Design Pattern: Leveraging Luck

In a recent appearance on Gabe Barret’s Boardgame Design Lab podcast, Richard Garfield, designer of Magic: The Gathering, spoke about the interplay between luck and skill in a game. Garfield made the point that luck appears in many games we normally see as purely contests of skill.

The argument goes like this. Chess is a perfect information game with no random elements. Most people would say that luck plays no role in chess. But Garfield suggest otherwise.

In a game of chess, players attempt to look ahead and predict the emerging game state based on different moves they might make. Many moves can easily be rejected as moves that will harm your overall position and decrease your chances of victory. But at some point in most games, especially between players of similar skill, players will choose among a set of moves whose long-term impacts are difficult to evaluate. Players may hypothesize about how different moves will impact gameplay, but these hypotheses are essentially guesses or experiments. The move itself is a ultimately a wager, subject to a kind of uncertainty that starts to feel more and more like luck. You make a move with a high level of uncertainty, and you then find out whether it was a good move later.

To some extent this is a matter of perspective. After the game, when experts analyze the positions and the crucial moves, and calculate all the variations, we can label one move a blunder and another a strong move.

This retrospective doesn’t seek to explain what players knew during the course of play, it only seeks to explain the value of the various moves themselves. In other words, the blunder might have been a genuine mistake, a miscalculation about the value of the move, or it might have been an oversight, a failure to notice some important factor and account for it. While the former is strongly aligned with the skill of the player, the latter is less so. Humans, even highly trained and capable humans, miss things. When a grandmaster misses something in the moment of play, it’s fair to say that’s unlucky.

The reverse is also true. A player might not realize, when making a great move, that it is as strong and decisive as it turns out to be. They may well have been debating between multiple moves, chose one path, and won the wager. Similarly, a move made for an entirely different purpose earlier in a game can have an outsize impact on the game at a later point – an impact neither player could predict. These too are a kind of luck.

Players who dislike luck don’t have problems with this kind of luck. Most, I suspect, would try and argue that this isn’t really luck at all. Yet the overall dynamic is quite similar. You’re faced with uncertain, difficult-to-evaluate choices thanks to opacity, and you pick one. The outcome is uncertain, and your choice doesn’t reflect skill, in the sense that you didn’t see through the opacity to know which choice would be better. You guessed.

Admittedly this is somewhat simplified, and the point here is not to equate chess to Sorry! Rather, the point is to demonstrate that soft randomness, luck-like structures, can be introduced into skill-testing games without spoiling the experience.

Consider these two examples. You move your 5-piece in Stratego to attack an opponent’s piece, as compared to attacking a territory with a single infantry unit with your tank in Axis & Allies. Most of us would see the former as a purely deterministic, non-luck encounter, and the latter as a random outcome. The odds of your victory in the first example are the probability that your 5 is lower than the opponent’s piece, and while I don’t have the distribution of pieces at hand, let’s say it’s 60%. Your chances of winning in the second example are your chances of hitting the opponent (3/6) and your opponent missing (4/6), or 12/36, which is 1/3.

Both encounters, from the perspective of the attacker, have some probability of success. Yet the experience of each is quite different. In the first case a successful attack would leave the player with a sense of skill. The player sussed out, through whatever cues, that the opposing piece was weaker! In the second case, both players would agree that the success of the attacker was luck. The decision to take the chance might be skillful, relative to the opportunity cost of the decision, the board state, and the potential rewards. But the outcome itself was luck. If the attacking unit was an infantry, hitting on 1 out of 6, and the defending unit was a fighter jet, defending on 4 out of 6, such that the overall odds of a successful attack was only 2/36 we’d say it was an especially lucky attack – but the choice to make it might still have been correct and skillful. An outside reward can justify risking poor odds, and the best choice of a bad lot is still a skillful decision. Sometimes, in the words of Bill Adama, you have to roll the hard 6.

Knowing how some players react to luck, this insight gives us methods for putting luck into games in ways that those players don’t find objectionable. Hidden information, player-generated outcomes rather than randomizer-generated outcomes, a large decision space, and the opacity of outcomes are all psuedo-random mechanisms that a designer can leverage to blur the hard edges of a game without alienating analytical and competitive players.

There’s so much more to be said about this topic, but I think we’ll have to leave it here for now. I’m curious to hear from all of you about what you think of Dr. Garfield’s concept of game-theoretic luck. Have at it in the comments!

Liked it? You can support my work on Patreon!