Ambition Against Humanity

One of the more interesting game design challenges is to combine two games. What would a mashup between Chess and Go look like? Or Magic: the Gathering versus Backgammon? How about Arimaa meets Oh Hell? Most of these mashups flat-out wouldn’t work; some might. Here’s my attempt to create one that, I think, would at least be interesting. Perhaps a bit depraved, but so it goes…

Combinatorial game theory gives us a mathematical definition for the sum of two games, but that rarely creates interactions between the two and, anyway, the games I’d want to mash together tend to be more complex (3+ players, hidden information) than typical combinatorial games. So that’s not what I mean to talk about here.

There are two typical techniques for combining two (or more) games. One is to put them in conflict. Each has its own winning (or losing) condition and it’s nearly impossible to perform well in both (see: Attika). This creates a “between-game” game of figuring out which one to play, while defending against other players’ attempts to win either. The other is to make one game support the other, insofar as success in one leads to having more resources in the other, from which the winning and losing conditions derive. I’m going to take the second approach.

What would happen if you combined Ambition (go here if you don’t know what that is) and Cards Against Humanity (go here)?

First of all, a single round of Ambition works with 4 players, but that number seems to be pretty strict. I haven’t been able to come up with a decent variant for a different number. However, a full game of Ambition can be played with 5+, by rotating people in and out of 4-player rounds (“tournament style”). There’s a lot to say about table position and fairness (no player getting two or more rounds in excess of another) and ending conditions that you need to consider if you want to run a serious tournament, and that stuff I won’t get into here, because it’s not relevant to the deliberately unfair mashup game. Chances are, if you’re combining Ambition with Cards Against Humanity, you’re interested more in hilarity than fairness…

So how does this mash-up work?

Players: 5 or more. You could play it with 4, but the strategies aren’t as interesting because no one ends up sitting out of the Ambition round. Since each round of Ambition plays with exactly four, this means that some players will have to sit out of each hand (as with tournament play). However, each player participates in the Cards Against Humanity component, which is used to select players for each round of Ambition.

Equipment: you need a Cards Against Humanity set, the equipment for Ambition (cards and chips/counters), and an additional deck for (silent) ranked voting.

Round structure: each round begins with a Cards phase, in which everyone plays. To keep anonymity around whose choice is whose, everyone votes silently, and the choices are shown only once all have voted. Instead of voting for one choice, it’s a ranked voting system (each player ranks all submissions) resolved with a Borda count. That is, if there are 7 players, then each 1st-place vote is 6 points, each 2nd-place vote is 5 points, and so on… down to last place, which is 0 points. So if John gets 3 first-place votes, 2 seconds, a fifth, and a last-place, his total score is 3*6 + 2*5 + 2 + 0 = 30 points. These voting points (with one exception, below, should a player get all last place votes) aren’t scored to the game; they’re only used to determine who plays at a round of Ambition.

The top three vote-getters, and the last-place vote-getter, begin a round of Ambition. However, it’s a deliberately unfair round. The first-place vote-getter gets an initial hand of 18 cards; second-place vote-getter gets 16, third-place vote-getter gets 14. Each of those selects a 13-card hand from that pool. The last-place vote getter gets the remaining 4 cards, plus the 9 cards not wanted by the other players. Unlike in the typical game, the 3-card pass at a round’s onset does not occur. Then they play a round of Ambition, according to the normal rules.

Tie-breaking in voting: If there’s a 1st-2nd, 2nd-3rd, or 1st-2nd-3rd tie in vote points, you don’t need to break the tie; just average the initial hand sizes together. For example, in a 1st-2nd tie, you’d have the tied player getting 17 cards each. In a 1st-2nd-3rd tie, they’d each get 16. If there’s a 3rd-4th tie– meaning one player will sit out– then tie-break in favor of the person with more first-place votes (if tied in this, then use second-place votes, and so on). If there’s still a tie after all that, meaning they have the exact same vote distributions, then the player who is farther behind sits in the round. (If they’re tied in even that, then flip a coin.) Ties for last-place are resolved similarly, except in “favor” of the person with the most last-place votes (and so on) and, if that fails to break the tie, then in favor of the player who’s most ahead in the game.

