Thursday, 7 November 2013


Most games feature an element of randomness, or something that behaves like it (e.g. hidden information, simultaneous decisions, unpredictable chaotic systems).

Sometimes I hear some games dismissed as being "just luck". Usually this isn't literally true (we're not talking about Snakes and Ladders), so why do people say this? Maybe because, even when you've made "good" moves you can lose for reasons out of your control. This isn't necessarily a bad thing - Tom Lehmann describes it as "one of the most powerful things that strategy games can teach us". But also, often this judgement is made rashly: things that appear purely random to a beginner can be taken advantage of by a skilled player. A game having elements of luck isn't opposed to it requiring skill, there can be deep skill in navigating chance.

I think of Race for the Galaxy. My skills have probably decayed a bit now, but when I played regularly I won most of the time. And at first some people dismissed this as luck - "you drew a lucky combo, I didn't get any cards that worked together" - until they realised I got lucky almost every game, and so could they. Partly this is learning to recognise good combinations among the cards you draw, and shifting course to accommodate them - often beginners will dismiss good cards because they're fixated on one "strategy" (and other times they'll insist on playing them to their detriment when they don't fit; navigating between these takes subtlety). Partly it's about learning to use the mechanisms the game offers for controlling and responding to your luck - there are so many small decisions in terms of which cards to keep or discard, whether to draw a greater number of cards or to have more control over which cards you draw, whether to reveal a card now or hold it back for later.

Ascension also is a game worth playing to study chance. Much of the game's depth comes from subtle manipulations of the randomised cards available to buy in the centre: responding to what's available, denying your opponent cards that fit their strategy, searching for the ideal cards for your own. And also recognising that removing a card from the centre may create an opportunity for your opponent, so sometimes it's best to not buy something that would benefit you just to avoid that risk (this justifies why cards in the centre are superior to always-available cards at the same price). Also there's trashing cards from your deck - beginners often find it hard to understand this because it feels like throwing away resources, but by removing the less valuable cards you increase the frequency with which you draw the better ones.

Okay here are some general concepts that I think can apply to a whole bunch of different games.
* The more random events occur, the more likely the overall distribution is to average out to something not very random at all (i.e. the Central Limit Theorem). Safer to take lots of chances rather than letting everything hang on just one. This applies in a stronger form to card games, since any given card is guaranteed to be drawn eventually if you go through the whole deck.
* So there are two broad ways of performing better at random events: increase the number of events, or increase the chances of success on each one. In an RPG: make more attacks, or improve your chances to hit.
* There's often a risk-reward trade-off; choosing between a high chance of a small advantage and low chance of a big advantage. Which one is correct depends on your position: if you're behind you want to take a long shot for a chance of getting ahead because the reliable option will reliably not be enough, and if you're ahead you usually want to play it safe to maintain your lead. When there's only one possibility that will let you win, no matter how unlikely it is, play assuming that it will happen. But usually you want to bear in mind all possible outcomes and have a plan for each.
* Flipping that around: if something comes together perfectly and someone scores extremely highly, it was probably a long shot rather than something you can count on happening again.

Don't be bitter and blame luck. Embrace it and understand it, flow with the chaos.


  1. Really interesting thoughts. I've always had a love-hate relationship with luck in games, but I've never quite understood when or why I liked it and when I didn't. This clears up some things in my head.

    I especially agree with the idea that increasing the amount of times that a random event occurs decreases frustration. Mechquest (an overall bad game, don't waste time on trying it) has long missions, where in order to beat it, you have to roll in the very end, and if you roll too low, you lose the entire mission or don't get the loot that you needed. Extremely frustrating. Whereas games like Spelunky or 868-HACK increases the amount of random events involved and thereby decreases the frustration.

  2. Thank you for this interesting note on luck.

    After your first bullet "the more random events occur, the more likely the overall distribution is to average out to something not very random at all" I'd like to add that this can be true in a surprising way.

    For example, with a random walk in one dimension (consider two player snakes and ladders without snakes or ladders and a single die yielding one or zero) both the following are true:

    1. You win half the time (excluding draws). This follows because your expectation of advantage over your opponent is zero.

    2. If you are ahead, the distance between the players is most likely to grow, in the long run. (Accumulated randomness makes no effort to equalize, or to make fair the situation).


    And the phenomena you describe in your last bullet point is normally termed regression to the mean:

  3. It's very easy to mistake adaptability and strategic planning with luck. I noticed this when I started playing Carcassone and I won almost every game with my friends. The issue is that I probably knew the set of tiles better than them and so I was able to rebuild my strategy upon the tiles in my hand and the tiles that were not in game yet. When a tile appears and it seemed to fit perfectly everyone said I was extremely lucky but I was just being adaptive and flexible.

  4. I think another thing to think about with luck in games is the curve at which it is appealing to different target audiences. For instance, coin flip board games for kids, or non-investment players and/or first time players. The high luck, low strategy works great for those markets and puts everyone on an even playing field. This type of game is especially frustrating for strategic players, especially hardcore strategy gamers like Chess players (zero luck involved and all the information is on the board). In-between the two extremes you have the casual players, to the more committed players and there is a market for each group. I found this blog post extremely useful because it is a very important question for game developers and players to understand when playing games and making games.