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.