Objective: points and strikes, earned during the rounds of Ambition, accrue from round to round. When a player accumulates four strikes, he loses and is eliminated from the game. Once K players (1 < K < N-3) have been eliminated, the game is over, and the player with the most points (among those without 4 strikes) is the winner of the game.

Note: choice of K, above, depends on what you want from your game; higher K means more players are eliminated on strikes, making avoidance of strikes more important relative to getting points. In tournament-style Ambition, typical K is 0.33-0.5*N, but if you’re looking to have a light flavor and don’t want player elimination, just use K = 1 (i.e. end the tournament as soon as one player’s eliminated).

Exception (Misere): if any player receives only last-place votes from each player in the Cards Against Humanity phase, the round of Ambition is not played, and that player scores 120 points (equivalent to the best possible outcome of an Ambition round). If someone chooses so horribly as to receive across-the-board last-place votes (including from herself) she did something right.

Strategy: note that this mash-up is an unfair Ambition tournament, with the unfairness derived from success in Cards Against Humanity. However, there are a few interesting considerations. Note Ambition’s two-dimensional scoring system. There are points, which are the normal objective; and strikes, which can cause you to lose even if you have the most points. If you have three strikes, you’re much more focused on avoiding strikes than if you have none; in the latter case, the risk of a strike is worth taking if there’s a good chance of getting a lot of points (e.g. a Slam attempt). Where you are in the game determines whether you’re more focused on avoid strikes or on getting points.

In general, in Ambition Against Humanity, you want to do well in the voting phase so you get to play Ambition rounds and score points. However, the third-place prize (getting into the round, but with a relatively mediocre hand) is not always desirable; sure, there are opportunities to score points, but also to strike. Conversely, the last-place (in voting) punishment isn’t always bad; you end up with a crappy hand, but that still gives you an opportunity to score. So you may find yourself trying to avoid a top-three finish in the Cards phase if you’re at two or three strikes; or, if you have relatively few strikes, you might go for full-on awfulness in order to get a last-place finish, just to get yourself into the Ambition round, or to attempt to get the 120-point bonus when a player completely fails in the voting.

Ambition and what it taught me: the 4-factor model.

Nine years ago, I came up with a card game called Ambition in which I attempted to remove card-luck from a trick-taking card game. This turned out to be a surprisingly difficult (and very fun) design problem. To give a 50,000-foot overview, the original game was one in which the goal was to get a middling score each round, making the objective more about manipulating the flow of the game (and the players) rather than trying to take (e.g. Bridge) or avoid (e.g. Hearts) tricks. The original game had only the middling objective, but as with Hearts and it’s “shooting the moon” reversal, I had to add high-risk, high-reward strategies for very strong (Slam) and very weak (Nil) hands. What I ended up building was a game where card-luck has a very small influence, because every hand has a credible strategy.

I’ve estimated that card-luck produces about 5% of the variation in a typical 2-hour game. (This could be reduced to 3-4% by reducing the Slam bonus, but that would also make the game less fun, so what would be the point?) For a trick-taking game, this is rare. Now, Bridge is an immensely skillful game, but it’s got a lot of card luck in the short term. For this reason, Bridge players duplicate the game in serious settings, which means that they play the same hands as everyone else in the club and are scored on their relative performance. A typical Bridge tournament might have 20 teams– or 40 people. I don’t think there are 40 Ambition players in a given state at any time, so duplication’s not an option.

