On the Dangers of Giving Games as Wedding PresentsorWell, it seemed like a good idea at the time...

[This is a letter I included with a recent wedding present.]

Dear Ben and Sarah,

Well, it seemed like a good idea at the time…

I think you’ll enjoy this game, Thunderstone. I’ve been playing it a lot with my son. Like Race for the Galaxy, this one works very well with two players, but can also handle more players. (Predictably, with more players, it becomes very chaotic, especially when thieves are in play…) I’m so certain you’ll enjoy it that I also got you the first expansion, Wrath of the Elements.

You might notice that this box is the Wrath of the Elements box. See, the first Thunderstone comes with a huge box, with lots of wasted space. That box is twice as big as this one, and only comes with about half the cards you see before you. Knowing that dealing with the larger box would be difficult for you, I’ve combined all the cards for both the main game and the expansion into this one box. (By the way, if you end up liking the game, this box will also easily hold the cards for the second expansion, Doomgate Legion.)

There was just one eensy teensy flaw with my plan. A minor thing really, hardly worth mentioning.

The original rulebook was too big for this box.

I considered several options: Just leave out the rulebook and point you to the online rules. Stick the rulebook in a separate, sturdy envelope, which is guaranteed to get lost in about 13.8 nanoseconds. Fold the rulebook in half and jam it in the box. Then I found the perfect solution. A post on BoardGameGeek described trimming the top and bottom off the rulebook—which is all wasted space anyway—with a paper cutter.

Fun With Words Did you know that a mangle was a British machine used in the 1800’s to press water out of clothes? It’s called a wringer in the US. A probably apocryphal story asserts that the word mangle came into the English language to describe the damage done to clothes by this machine, but I think the causal chain is more likely to run in the other direction, with the machine being named after the word.

Umm, where was I? Oh yes, paper cutter.

Anyway, so I bring the rulebook into school and take it over to the room with the paper cutter. I line it up carefully, and pull down the chopper…which cuts about an inch into the rulebook and sticks. I push down a little harder…and the entire back of the paper cutter lifts off the table, the chopper twists the rulebook and pulls it partway off the bed and…

Hey, have you ever had a jam in a paper shredder? And cleared it by pulling half shredded paper back out the top of the machine. The papers come out looking pristine partway down the page, and then at a certain line of demarcation (you know, that line really ought to have a cool name, like the Maginot Line or the Mendoza Line), the rest comes out drooping in sad, wrinkled tatters. What’s the word? Oh yeah, mangled. Why do I bring that up? No reason, really.

Hmm, where was I? Right, paper cutter!

So I lift up the chopper and pull the rulebook out and…let’s just say it’s not looking too good. I flip it over—the rulebook, not the paper cutter, although that might have worked better—and try again on the other side. Let’s just say that that side left me longing for the Golden Age epitomized by the results of the first side. A few more minutes, and a few muttered imprecations later, and…

You know, my wife use to do scrapbooking, and they sell these funny little scissors that are designed to make an artistic ragged edge. Expensive little buggers. If only I had known, I could have saved her a lot of money.

So…Thunderstone! Great game! I think you’re going to like it. [a few personal comments deleted]

Congratulations!

Chris

Games for Programmers: Black Vienna

The next in an irregular series of board game recommendations for programmers. Of course, you don't have to be a programmer to enjoy these games, but if you are a programmer, then I think there's a pretty good chance that you'll like them.

O frabjous day!

My favorite deduction game, Black Vienna, has long been out of print, but now you can give it a try online, thanks to the efforts of Greg Aleknevicus. Go check out Black Vienna Online. It's free and easy to use. The user interface isn't going to win any awards, but it gets the job done. I'm thrilled that this game can now reach a wider audience.

Most deduction games are for two players, but Black Vienna handles three to six players. Your goal is to figure out the members of the infamous “Black Vienna” gang. There are 27 suspect cards, labeled A-Z and Ö. At the beginning of the game, three of these cards are chosen randomly and set aside. Those are the members of the gang.

