The topic for today and Thursday is a discussion of the many ways games can end, and some of their ramifications. I intend to talk more about multiplayer games than two-player games, because I think the “end conditions” for two-player games. It’s hard to distinguish a Race from Elimination, for example. But if there are interesting points to be made, it may turn this series even longer.

Each one of these might be thought of as a mini-Pattern relating to a specific part of the game. And they’re important for the same reason that the end of a book or movie is important: you want the tension building to a climax, you don’t want to wait around for a foregone conclusion or think “whoa! it’s over?”

Elimination: I’ve already talked about this pattern, which is generally out of favor in Euro-style games but definitely still alive and well. Most of these games feature either a momentum-building effect (hotels in Monopoly, continent and card bonuses in Risk) or else attrition (Perudo and many others); without one of these factors, the game might drag on without end.

Dominance: This pattern looks similar to Elimination, but victory is achieved when one player controls a certain fraction of the available resources, instead of having to eliminate all opponents. At the point Diplomacy calls the game by Dominance, the dominant player could probably brute-force a victory even against all remaining players. By contrast, in A Game of Thrones, the winning player has to be doing well, but the Dominance victory threshold is well short of the level where the winner could fight off a concerted attack by all opponents.

Race: The winner is the first person to achieve a certain condition. This might be a fixed number of victory points (Catan, Blue Moon City) or to reach a certain goal or destination (Elfenland or even Sorry!). In a common extension of this pattern, the turn is finished up to make sure that all players have the same opportunities. For example, Power Grid is won when a player reaches 21 cities, but if more than one player reaches this number in the same turn, it’s won by the player who has the most. (This is very possible.) Ties are broken, in this case, by the amount of game currency remaining.

Fixed Turns: The game lasts for a predetermined number of turns. The turns may be tracked explicitly, as in El Grande or Risk: Godstorm, or it may be implicit, such as in Carcassone (ends when all the tiles are gone). One advantage of this pattern is that it gives the designer very tight control over the flow and pacing of the game. (And the players won’t be surprised by the length of the game.) The corresponding disadvantage is that the end of the game can be anticlimactic, since its approach is seen all game.

X Through the Deck: This variant of Fixed Turns applies only to card games. You play until the deck is exhausted, then reshuffle it and begin again; the game ends when this has happened some number of times. The world’s best bean-oriented game, Bohnanza, uses this mechanic, and I have used for a couple of my own games as well.

Teaser: The titles for next time include Total Points, Secondary Condition, Variable Fixed Turns, Exhausted Moves, Hybrid, and Unlimited.

Discussion point: Am I on track to miss something? Let me know so I can look good by including it next time. Also, are there any neat intricacies about two-player games that I’ve missed?

I was introduced to a new game this weekend. It’s called Perudo, sometimes known as Liar’s Dice; you might know it as the dice game they’re playing in Pirates of the Caribbean 2. Evidently there are some other, somewhat more complicated rules that some people play by, but these rules are simple and fun. Try it. The strategy is surprisingly deep and like the Forehead Game, it plays better than it reads. It feels like a more strategic version of the Science Bowl-favorite card game BS.

Players: 2-8 or so, but 4-6 is probably best.

Equipment: Each player needs 5 6-sided dice and a small, opaque cup.

Play time: 20-30 minutes. With more than 6 players, you might want to reduce the starting dice to 4 for everyone to speed the game up.

Play: Choose at random a player to start. Then each player rolls the dice by shaking them in the cup and then turning the cup facedown on the table. The starting player names a number and a rank of dice, for example, “two fives.” This is a statement that the player thinks that between all the players’ collective dice, there are at least two fives. Ones are wild and count as everything.

The next player clockwise must make a similar call, but must increase either the rank of the dice at the same number (“two sixes”) or increase the number at any rank (“three twos.”)

If you bid ones, the bid counts as double in number. For instance, “three ones” can be called over “five sixes” and the next player needs to call at least “six twos.”

After any call, any player may accuse the caller of bluffing (say “lies,” “I doubt it,” “BS,” or somesuch.) When this happens, all players reveal all their dice, and determine whether the call was good (there were at least the called number of the given rank) or bad. If the call was good, the accuser loses a die. If the call was bad, the bluffer loses a die. Then all players reroll their dice and a new round begins, starting with the player who lost a die. Note that the number of dice available in the game steadily decreases as time goes on.

When a player has no dice remaining, that player is eliminated. The last player with any dice remaining is the winner.

Basic Strategy: Your calls don’t have to have anything to do with the dice you can see. As long as nobody is likely to bother accusing you, why give away information? Also, just because you think someone is probably bluffing is no reason to call them on it. Let someone else take that risk if they feel like it. The only reason you should accuse someone of bluffing is that you don’t expect to have a believable call to make on your next turn. Most often, you should probably be calling the person immediately counterclockwise to you, unless the second person back makes a call you believe to be very unlikely and you think the immediate person back has a chance of making a better call.

When it gets down to two players, the strategy gets weird and I don’t understand it very well yet.

It’s like bonus day! Four mini-essays, in response to the excellent comments to Tuesday’s article here.
To Fuleng, who indicated displeasure with secret scoring in Knizia games: Secret scoring does seem to be out of line, in particular, with Knizia’s intent for Tigris and Euphrates, which, (I hope!), was to be a deep and intensely strategic game. Perhaps my opinion of the mechanic has been colored by too much Puerto Rico. (Is there such a thing?) Taj Mahal certainly copes well without it. And your point about the penalty for interruptions is well-taken, because it’s everyone who suffers. El Grande is particularly nasty in this regard, because while the number of soldiers you put into the Castillo is public, they’re kept hidden once there.