Why’d I want to eliminate card luck from a trick-taking game? The short version of the story is that I had caught that German board game bug, but I was in Budapest for a semester (at this program) and had only a deck of cards. But I’d fallen in love with the German design aesthetic. Also, experience had led me to conclude that the games regarded as being the most interesting, and the ones that become culturally important, tend to be skillful games. Go, Chess, and Bridge are all very deep and skillful games, which makes their outcomes meaningful and indicative of genuine skill (or decisive). Poker becomes skillful with enough patience; viewed as one game played over a person’s life, it converges, as most games well. This led down the rabbit hole of “luck/skill balance”. What is it? Oddly enough, I concluded that it doesn’t exist, at least not when framed as a linear dichotomy.

The idea of “luck vs. skill” places Go (a very deep, skillful game) at one end of a continuum and Bingo (which is pure chance) at the other. As this ideology goes, luck games are cotton-candy junk food, and skill games are, if a bit dry, respectable and rewarding. Supporting this is that the culturally successful and long-lived “mind sports” tend to be highly skillful, which seems to imply that if you want to design a “good” game, you should be aiming to get rid of luck. The problem with the luck/skill dichotomy is that there are a number of game mechanics it fails to model. For a trivial example, Rock, Paper, Scissors contains no randomizer but (at one iteration) is effectively “random”, because it presents simultaneous decision-making with a perfectly-symmetrical strategic shape (i.e. no strategy is functionally different from any other). Rock, Paper, Scissors at one iteration can be considered to be effectively a luck game, so what about the iterated version. Is the long-term, iterated game luck-driven or skillful? That’s a surprisingly hard question to answer, even theoretically. For a more practical example, consider multi-player German-style favorites like Puerto Rico, an excellent game sometimes criticized for the influence of table position (i.e. the difference between sitting to the left vs. the right of the best player can have a measurable affect on one’s outcome). There are almost no random elements to this game, but play order becomes an influence. Is that aspect– knowing where to sit– luck or is it skill? (Answer: it’s meta-game.) But the biggest problem with the luck/skill dichotomy is that it breaks down completely when there are more than 2 players. In a 3-player game, an unpredictable, nonconventional, or outright incompetent player can make strategic choices that favor one player over the other– an effect deriving neither from a truly random element of the game (such as dice or a deck of cards) nor from those players’ individual levels of skill. This “interaction term” element is strategy: a mix of luck and skill inherent in simultaneous, poly-agent decision making.

The difference between a demonstration of skill and “strategic luck” is that the former will generally affect opponents’ outcomes in a non-biased way. If Alice does something that gives her an advantage over Bob and Eve both, she’s playing skillfully, not getting lucky. If she does something that unintentionally or chaotically gives Bob an advantage over Eve and Bob wins, that’s strategic luck favoring Bob.

In two-party games, there is no strategic luck. If the opponent’s strategy causes one to lose, that was (by definition) skillful play, not strategic interference. Likewise applying to two-team games (like Bridge) it is accurate to say that friendly “strategic luck” is skill.

However, in games of 3 or more players, it’s pretty much impossible to eliminate strategic luck (not that I’m convinced that it would be desirable to do so). This is reminiscent of Arrow’s Impossibility Theorem, which state that it’s impossible to design a “perfectly fair” voting system, where “fair” means that the presence or absence of a candidate C should not affect the relative performance of A and B (i.e. no “Nader effect”.) Games with three- or more players face an inherent trade-off between (a) restricting interactions between players, making the game less fun, versus (b) encouraging them but introducing strategic luck. So with large groups, it’s often better for a game designer to just own the strategic luck and make the alliance-forming (and -breaking) aspects a core element, as with Diplomacy or Apples to Apples.

This may be why the games that develop the mind sport culture always seem to be 2-party games. A game of 3 or more players without strategic luck would have to be structured too much like “multiplayer solitaire” to be fun, but one with strategic luck is unlikely to develop a tournament scene, as the cultural purpose of those is to determine “the best” player. (When there’s strategic luck, the best player can be undefined. Alice may be superior to Bob when Carla sits at the table, while Bob is better than Alice when Dan is playing.)