The remaining 24 suspect cards are dealt out evenly to the players. (With 5 players, one of the players gets only 4 cards.) These are the cards of suspects for whom you can provide alibis.

On your turn you conduct an investigation. There is a pool of available investigation cards, each showing three suspects. You choose one of the available investigation cards and place it in front of another player. That player marks the card with plastic chips, according to how many of the suspects are in her hand. For example, if I have the cards BGMTXY and somebody plays the BQT card on me, I would mark it with two chips (for the B and the T). Other players would then know that I had two of the three suspects, but not necessarily which ones.

The turn then passes to the player who was just investigated.

One nice thing about Black Vienna as a game is that every player is involved on every turn. Even if you are not actively part of the investigation, you still need to update your information with the results of the investigation, and follow any chains of deductions to their conclusions.

Example Deductions

Some deductions are obvious. For example, if I played two chips on the BQT card, and you have the Q card in your hand, then you know that I have the B and the T. Other deductions are less obvious. Here's an actual example from a recent game. Call the other players Caitlin, Monica, Drew, and Dom.

Monica played one chip on GPX, but I had the X, so I knew that she had either G or P (but not both). Similarly, she also played one chip on DHR, but I knew Dom had the R, so Monica had either D or H. Finally, she played two chips on LNV.

Drew played one chip on DVY and zero chips on FÖY, so he had either D or V. Between Drew and Monica, they had at least 4 of the 5 cards DHLNV and at least 5 of the 7 cards DGHLNPV (possibly more if Drew had any of GHLNP).

Meanwhile, I knew all but two of Caitlin's cards. The only possibilities for those last two cards were DGHLNPV. Monica and Drew together had at least 5 of those 7 cards, so Monica, Drew, and Caitlin together must have all 7.

This tells me that none of these 7 cards are in the gang, and none of these 7 cards are in Dom's hand. It also tells me that Drew does not have any of GHLNP.

Finally, I can be more specific about Caitlin's cards. One of her two cards is G or P, and the other is one of DHLNV.

Online Play

The online implementation is asynchronous. You do not need to be logged in at the same time as other players. Instead, the system emails you whenever a turn is taken with the results of the investigation. When it is your turn, you can log on and take your turn at your leisure. This means that a 45-minute face-to-face game can take days or even weeks when played online, but it also means that you can play the game with odd minutes here and there, instead of having to carve out a solid chunk of time. An additional benefit is that it is easy to play with friends in different time zones. For example, I frequently play with friends on the other side of the country.

However, the greatest benefit of the online implementation is that it does away with the greatest weakness of face-to-face play—player errors. Not errors in deductions, which would be your own fault and would only affect you, but errors in answering investigations. If a player carelessly puts out, say, one chip when he should have put out two chips, it ruins the game for everyone. Even if the player notices the error a few turns later and tries to correct it, it's far too late. By then, the other players have already updated their notes with deductions made from the faulty answer, and typically have no way of backing out of those deductions.

If you want to give Black Vienna a try, see the detailed rules of the game and the instructions for the online interface.

Addendum: I've played in several three-player games recently. It's ok with that number, but I think it's significantly better with four or five players. (I haven't tried six yet.) With three players, the deductions are less interesting, and there is a greater chance for one player to get lucky.

Games for Programmers: Jotto

The next in an irregular series of board game recommendations for programmers. Of course, you don't have to be a programmer to enjoy these games, but if you are a programmer, then I think there's a pretty good chance that you'll like them.

However, you might not want to play this particular game with your spouse. Here's why...

“End. E-N-D”, she guessed. “One”, I replied.
“Cab. C-A-B”, I guessed. “One”, she replied.

We were driving to a campground in Massachusetts. My wife and I were in the front seats of the minivan; our daughter was in the middle seat, watching a DVD; and our son and his friend were chatting in the back seat.

We had been on the road for several hours, and I was feeling a bit tired. I needed to do something to help keep me alert. “Jotto?”, I suggested to my wife. “Ok.“

“Icy. I-C-Y”, she guessed. “Zero”, I replied.
“Fed. F-E-D”, I guessed. “One”, she replied.