To John, who commented that Settlers seems to have a “secret scoring” feel to it: You’re right in that a lot of players don’t tend to watch what others have in their hands even though it matters a lot towards opponents’ threat to win. Part of the reason might be that in the beginning of the game, it’s not as big of a deal unless you are directly competing for expansion space with a particular opponent. It might be a neat advanced strategy to count how many resources, if they were the ideal ones, a given opponent would need to reach 10 VP, and use that as an internal victory meter.Of course, you would then need to adjust for things like a excess of unneeded resources, other players’ willingness to trade, the presence of ports, and so on.

To Nevin, who expressed discontent with scoring rules that “string along” players who have little chance of actually winning: This business of how much an early lead should help later play is certainly a difficult one from a design perspective. Ideally, there would be tradeoffs available; for instance, in the early Puerto Rico game, you can try to rack up a VP lead shipping cheap goods like indigo and corn, or you can try to develop and trade more expensive goods in the hopes of being able to buy large, useful buildings later. If these tradeoffs don’t exist at all then you’re completely right: you might as well just play two separate games, one for the beginning and one for the end, and declare a winner of each separately. Can you list a couple of games you’re particularly dissatisfied with? I find that in Catan, even if I get a really lousy start due to poor luck or poor strategy, I can have a satisfying game by making a personal goal to reach a “respectable” number of points, say 8, by the time the winner finishes.

To J. Vogel, who asked if there were games where players don’t know where they stand: I saved this one for last because it’s something I’ve thought about before when trying to design games. It’s certainly tricky, because the paradox is that the players need to be able to work meaningfully towards a goal, and yet not know how close they are. One way this can work is when the goal is “beat the other player or players”, but you don’t know what they have. In Poker it’s a matter of how much you’re willing to bet that your cards are better. In games like Gin and 31 you need to find the right moment at which you believe your hand is better than the other person’s; both games, since they have a large penalty for being wrong, also have the element of “how sure am I?” The intuitive way to get a game element like this is to have some component of the score be secretly chosen; perhaps score chips are secretly chosen or you choose a goal randomly and get bonus points for meeting it. The goal could even be revealed to the other players. However, this seems like it would add a dissatisfying element of chance to the game.
This is actually going to tie in with an upcoming article, when I talk about how games are ended. To spoil it a bit now: Evo handles this creatively, because the goal is “have the most points at the end of the game”, but you don’t know when the end of the game is going to be. The game proceeds for 6-8 turns, depending on the number of players; after that, after each turn, the game has an increasingly likely chance to end right then. It works particuarly well in Evo because that game provides many chances to make short-term gains at the cost of long-term growth.

Secret scoring is a mechanic that seems very strange to me. And yet many popular games use it; many by Reiner Knizia, such as the recent Blue Moon city and classic Samurai, but also hits like Puerto Rico. The reason it’s strange is this: all points are awarded publicly, but you keep the number you actually have secret from the other players. (A screen is involved, or chits that can be worth varying numbers of points and are kept face-down.) So there’s no reason why you couldn’t keep track of how many points each player has. But it’s not made easy, and in the cases I’ve seen, players don’t tend to.

The reason for using secret scoring, I suspect, is to discourage laborious, extensive analysis as the game nears its end. Nefarious reader Fuleng brought this up as a possible weakness in Power Grid, which lacks secret scoring; unless the game is a runaway victory, players are well served by calculating the exact sums of money each opponent will need to obtain needed reactors, get fuel for them, and connect the last few cities. It makes it a less novice-friendly game that it would otherwise be. If not for the secret scoring, Puerto Rico might similarly drag down near the end, with players keeping a tally of other players’ totals and pushing the game to an end, or trying to delay it, based on whether the last few points could be scraped together.

Secret scoring also sends the implicit message to the players that the game is not meant to be played with intensive calculations near the end. Heck, you’ll win more games per hour if you cross your fingers and play with your best guess instead of keeping track of secret scores in your head and taking 20 minutes to work out the best course of action; not to mention that your fellow players are much less likely to get bored and go watch television. If these games were played for serious prize money or something, would I expect the best players to keep score in their heads and perform thorough analysis? Yeah, I would; I would also expect “tournament rules” without secret scoring to develop, to take the burden off since the analysis is going to happen anyway. But for the majority of board game play, where having a game take 45 minutes rather than 75 is a huge advantage, I think secret scoring successfully keeps bright players from overthinking the games.

As promised, here is the followup riddle. This one is hard… very hard. There’s a solution, with commentary, behind the cut. Although intrepid reader John Rhoadhouse did find it independently!

You are faced with three creatures, numbered 1, 2, and 3. One of them always tells the truth, one always lies, and one may tell the truth or lie arbitrarily. You need to find out which is which in three yes-or-no questions. Here is the catch: Although they understand questions posed in English, they do not speak it. The words they use for “yes” and “no” are “ja” and “da,” but you don’t know which is which.

This is where Hint 0 comes in. If this riddle were posed by, say, some guy named NarutoFan69 on the offtopic forums for your favorite Webcomic, you would be justified in reasoning:

1. There are 12 different possibilities for a setup: 6 arrangements of the three creatures, multiplied by 2 for the meanings of “yes” and “no.”
2. With 3 yes-or-no questions, you can distinguish between a maximum of 8 (2³) different outcomes.
3. So there’s no good solution, and NarutoFan69 is posting a lame trick question (“read the name tags LOL”).

But hopefully you trust me not to give you a riddle without a good answer. The answer is behind the cut, although solving it yourself is a mark of great honor.

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