An interesting article, one that you should read, came out this morning on Gone Gaming. It talks about the difference between a winner-take-all game (which most Euro-style games are) and games that include a margin of victory—either with score thresholds for an exceptional win (like Cribbage or Backgammon), or with a payout proportional to the magnitude of the victory, like in limit Poker.

Thinking about this got me wondering about why what you call a victory makes a difference at all—especially when no money is involved! The answer, I think, is that with or without money, every game is played for some kind of stakes, implicit or explicit.

Implicit stakes might include “honor,” “bragging rights,” or the acknowledgement from opponents that one is a skilled player. They can be different from player to player within the same game. Some players just want to come out on top—others want to win big, or to reach a specific score, or crush a specific other player whether or not they win themselves. You don’t even necessarily need to win the game to win an implicit stake; to use a metaphor from sports betting, you just need to “beat the spread.” For instance, if I sit down to a new board game and manage to do pretty well against experienced players—well enough that they regarded me as a serious contender in the game—I consider that a success, a validation of my general understanding of games, even though I lost. Likewise, if I sit down in a chess game against a serious club player (400 points better or whatever) and put up a good fight, I’ll probably feel good about the game even if I lose.

Explicit stakes most often involve money, but might also be explicit honorific awards—the championship title in a tournament, say. Explicit stakes have some very different properties from implicit stakes. First, an explicit stake is much more likely to be worth a similar amount to different players. I might really want to win the Settlers of Catan game while you don’t care, but assuming we are from reasonably similar walks of life, $20 means the same thing to both of us. I think that this is why Poker plays so poorly when there is no money on the table: without the explicit cash to normalize the stakes, players often feel like they have nothing to lose, and important aspects of the game like bluffing and risk management become meaningless. Second, explicit stakes make the game much more like to end up as a zero-sum game. Two players can both feel good about a well-played Chess or Go game, but only one person can win a title or trophy, and for every dollar I lose at Poker, someone else wins one.

The extra complicating factor in all of this, of course, is that hope that you get enough enjoyment from the play of the game or the social atmosphere that even if you lose whatever stakes you were playing for, you feel the time was well spent.

For the first time ever, I tried to play Shadows over Camelot with the addition of the loyalty cards yesterday. It was a four-player game, so the presence of a traitor would have been pretty devastating. As it turns out, however, we kept everything under control and we were all loyal.

Also, as it turns out, everyone playing was a seasoned gamer, so there would have been no mistaking inept play for rank treachery. Perhaps I am exaggerating this fear.

It seems to me like the traitor is really strong. In a four-player game, the traitor wouldn’t even have to be subtle–just waste time and put a catapult out every turn. Eventually the knights will have to waste a bunch of time and resources to stall the catapults, and while they do that they’re still drawing black cards or losing life. When 6 swords come out, it’s even worse, because the loyal knights have to accuse the traitor (or else he’ll accuse one of them and turns a white sword black) and then he’ll be stealing their cards as well. The one white sword for the successful accusation doesn’t seem to be even remotely worth it.

I think the traitor doesn’t gain much by trying to fake loyalty, unless things are going bad far enough that the two-white-swords-turn-black effect at the end is enough to tip the balance for evil.

I’d like to try a four-hand game with a known traitor–announced beforehand to see if the good guys even have a chance, because intuitively it looks really bad right now. If it’s as bad as it looks, I would have some proposed changes. First, the successful accusation could be worth more than one sword, or it could turn a black sword white; second, you could delay the choice of loyalty cards until a certain number of swords have been placed. (The three-player game already does this, for six swords; you could subtract, say, an extra sword or two for every player above three.)

In other news, now that daylight savings time has actually ended, I need to finish writing my articles by midnight proper, not 1 the next morning, to have them count for the previous day. Oops.

Solve this one yourself and be smarter than me. In retrospect it seems so obvious…

You are blindfolded and put in front of a table with 100 quarters. I tell you that 30 of the quarters show heads, and the rest show tails. How can you put the quarters into two piles such that the two piles have the same number of quarters showing heads?