Jotto is a two-player deduction game, kind of like Mastermind but with words. In fairness, I should say that Mastermind is like Jotto but with colors, since Jotto is older than Mastermind.

Each player secretly chooses a five-letter word with no duplicate letters. The usual restrictions apply—no proper nouns, etc.

The players take turns guessing each other's words. For each guess, you tell the player how many letters were correct. Unlike Mastermind, it doesn't matter whether the letter is in the right position or not. For example, if you guessed BOARD and got one letter right, the answer might be PLAYS (the A matches, in the same place) but it could just as easily be GAMES (the A matches, not in the right place).

“Map. M-A-P”, she guessed. “One”, I replied.
“Jig. J-I-G”, I guessed. “Zero”, she replied.

Jotto is a favorite game for situations where it would not be feasible to set up a board or deal out cards. For example, you can easily play it in a restaurant, or waiting in line, or on a long drive. All you need is two pencils and two pieces of paper.

“Age. A-G-E”, she guessed. “Two”, I replied.
“Out. O-U-T”, I guessed. “Zero”, she replied.

In fact, you don't even need the pencil and paper! Most of the time, we play it in our heads with three-letter words instead of five. This is a great variation that allows the driver to play in the car. It also lets you play in situations where you are moving too much to be able to take notes comfortably, such as jogging or hiking.

For this game, I picked AXE as my word.

“Axe. A-X-E”, she guessed. “Got it. Dang that was fast!”, I replied.
“Men. M-E-N”, I guessed. “One”, she replied.

I started playing Jotto this way with my son when he was 10. We still enjoy it and play it often, but it has become kind of a running joke, because we almost always finish within one guess of each other. This is the first time I have played mental Jotto with my wife, and she's killing me! She got it in five guesses, and I'm not even close!

Ok, with ones for both FED and MEN, I guess that it probably has an E. Next, I want to figure out which letter from CAB was correct. I'll try the A, and I'll also throw one of the other letters from FED to help confirm that it really was the E.

“Far. F-A-R”, I guessed. “One”, she replied.

Good. It probably really was the A. What has an E and an A?

“Sea. S-E-A”, I guessed. “Two”, she replied.

Now I'm getting somewhere. It looks like the E-A is correct. What else has an E-A?

“Pea. P-E-A”, I guessed. “Two”, she replied.

Hmm. I'm nearly certain now that the E-A are correct. What else has an E-A? It can't be TEA because I already got a zero for OUT. What if it's A-E instead of E-A?

Wait a minute. No way. No, she couldn't possibly have picked...

“Axe. A-X-E”, I guessed. “Got it”, she laughed.

Oh, man. We really have been married too long.

Originally written as a session report for BoardGameGeek.

Games for Programmers: Schotten Totten/Battle Line

The next in an irregular series of board game (or, in this case, card game) recommendations for programmers. Of course, you don't have to be a programmer to enjoy these games, but if you are a programmer, then I think there's a pretty good chance that you'll like them.

In programming, the specifications you thought you were implementing are practically guaranteed to change by the time you're done. Unless you have the power to “just say no” to the changes, the best approach is often to stay flexible by delaying commitments for as long as possible. You try to keep your options open by putting off irreversible decisions to the last possble moment. Schotten Totten (by noted game designer Reiner Knizia) elegantly captures this feeling in a short, two-player card game.

Schotten Totten is nominally about two Scottish clans squabbling over territory. Nine boundary stones are placed between you and your opponent, in a line from left to right. You win by being the first to claim either three adjacent stones or five stones altogether. To claim a stone, you must play a better three-card group on your side of the stone than your opponent does.

(photo by Scott Alden)

There are a total of 54 cards, numbered 1-9 in six different colors. Three-card groups are ranked as follows, from best to worst: straight flush (three consecutive numbers of the same color), three-of-a-kind (three of the same number), flush (three of the same color), straight (three consecutive numbers), “wild rabble” (anything else). If both players play the same kind of group, then each player adds their cards together and the player with the higher sum wins. If there is still a tie, the player who completed their group first wins.

