The game-theory concept of luck is famously elusive. Luck sometimes operates like an “invisible hand”, affecting player decisions on a fundamental level, but often without making its presence in a game known. Luck even undergirds crunchy strategy games that brag about their emphasis on tactical skill, and thus it is crucial to understand luck in order to become a better tactician.
Richard Garfield, designer of Magic: The Gathering (and many other titles), has argued that luck and skill lie on a continuum, a scale which determines how often the more skilled player wins. Under this metric, an “all-skill” game is something like arm wrestling, where a fourth-grader could never beat a body-builder. In other words, these aren’t really games, but deterministic evaluations. Any game where a less-skilled player could conceivably win, Garfield argues, is a game with an element of luck.
This is an instructive definition precisely because so many tactics and strategy games claim to rely heavily on skill, but are in fact tightly designed so as to enable surprising come-from-behind victories. For example, though Chess is heavily skill-based and has no dice-rolling or elements of randomization, luck asserts itself in the myriad of choices facing the player. Unless one has made a dedicated study of the game, it’s not immediately obvious whether it’s wisest to move the queen-side knight or the king-side first (let alone the other 7 types of pieces!). Moreover, even if one memorizes all the optimal moves, the same cannot be said for the opponent, and they may employ the perfect counterattack without knowing it — in other words, by luck.
[If] the luck of a tactical game can completely negate the player’s carefully considered decisions … the game is essentially reduced to Yahtzee with guns.
In contemporary tactical video games, luck is a much more transparent matter. In real-time games like Civ or League of Legends, luck exerts itself similarly to chess, where decision trees are much too broad to solve perfectly (and, the “timer” creates opportunities for mis-clicks and other unlucky errors). In turn-based games like the XCOM series, most actions have a chance-to-succeed, and even the levels are randomly generated. This luck is both more and less important than it appears to be, and is very important for this genre of games.
Every time a player makes an offensive action in XCOM, that action has a randomized chance to hit. (Tabletop games like Risk or Warhammer 40K use dice in an analogous fashion.) However, due to regression to the mean, the more dice are rolled, the closer one’s results will converge to the expected value. So, even if an XCOM unit’s next attack only has a 50% chance to hit, their 4-person squad over the 10 turns of the level may have a global expected damage output of closer to 80% or so. In other words, the luck of an individual event is largely mitigated by the large number of such events that occur within a single level, play session, or campaign. The more luck events that occur, the more deterministic their outcome! The most obvious component of luck in this genre of games is actually the least meaningful.
At first glance, this might seem contradictory to anecdotal evidence — after all, many a failed XCOM mission was due to the disastrous consequences of a single missed shot. The tug-of-war inherent in strategy games can best be understood by making analogy to the physics concept of equilibrium:
In the above schematic, neither ball will move unless acted upon — but, an errant gust of wind is much more likely to displace the ball in unstable equilibrium. In the same way, small events of bad luck can snowball relatively easily in XCOM to destabilize the whole mission, either in the player’s favor or against it. (Conversely, I suspect that one reason Risk games take so blasted long is that the equilibria established in that game are too stable relative to the cautiousness of its players.)
XCOM-like tactical games are especially unstable in the first few hours of gameplay, where entire campaigns can hinge on a single shot, which is what gives games in this genre their vicious reputation. However, though the equilibria of individual missions don’t change throughout a campaign, the campaign equilibrium grows more and more stable as the player gains access to healing abilities, better item quality, or larger pools of healthy soldiers. This is excellent game design since it keeps each mission tension-filled, while also giving players a safety net that rewards their hours of good tactical decisions. After all, if the luck of a tactical game can completely negate the player’s carefully considered decisions prior to that point, the decisions are wasted and the game is essentially reduced to Yahtzee with guns.
Luck has a big effect on gameplay balance, but its effect is even greater on the experience of the player. I’ll demonstrate with a particularly memorable XCOM mission:
Early in a campaign, I was running hot with a particular squad, taking down alien outposts and bases with ease. I was most proud of my sniper, Lu “Slayer” Choi. One day, Slayer led her team into enemy territory on another routine “clear the zone of hostiles” mission. I was feeling pretty cocky (having forgotten about regression to the mean) and sent my squad dashing to good cover, in preparation to execute my usual approach to these missions. Of course, it so happened that my luck regressed to the mean — with my team’s last movement point of the turn, Slayer made eye contact with a group of aliens, triggering their alarms.
I watched helplessly as the aliens systematically flanked my team, critically wounding my grenadier and medic. I responded on my turn with an unusual strategy that cleared a few of the aliens but over-extended my troops, leaving my medic out in the open. Sure enough, he was hit with a barrage of laserfire that would have been lethal — but I got lucky, and he started bleeding out rather than dying outright. I sent my wounded grenadier to the EVAC zone with the medic over his shoulder, getting them to safety at the cost of going down to only 2 squad members. Slayer and her surviving teammate crept up to the alien facility (a little more cautiously than before), knowing that 6 aliens remained in the combat zone. One pod of aliens went down easily after an errant shot detonated a large barrel of gasoline. The other group, though, contained among its members the psychic Sectoid alien, who promptly mind-controlled Slayer’s compatriot. Slayer could cut her losses and evacuate, leaving her teammate to be eaten by aliens, or take a 50% chance-to-hit shot of killing the Sectoid, ending its psionic control and winning the mission. The choice was easy — Slayer lined up her scope, took a deep breath, squeezed the trigger…
The Sectoid exploded in a haze of green mist; Slayer lived up to her name, and went on to become XCOM’s most decorated soldier. Ever since then, I’ve used XCOM’s customization options to recreate “Slayer” Choi in every subsequent campaign, and to create other Choi sisters with similarly cool names and face-paint. I shed a silent tear every time a Choi sister bites the dust.
The influence that small luck events exert on the equilibrium of a tactical game does all of the emotional heavy lifting. Too much luck, and the player becomes an agency-less balloon adrift on the wind. Too little luck, and the game can be solved algorithmically like tic-tac-toe, making it unworthy of a second playthrough. The right amount of luck creates drama and tension, compensates for inexperience, and rewards players who can adapt their strategies and take calculated risks. More than any other single quality, luck is the key to making tactical games fun.