No, you can’t use any other sense to determine what side of a quarter is which.

Hint 0: It only looks impossible.

Hint 1: Try it with a very small number of quarters, like 3.

Suppose you need to keep track of victory points or some common resource using tokens or chits. Suppose, furthermore, that you would like to have two denominations—a single unit token and some higher value. To minimize the number of chits that have to change hands, what values should you use?

I’ve created two tables. Both show the number of chits that must trade hands as a function of the higher denomination (across) and the number of chits traded (down). The top table assumes that change cannot be made, while the bottom table assumes that it can.

Things to note:

• If players usually won’t be able to make change, and transactions are fairly small, 3 or 4 is likely the best choice. Assuming transactions evenly distributed in size from 2-10, the average transaction is 2.4 chits.
• If players are often able to make change, 4 and 5 are better choices, with an average transaction size of 2.2 chits. Denominations of 2 and 3 do not benefit at all from change-making.
• Large denominations like 10 are probably only a good idea if your transactions tend to be very large, or if players will be accumulating many dozens of points.

I played another new-to-me game the other day: the Spiel des Jahres winner from a few years ago, Torres. It’s definitely a solid game, and one of the mechanics reminded me again that I need to write this article. The topic: Building vs. Ownership.

In most games, when you, on your turn, put a piece onto the board, that piece is yours forever. Often it is even your color. Settlements in Catan, Caballeros in El Grande, trains in Ticked to Ride… these all stay yours. Or there might be another means of tracking ownership, like the deeds of Monopoly. In other games, like Puerto Rico, you even have your very own board.

By contrast, in Torres, you can take actions to place or heighten towers, but the towers and castles can be used by any player. (Torres is Spanish for “towers”.) You can also deploy knights which establish your stake in towers. The number of points you score for a given castle (collection of adjacent towers) is the height of your highest knight in the castle, multiplied by the surface area of the castle. Knights keep other players’ knights from sharing the same space, but as castles increase in size and value, it becomes harder to keep opponents from climbing up on the unused sections of “your” castles and gaining points.

So what do you gain by placing towers? Two advantages. First, because you add the towers on your turn, you get the first chance to move a knight to a good spot on that tower. Second, you can make sure to add to places where you will have the advantage—ones that may be difficult for your opponents to take advantage of, or you might, for example, add to the surface area of a castle where all players have a knight, but yours is the highest.

In many ways it’s not like you’re placing pieces that you don’t have any control over—it’s like you’re laying out your pieces and the board at the same time, and you get to try to make board configurations that are to your advantage. There are some other games that work in a similar way:

In Carcassone, any player usually has a chance to put a meeple on a field, city, or road, but the player who plays a tile that creates that region has the first chance to do so. To contest your ownership, a rival player has to put a meeple on a different field, city, or road and then connect them, which is usually pretty difficult. (Although it can certainly be worth it, especially for fields!) Also, as in Torres, you can try to enlarge the areas you already have some control over to try and increase their value.

Tigris & Euphrates has a similar mechanic, although I haven’t played that game in a long time. Part of my frustration with the game was trying to figure out how I was supposed to parlay all of my construction efforts into a good score.

I have been calling the logic problems posted here “riddles.” In an offline discussion, reader MJB asked me why this was so. To him, the best examples of riddles were those posed by the Sphinx to Oedipus or those exchanged by Bilbo and Gollum; exercises in unraveling metaphor. He suggested that “puzzles” more accurately reflects the nature of these problems, which are based in logic.

I defended my choice, because the choice of “riddle” over “puzzle” was something I actually did think about, although it was really an intuitive judgment; nothing I thought about so deliberately as I did in this discussion. To my mind, the best examples of puzzles are exercises like Sudoku, crosswords, cryptograms, jigsaws, or any of the various puzzles you find in Dell newsprint magazines. These are a lot of fun and satisfying to work out, but they seem fundamentally different and the thrill of victory is not quite as strong. That’s why I went with “riddle,” because the problems I relate seem so different than these puzzles. Certainly no publisher could print a whole magazine full of the kind of riddles I enjoy every month!