You start the game with six cards. Each turn you play a single card on your side of one of the stones, and then draw a replacement card. (For beginners, the play-then-draw order can be a little confusing because most players are more accustomed to draw-then-play.) Towards the end of the game, if there are no more cards to draw, then you simply skip that step.

Once you have played a card on a stone, you're stuck with it. There is no way to take it back or replace it or cover it up. Most of the time you will not have all the cards that you want when you start playing a particular three-card group. The tension in the game comes from trying to avoid commiting to a particular kind of group for as long as possible. For example, suppose you've played the blue 6 on a stone, and now you have the blue 5 and the red 6 in your hand. If you play the blue 5 next, then you are commiting to trying for a straight flush. If you play the red 6 next, then you are commiting to trying for three-of-a-kind. The straight flush is stronger, but there are only two other cards in the deck that will complete the straight flush (the blue 4 or the blue 7). On the other hand, there are four other 6's in the deck, so you have a better chance of completing the three-of-a-kind. What you will probably do is delay playing on this stone by playing somewhere else, but that just means making a commitment there instead of here. If you do play on this stone, be prepared for the frustration of drawing exactly the card you needed for the group that you just ruled out!

(Technically, if you play the blue 5 on the blue 6, you are not commiting to trying for a straight flush. Any other blue will complete a flush, and any 4 or 7 will complete a straight. However, you almost never want a plain flush or a plain straight until close to the end of the game, because they are just too easy to beat.)

Each stone is awarded when both three-card groups are complete. However, there is a twist here that may appeal to programmers, who tend to excel at logical thinking. You can also claim a stone early if you can prove that your opponent can't beat your hand. For example, suppose you have three 7's on your side of a stone, and your opponent has the green 1 and the green 2 on his side. If the green 3 has already been played somewhere else, then there is no way your opponent can complete the straight flush. The best he could do would be a plain flush, which would lose to your 7's. Therefore, you can claim the stone without waiting for him to complete his group.

Note that the proof must be accomplished with cards that have already been played. In the above example, if you were holding the green 3, you could not claim the stone until you played it. Sometimes this means that you will play a card in a place where you would prefer not to, just to be able to claim a stone elsewhere.

Claiming stones early is important for two reasons. First, there are situations where both players can fulfill the victory conditions, so it is just a matter of who claims the stones first. For example, both players might be able to get three adjacent stones, or one might be able to get three adjacent stones while the other can get five stones altogether.

Second, and getting back to the theme of this recommendation, claiming a stone early helps you keep the pressure on your opponent. Once a stone has been claimed, neither player can play cards on that stone anymore, even if they have room to do so. You never want to give your opponent an easy place to dump a card. Not only does that let them rid themselves of a useless card—when you can only hold six cards at a time, freeing up an otherwise useless slot is huge—but more importantly it lets them avoid making a commitment someplace else.

How to get it

Schotten Totten can be hard to find in stores. Fortunately, its sister game, Battle Line is much more widely available. Battle Line is almost the same game, but with different artwork, with cards numbered 1-10 instead of 1-9, and with 7 cards per hand instead of 6. Also, Battle Line adds a separate mini-deck of so-called tactics cards, which let you change the rules in various ways. For example, one tactics card forces you to play 4 cards on each side of a particular stone instead of 3. (Actually, newer editions of Schotten Totten include the tactics cards as well.)

Personally, I like Schotten Totten better. I prefer the smaller, more claustrophobic scale. Also, I prefer the game without the tactices cards, which make the game too chaotic. Fortunately, if you get Battle Line you can experiment with or without the tactics cards, with our without the 10's, and with 7-card or 6-card hands, to see which way you like it better.

A good place to look for both games is BoardGamePrices.com, which summarizes prices and availability at a host of on-line game retailers.

If you want to try the game out before buying it, there are excellent implementations of Schotten Totten at both flexgames and Yucata.de. (The latter site defaults to German but can be set to English by clicking on the flag.)

