before the end, it is counted in your "Games Abandoned" number. So the absolute stats are  a little more lenient. They forgive you if you take a seat by accident, perhaps with a very poor losing position, and quickly leave.

These new statistics are being recorded for a couple of different reasons.

First - the original way that statistics were recorded at World of Card Games was confusing to many. These statistics are now shown as the "Relative Win Ratio". An example will explain the counting used: If you came in 1st place in Hearts, you were counted as winning against 3 other players. If you came in 2nd place, you were counted as winning against 2 other players and losing against 1 player. This counting method is relatively expressive - a person who comes in 2nd place a lot is probably a better player than someone who comes in 3rd place a lot, but if you count both placings as "losses" then you'll never see this distinction. However, most people expect a single winner for a game! This new statistic provides that clarity.

As an aside, the above counting method would not lead to confusion in team games like Spades, because there are exactly two winners and two losers (the winning and losing teams) in that type of game. It was really only a problem in Hearts, 3-5-8, and Go Fish.

Second - it has been proposed that some players are leaving a losing position  shortly before a game ends so as to avoid having a loss counted against them. With the new forfeit rule, there will be no encouragement to leave a game early. I am a little skeptical that this will help with the "quitting players" problem, but we shall see.

These new statistics are experimental, so don't get too attached to them yet. In the next few weeks or months, I may make modifications based upon feedback; in that case I'll probably wipe the new stats and start fresh. Stay tuned.

1k Facebook likes!

This morning, I noticed that there are now 1000 Facebook likes on the World of Card Games main page! Thanks to everyone who gave it a thumbs-up, and who helped it to grow by inviting their friends to come play as well!

If you haven't seen it already, read Part I for context.

There have been various suggestions for solving the problem of quitters. There is speculation that people who quit games early are protecting their statistics. This is because the Win/Loss ratio shown in your stats does not account for abandoned games; it just gives the ratio of all games won to all games lost. A loss is not recorded against you until a game ends, so leaving early does not show up in your stats.

If this is true, it might help to penalize people who are leaving the game early. It has been suggested to penalize such drop-outs with 1 (or more!) losses in their stats. Another suggestion involved imposing a penalty in the form of a time delay before a quitter can join a new game.

The problem with such solutions is that 1) it doesn't seem likely that they will work and 2) they will cause innocent drop-outs to be penalized as well.

There are reasons that a person might unintentionally leave a game. I've been in games where someone innocently clicked the "leave table" link. And sometimes a person reloads the web page and finds that they've been kicked out of their game. In such cases, the player rushes to get back to their seat, because they want to stay in their game. Since there's no way for the site to tell why someone left the table, inadvertently penalizing such a player with a delay (or a loss) just seems cruel.

There are a couple of reasons that I think a penalty won't work for intentional quitters.

I suspect that a number of quitters are just trying to avoid the psychological impact of something "bad" happening to them. We've all seen quitters leave just before they get hit with the Queen of Spades in Hearts, or before taking a trick when they've bid nil in Spades. People do this even early in the game, when there's plenty of time to make up for such a setback. People who do this will continue to quit, no matter what penalties are imposed.

On top of that, the statistics are not shared. If you're quitting to make them look good, then you know that your stats are meaningless. Given that fact, I have a feeling that quitters are not motivated by their stats.

In any case, as an experiment, I will soon be introducing a new statistic. It is designed to more clearly show whose stats look good because they're really winning more than average, and whose look good because they're evading losses.

Possibly the most frequent complaint that I get at World of Card Games is about people quitting games. I've been collecting some statistics to see how the site is affected by habitual quitters. Here are the results!

The charts below are histograms that show the number of players divided up according to their quitting patterns. Players who rarely quit - between 0 and 10% of their games - are "bucketed" in the first column. Players who quit a lot - 90%-100% of their games - are bucketed in the last column. The rest are divided into buckets between those percentiles.

Private tables are ignored in these statistics, as are tables with only a single human player. Quitting from such tables is not a major problem. On the other hand, if you enter a game and then quickly leave, you are getting counted as a quitter for the purpose of these statistics. So the charts may make things look a little (or a lot?) worse than they are.



Euchre is a fairly quick game - you are usually done in 10 minutes. Quitters are not as big a problem, here.
One noticeable thing is that the games that take longer tend to be affected more by quitting. I do wonder how big a factor this is in quitting.