Thinking about it some more, the difference seemed to be that puzzles come in similar kinds, and their solutions follow a common pattern. There are only so many techniques that are used for, say, a Sudoku or a cryptogram. Finding when to use these techniques and choosing the right one comes with experience, but the similarities are clear. But, MJB asked, aren’t some of the truth/liar style riddles like that?

I believe they are not. The easiest riddles of this form, the most classic ones, involve casting a question that a liar and truth-teller will give an acceptable answer to. About the strongest common thread is that you need to establish exactly what you will and won’t be able to know at the end of the riddle. For instance, you might ask 3 yes/no questions without ever having the luxury to know what the words for “yes” and “no” are!

Furthermore, coming up with a problem of a similar form is hard. Try it! It’s as hard as coming up with a satisfying metaphorical riddle, one that leaves you thinking “I should have known that!” rather than “how the heck was I supposed to know that?” at the end. By contrast, coming up with a puzzle is easy. Want a cryptogram? Take a quote, add the substitution cipher your computer gives you, and BOOM. Sudoku? Take a grid of number and subtract some of them. Jigsaw puzzle? Take a photograph, print it on cardboard, and cut it up.

But it was the crossword puzzle that really drove home the distinction for me. Creating a crossword is not a mechanical process. Creating the grid of words takes time and effort; then you need to come up with clues. But just like the other puzzles, you start with the answer and go from there. And that, I think, is the distinction between riddles and puzzles. In a puzzle, the answer comes first. In a riddle, the question comes first—the really hard part of making a riddle is finding an interesting question. I think MJB accepted this reasoning, and I’m actually quite proud of that.

(And if it’s not clear, the kind of riddles I enjoy are the “logic” riddles, as opposed to what might be called “metaphor” riddles.)

Do you have any other thoughts as to what makes a puzzle different than a riddle? If so, please share. I have some ordinary articles planned, but I’m sure further riddles will feature before too much longer.

From the XKCD forums. Recast here for clarity and because I am not confident that the poster posted with enough clarity. I think I have the solution but, unlike most days, I am not 100% confident.

For those who are unfamiliar, Texas Hold’em is a particular kind of poker that has become very popular in recent years. Here’s how it works: A single deck is used. Each player gets two cards face-down. There is a round of betting. Three cards are flipped face-up, and there is another round of betting. Another face-up card, another round of betting, then a final face-up card, and a final round of betting. Everyone who is left makes their best 5-card poker hand from their own two hidden cards plus the five common cards on the table, and the best hand wins. You are under no obligation to use any cards from your own hand; if the board contains AKQJT of one suit, all players who have not folded will tie with a royal flush.

To simplify the problem, since betting is not relevant to this riddle: In Texas Hold’em, the goal is to make the best poker hand possible out of your two hidden cards plus five that are face up and common to everyone. High pairs, especially aces and kings, are regarded as excellent hands.
The riddle is this: One player has a pair of kings–a strong hand! Adding as few other players as possible, construct a setup where that player has no chance to win any of the pot. That is, no matter what 5 cards end up being common to all players, he cannot hope to even tie for the best hand.

I think I have the solution that requires 6 other players, which is what the poster alludes to.

Baseball is an old game, played professionally for well over a hundred years. I don’t usually talk about sports here, in large part because I can’t play them on any kind of competitive scale. However, several have interesting and esoteric rules that developed over time. Here are a couple:

Infield Fly Rule: This rule applies in the following situation: Runners on first and second (possibly third as well), less than two out. If the batter hits a shallow fly or pop-up that should be easily fielded by an infielder, the batter is called out while the ball is still in the air. If this were not the case, the fielder could choose to let the ball drop and make an easy double play. (If the runners led off to try to prevent this, the fielder could catch the ball and still make the double play.) The infield fly rule removes the incentive for fielders to clownishly drop balls and mitigates the risk of getting very easy double plays.