What the heck is a math trade?

Many sites exist for trading objects or services of various kinds—my favorite example is a site for trading right or left shoes. Over on BoardGameGeek, there is a very active community of users who trade board games. The site lets you list games that you are offering and games that you want, and then automatically finds possible matches. Even with this support, however, finding and negotiating individual trades can be tedious. Enter Math Trades, which have been running regularly on BoardGameGeek for several years.

One frequent difficulty with individual trades is that, although you have something I want, I might not have what you want. What if we were able to get a third person involved? Suppose you have what I want, Tina has what you want, and I have what Tina wants. Then we can arrange a three-person swap. SwapTree is a site that will find such three-way and even four-way trades for you automatically.

But why stop there? Why not look for five-way loops, or even hundred-way loops? That's what happens in a Math Trade.

How a math trade works

First, a moderator announces the opening of the trade and lays down trade-specific ground rules. Everybody who is interested in participating lists the items they choose to offer in the trade. At a pre-determined time, the list closes to new entries.

Next, the participants review all the offers and decide which ones they want. For each item you are offering, you create a wantlist that says, in essence, “I would be willing to trade item 57 (my item), for item 22 or item 34 or item 119 or item 576.” Everybody sends their wantlists to the moderator by the announced deadline.

After a brief period for finding and correcting errors, the moderator runs special math trade software to find the most trades possible. The moderator then publishes the results, the participants exchange addresses, and drop their items in the mail.

A lot of trades

Note that the “most trades possible” can be quite a lot. The largest math trade to date involved 2320 items, of which 994 traded. These 994 items were broken into 7 trade loops, including one monstrous loop of 920 items. Just imagine standing in a circle with 919 of your closest friends and everyone handing their game to the person on their right!

(Actually, this trade involved 316 users, many of whom were trading multiple items. So that loop of 920 items wasn't really 920 people.)

Although math trades have been run regularly on BoardGameGeek for almost three years, it is only recently that trades of this size have become possible. About six months ago, I wrote TradeMaximizer, which has become the de facto standard software for math trades. TradeMaximizer improves on previous software by guaranteeing to find the maximum number of trades possible, and by doing so quickly, in under a minute for the large trade above and in just a few seconds for most trades. Previous software ran in hours or days, and even then might not find all the trades possible. I'll describe TradeMaximizer in detail in an upcoming post.

Beyond games

There's nothing specific to games in the idea of math trades or in TradeMaximizer. I know of math trades run for metal CDs (using earlier software) and for geocoins (using TradeMaximizer). If you have run a math trade in another community, or think you might like to, please post a comment here and let us know. Don't be afraid! They're easy to run if you keep it relatively small, and a lot of fun.

Probably the coolest application of math trades is for trading...kidneys!

No, this isn't some urban legend about waking up in an ice-filled bathtub. This is serious, life-or-death stuff.

When somebody needs a kidney transplant, they can often find a family member or friend who is willing to donate one. But what happens if the donor's kidney is biochemically incompatible with the intended recipient? Well, sometimes you can find two such donor-recipient pairs where each donor is compatible with the other recipient. By donating to the other recipient, each donor ensures that their intended recipient gets a compatible kidney. Three-way trades and four-way trades are also possible. Unlike ordinary math trades, however, larger loops are not supported. Oh, you can find the loops, but doctors won't perform the surgeries because the risks of something going wrong (such as somebody backing out at the last minute) are just too great.

A trio at CMU implemented a system that is now being used to find matches in a national list of donors every two weeks by the Alliance for Paired Donation. Their system differs from an ordinary BoardGameGeek-style math trade in two fundamental ways. One is the deliberate limit on the sizes of trade loops (which actually makes the problem harder, not easier). The other is the presence of altruistic donors—donors who give their kidneys to strangers without asking for a kidney for a friend or loved one in return.

Games for Programmers: Zendo

In addition to teaching and programming, I also enjoy playing board games. This is the first in an irregular series of game recommendations for programmers. Of course, you don't have to be a programmer to enjoy these games, but if you are a programmer, then I think there's a pretty good chance that you'll like them.