[tl;dr: so far as I can tell, cards are dealt perfectly randomly at World of Card Games. If you think that the deck is stacked, it's probably an odd run of bad (or good) luck that you're seeing.]

Sometimes, players will tell me that they think the deck has not been properly shuffled. They've had an unusual run of bad luck. Perhaps in Euchre, they haven't seen a bower in their last 5 hands, and it looks suspicious. In Gin Rummy, their opponent was dealt a Gin hand immediately. Or in Spades, they've been dealt a hand with no trump cards too many times to be believable.

At World of Card Games, the cards are dealt randomly, and I see no way that the deck could be stacked. Here's how the deal of cards works in every game on the site:

1. Every time that cards are dealt, an entirely new, ordered deck of cards is created by the system. It's as if I took a fresh pack of cards out of a sealed deck; the old deck is not re-used.
2. Then, these cards are "shuffled" using a random number generator.

That's it! It's very simple. You may see odd results, just like you might see a long run of "heads" in a repeated coin toss. But it's just random.

For those who are curious, just what is the probability of getting a trump-less hand in Spades? Here's an explanation:

A hand in Spades consists of 13 cards from a deck of 52. The number of combinations of such cards is 52! / (13! * (52 - 13)! ). According to Google's calculator, that is 635,013,559,600 (over 635 billion). That number includes all trump-less hands, and all hands with trumps as well.

To be clear, this does not count combinations in which the cards are merely reordered. For example, this count includes an entire hand filled with Spades, but only one such hand - the order of cards in the hand does not matter. For those who are hoping, this means the chance of ever getting a hand completely filled with Spades is 1 in 635 billion. "Not very likely" would be an overstatement.

all spades - dream on!

Okay, so how many of these hands are there that exclude trumps (Spades)? That is computed by taking all combinations of cards from a trump-less deck. A trump-less deck contains 39 cards (52 cards minus 13 Spades suit cards). Applying the formula for combinations again, we get 39! / (13! * (39-13)!). Google's calculator says this is 8,122,425,444 - about 8 billion different combinations of non-Spades cards.

So, there are about 8 billion trump-less hands in all 635 billion possible hands of Spades. The probability of getting a trump-less hand is the ratio of trump-less hands to all hands, which is about 1.28%. Not very likely, but it happens.

To test all this out, I ran a million simulations of Spades cards being dealt exactly as they are done at World of Card Games (using the same computer code). Here are the results:

• There were 4,000,000 hands dealt in total
• There were a total of 51368 trump-less hands, which is, indeed, 1.28% of 4 million [100 * (51368 / 4000000) = 1.28%]
• The count of trump-less cards for the first player was 12772, second player was 12790, third player was 12996, and fourth player was 12810.

In case you are wondering about that last bit, a certain amount of variation is expected between the different players. Notice the third player was getting slightly more of the trump-less hands in the above experiment. When I ran the experiment again, it was the second player who got most trump-less hands (12945). A little bit of variation is expected because of the random nature of the events.

I recently got an email from a player who thinks it would be better if the "stats" area in World of Card Games did not show your Win Ratio. Their idea is that people are too concerned about their win/loss ratio, and this motivates them to quit games when they are losing. They thought that without this ratio being displayed, people would be less likely to quit.

What do you think? Should I get rid of the Win Ratio under the stats area?

A few months ago, I started collecting statistics on the table options that people are using at World of Card Games. I thought it might be interesting to some people, so I'll share the results here.

In all of the games, the most popular table options are the default ones: robots allowed, do not require registered players, no private table setting. That may mean people don't realize that they can change them, or perhaps they don't want to be bothered. Here's the breakdown by game:

• Hearts: 60% of tables have the default options.
• Spades: 53% "
• Euchre: 56% "
• Go Fish: 94% "

The second most popular option is to use a private table with no table name (table name is set to "none") - this setting is used by players who want to play with robots only. Here's the breakdown for that:

• Hearts: 29% of tables are private, for playing with robots only.
• Spades: 19% "
• Euchre: 22% "

The third most popular option is to forbid robots. Some people really dislike the robot players (I admit, they need improvement!). Here are the statistics for that category:

• Hearts: 7% of tables forbid robots.
• Spades: 11% "
• Euchre: 17% "

Well there you go! Very few people have the "Registered Only" option set. That's interesting. If you set this option, only registered users will be allowed into your table. This may be useful if you want to recognize who you're playing with. Guest numbers change, so if you played with Guest #10 yesterday, they may be labelled as Guest #251 today.