As for Ambition, I removed the card luck but I introduced some strategic luck. A “bad” hand can lead to a great outcome based on unrelated prior decisions by other players. Strategic luck is noticable. Which made it not quite like Go or Chess where a superior player can expect to win 95+ percent of the time, but more like a German-style game where pure chance factors are uncommon (you rarely feel “screwed” by the cards) but strategic luck is tolerated. And that’s fine. It adds to the fun, and it’s a casual game, after all.

Luck, skill, and strategy are 3 factors that determine players’ outcomes in a game. Pure chance elements can be isolated and assessed mathematically. Skill an usually be quantified, by observing players’ outcomes and adjusting, as with the ELO system. As for strategy? It’s completely impossible to quantify this element in a general way, because the strategic variables within a game are, in some sense, the spinal shape of the game itself. Pure chance elements can be analyzed through statistical means, but there’s no general-purpose way to measure strategic luck. I’m not sure if I can even precisely define it.

I said there would be 4 factors, so what’s the fourth? The most interesting one, which I call flux. To explain flux, consider one important observation pertaining to supposedly “purely skillful” games: they don’t have the same outcome every time they’re played. If they did, they’d actually be frustrating and boring, even for nearly exactly matched players. Thankfully, that’s not the case. Alice defeating Bob does not mean that Alice will always beat Bob. What this means is that there’s something subtle– an energy– that makes the game a real contest when it’s played between players who are close in skill level.

Flux is minute-to-minute variation in a player’s skill and strategic effectiveness. Positive flux is being “in flow”– the state of consciousness that makes games (and programming, and writing, and many other things) fun. It’s a state of mind in which a person has above-normal concentration, confidence, ability to assess risk, and effectiveness in execution. Negative flux is the opposite, and it’s described by poker players as being “on tilt”. It’s being out of flow. When players of equal or near-equal skill compete, it’s often flux that determines the winner. And that’s what makes such contests exciting– the fact that the game is skillful and decisive (so the outcome actually matters) but that, because the contestants are close in skill level, the end-of-game binary outcome (winning vs. losing) is going to be determined by minute-to-minute fluctuations in animal energies. Flow. Flux. “The zone.”

Luck, skill and strategy are all important tools in a game designer’s arsenal as he pursues his design goal (which is not to land at a targeted point on some bullshit “luck/skill continuum”, but to design a game that’s fun to play). Luck gives more players a chance at . Skillful elements make the game decisive and more . Strategy, on the other hand, is what makes multiplayer games interactive and social. All of these elements can be quite effective at making a game fun. But it’s the tense real-time drama of flux as players go into and drop out of flow that really makes a game interesting.

In which I break my own reasonable policy against “meta” posts

I generally dislike “meta” posts that bloggers tend to write about their own blogs, themselves, or their writing processes, but I’m going to write a short one in the wake of the publicity this essay has received following its appearance on Hacker News. I do intend a follow-up piece to it, probably later this week, since it has sparked a lot of interesting discussion and criticism.

First blog note: I just turned off comment moderation, as I felt it was an impediment to discussion. A lot of posts sat in the dark for a few hours when they should have been out in the open, generating more discussion. My blog’s traffic level used to be low enough that the cost imposed by this delay was minimal, but I found out (around 5:30 this afternoon) that I had 40 new comments. I regret that this blocked hours of discussion and cross-pollination.

Second, I’ll use my 15 minutes of fame to plug something cool that I’ve worked on. I’ve invented two card games, Balls and Ambition. Old rules for Balls can be found here. The next release of Balls (scoring improvements, simplifications) will occur around March 20, 2011. I’d like to do a final release of Ambition this spring, but I don’t always have the time for proper playtesting, and that’s the major bottleneck to the design process.

Fscking Ace: a simple, depraved gambling game.

Fscking Ace is a simple game of cards. It’s not highly skillful or deep, but it’s fun and twisted. As this is a gambling game with wide swings, I’d recommend not playing at the specified increment of $1, unless one has an appetite for risk. For low-stakes “fun games”, divide dollar amounts by 100, playing with pennies instead of dollars, or decide that they are “points” that count for bragging rights only.