Zendo is a game about debugging. Ok, it's not really about debugging, but you'll see what I mean in a moment.

Zendo is a logic game played with a bunch of Icehouse pieces (plastic pyramids in several different colors and sizes) and some markers.

(photo by Terraliptar)

During the game, pyramids will be placed in groups (called “koans”) that either satisfy or don't satisfy some secret rule. The players try to figure out the rule based on these examples. For example, consider the following group:

(photo by Ted Alspach)

This group might satisfy the rule “at least one piece off the table” or “exactly one tilted piece” or “fewer than two green pieces” or “contains pieces of three different sizes”. It would not satisfy the rule “no two pieces of the same color”.

One player is designated as the master, who chooses the secret rule and judges whether proposed groups satisfy the rule. The master initially sets out one group that satisfies the rule (marked with a white stone), and one that doesn't (marked with a black stone). The other players take turns proposing groups, which the master then marks with white or black stones. Later in the game, players try to guess the rule, based on the evidence they've seen. If a guess is correct, that player wins the round, and a new master is chosen for the next round. If a guess is incorrect, then the master creates a counter-example, either a group the satisfies the secret rule but not the player's rule, or a group that satisfies the player's rule but not the secret rule. Either way, the master marks the counter-example with the appropriately colored stone.

That's the basics of the game. There are a few more details that can be found in the complete Zendo rules. (That site also offers a fascinating design history of the game.)

As a player, you are constantly coming up with possible rules and checking whether they are consistent with the examples that are already on the table. Often you will have more than one possible rule in mind. When it's your turn, you try to design a group that will help narrow down the choices. Ideally, you want a make your group so that either a positive or a negative answer will support some possible rules and deny others.

The primary challenge as master is coming up with a good secret rule, one that is not too hard and not too easy. Of course, too hard and too easy will depend on who you are playing with. Looney Labs sells a pack of Zendo rule cards to get you started. These rules are fairly easy and are perfect for those new to the game. Eventually, you will want to start creating your own rules.

Debugging

Debugging is a fundamental skill of the programmer. When its your own bug or you're operating under severe time pressure, negative emotional reactions can make debugging quite stressful. But when you are helping somebody else debug their code, it can be quite fun, kind of like a logic puzzle.

There are two basic approaches to debugging; most debugging sessions combine both. In one approach, you step through the code, re-thinking each line and looking for something suspicious.

In the other approach, you look at the observable evidence—for this input, it's producing that output, when it should be producing this other output, or the web site crashes every day between 5pm and 6pm— and try to come up with a hypothesis for what might be going wrong. For example, you might hypothesize that something is going wrong when two clients happen to have the same name, or that somebody is mixing up row-column coordinates with X-Y coordinates. Often you try to come up with an experiment that might confirm or deny your hypothesis, or help select between several competing hypotheses. Once you have a fairly solid hypothesis, you can usually narrow down where in the code to go looking for the error.

It's this latter approach to debugging that Zendo captures so well, that of making and testing and refining and discarding hypotheses.

Of course, that's the perspective of a computer scientist. Other kinds of scientists might prefer to think of Zendo in terms of the scientific method.

How to get it

Zendo used to be sold in a nice boxed set, but that is long out of print. In fact, I didn't get my copy until after it was already out of print. I got it as a gift from my BoardGameGeek Secret Santa, a charming annual tradition where hundreds of boardgamers anonymously send Christmas presents (games, naturally) to other gamers around the world, usually gamers that the sender doesn't even know.

You can still buy the pyramids from Looney Labs, where they are sold as Treehouse sets. You would need at least four sets to play Zendo—five would be better. It's kind of expensive that way, but fortunately there are a whole bunch of other games you can play with the pieces. You would still need a set of markers, but poker chips or coins in several denominations work fine.

In fact, with only minor modifications, it's easy to improvise a set of pieces for Zendo out of common household objects, such as bottles of beer.