To summarize:

• If the runners don’t lead off, the fielder lets the ball drop. Now the runners are each forced to advance and two can probably be picked off for a double play.
• If the runners lead off, the fielder catches the ball and throws a runner out for a double play.

Dropped Third Strike: If a pitch is the third strike, either because the batter doesn’t swing or swings and misses, but the catcher doesn’t catch it cleanly, the batter is not out but instead entitled to try to run to first. (A “not clean” catch may bounce off the ground first, or may be a bounce off the catcher’s mitt.) The catcher can attempt to either tag the batter out or throw him out at first…

unless there are fewer than two outs and there is a runner on first. As in the infield fly rule, this prevents catchers from intentionally dropping a third strike, then throwing to second and first for a double play before the runners realize what’s going on.

By the way, no matter what happens, this is scored as a strikeout for the pitcher. Scoring could be its own article, if not an entire book.

Ground Rule Double: Many ballparks have a ground rule that if the ball is hit to certain places where it cannot be fielded, it counts as a double for the batter, and all runners advance two bases. For example, a ball lodged in the ivy at Chicago’s Wrigley Field or in the rafters at Minnesota’s Metrodome counts as a double. The most commonly known example is a ball which bounces over the outfield fence, but this is actually not a ground rule at all—this an official rule of baseball, not part of the ground rules for any park.

And for your hyperlinking pleasure:

If you aren’t very familiar with the rules of baseball, Wikipedia is there to help, as always; on the other hand, if this is all old hat to you, there is a neat and difficult quiz you might want to look at.

A continuation of the previous article…

Total Points: The game ends when a certain total number of points are reached, no matter who scored them. This is kind of an oddball pattern used oddly by Killer Bunnies (at which point your chance for winning is equal to the proportion of points you’ve collected) and Shadows Over Camelot, which ends when 12 swords (either white or black) have been earned by the knights.

Secondary Condition: The game ends when some condition not strictly tied to the turns or scoring is met. For example, Puerto Rico ends when the colonists are all gone (usually) or when the VP chips are gone or one player’s city is filled. If a player wants to lock in a lead, that player can push towards one of these conditions, but that might not be the line of play that scores the most points. Likewise, Thurn & Taxis ends on the turn when one player meets one of a couple of conditions. Both of these conditions are worth points themselves, and there’s even a bonus point for hitting the mark first; but a player who’s been pursuing other goals very effectively could still pull off a victory.

Variable Fixed Turns: The game lasts for some number of turns that can’t be affected by player actions, but the players don’t know ahead of time how many turns that will be. This makes the pace of the endgame different, because it makes the shift from long-term to short-term goals blurry and an interesting point of strategy. For example, Evo lasts for 8 or so ordinary turns (depending on the number of players); at the end of the next turn, if a 1 or 2 is rolled on a die, the meteor lands and ends the game. The next turn, it hits on a 1-4; the next, on a 1-5, and in the one game out of 36 that it hasn’t ended already, the meteor always hits on the following turn.

Exhausted Moves: The game ends when no player can make any more moves. This might be due to a filling board or depleting resources or both, as in Blokus. The end of the game is typically a struggle to squeeze the last bit of points or other resources out of whatever’s remaining. The ending of Go feels this way to me, although technically you’re only running out of useful moves.

Hybrid: A game might have multiple end conditions; typically whichever one triggers first ends the game. A Game of Thrones, for example, ends after 10 turns if no player has won by Dominance at that point. Cooperative games often fall into this style. Shadows Over Camelot lasts until 12 Total Points have been gathered, but can also end by the elimination of all the players, or if 12 catapults ever wind up outside Camelot. The Lord of the Rings board game has a Race ending condition for the good guys, and a Secondary winning condition for the bad guys; Sauron could eat the Ringbearer without the other hobbits being in particular danger.

Oh, how I loathe them. Which is why today’s XKCD warms my heart.