Disclaimer: I’ve never played this game for money. I probably never will. I’m not much of a gambler and, at any rate, a good dealer doesn’t taste his own poison.

Number of players: This can be played with 3 or more players. Use a double-deck if there are 6 or more players, a triple deck if there are 11 or more, and so on.

The deck: The pack contains 48 cards: all diamonds, clubs, and hearts, the Ace, 2, 3, 4, 5, 6, and 7 of spades, and two jokers. The colored joker is the $10 joker; the other is the $5 joker. (Mark one if they are identical.) If a double deck is used, then remove one Ace of Spades, leaving 95 cards. Remove two Aces of Spades from a triple deck, forming a pack of 142.

Optional: when using multiple decks, players may wish to remove the extra 2’s, because these “doublers” magnify wins and losses. With more than one deck in play and lots of doublers, the potential for catastrophic loss or enormous gains (each being the other, given the game’s zero-sum nature) is substantial.

Starting a round: Choose first dealer using the most distasteful mechanism you can come up with (highest or lowest salary, who can tell the most offensive joke, highest or lowest number of previous sexual partners). Or just draw lots. Whatever works. Dealer shuffles the pack and places an unused card (such as an unused spade) under it, making it impossible for any player to see, by accident, what’s on the bottom.

Playing a turn: Turns begin at the dealer’s left and progress clockwise at the beginning of the round. (Play order may be reversed, as described below.) Each player, on his turn, must turn over at least one card. If it’s a spade, his turn ends. Otherwise, he may keep turning over cards, until drawing a spade, or he may decide at any point to end his turn. If he chooses to end his turn, he scores the cards turned up. Most cards are worth $1, but the jokers are worth $5 and $10. If he draws a spade, he scores nothing for that turn and it ends.

For example, a player who drew, for his first four cards, 7♦-4♣-K♣-$5Jo, would score $8 for that round if he decided to stop. The joker is worth $5 and the other cards are $1. If he drew again and caught a spade, he’d score $0 for that round. The cards drawn by him that turn would be discarded, and his turn would end.

The red twos, if drawn and scored, are worth $1 base but also double the values of regular (non-Joker) cards that one has scored (from $1 to $2, $2 to $4, and so on). Twos of clubs are worth $1 but double the values of jokers that one has scored. (If multiple decks are used, they compound. For example, three 2♣’s makes a $10 joker worth $80.)

If a player’s turn is ended by a 2♠, he keeps it (as if it were scored) instead of discarding it. If he loses the round, his losses will be doubled. Also, when a player’s turn is ended by a 7♠, the order of play reverses (from clockwise to counter-clockwise, or vice versa). The 3, 4, 5, and 6 of spades have no special effect.

Ace of Spades, ending the round: If a player turns up the Ace of Spades, the round ends immediately. That player becomes the loser of the round, hence the name “Fscking Ace”.

The loser pays each player for the cards they have scored, plus an additional $1, to each player. A bonus of $5*N, where N is the number of players, is given to the player who scored the most cards. (In a tie, this bonus is divided among the tied players.) Due to Jokers and doublers, this is not necessarily the person who scored the most money.

The person who would have played after the one drawing the A♠ will open play in the next round. There is no ending condition other than peoples’ continuing willingness to play this evil, evil game.

Balls, a 3-player trick-taking card game

I’ve been looking for a great three-player trick-taking card game for a while. I designed Ambition, a four-player trick-taking card game, back in 2003. I believe Ambition’s one of the best playing card games out there, but it scales quite poorly. It works best with exactly four players, but not well with three. So, if nothing else, I need something to play when a fourth for Ambition is unavailable.

Skat I found appealing in concept, but loaded with a bit of cruft. I wanted to improve it or, better yet, develop a brand-new three-player trick-taking card game. Throughout December 2010 and January 2011, I spent much of my spare time play-testing a brand new (and, in my opinion, quite good) game of cards. It’s called Balls, and the rules can be found here.