Most tabletop games contain random elements. Many depend entirely on cards, dice, or bags of tiles. Even very abstract games usually have some randomized initial state, giving a different puzzle each time you play.

In this article, I’m going to discuss randomness in games – why it’s important, what mechanics generate it, and how it can be controlled. I’ll then show how I used these concepts in the design of Sub Terra, and how they evolved for the upcoming Sub Terra II: Inferno’s Edge.

Wish me luck!

CRITICAL HIT

“Randomness” is a bit of a vague term, so I should probably start with a definition. In this context, I mean “a game event exists where the outcome is uncertain to at least one player”. There is some element of the game that is outside the players’ direct control.

Randomness achieves four main things:

 

  • Randomness increases replayability
    Players like novelty. If a game session unfolds the same way every time you play, it’s (a) not really a game, and (b) not that fun to repeatedly participate in. If a game has no random elements, then the only things ensuring each game session is different are the actions the players take. For this to be unpredictable, the game has to have a certain (high) level of complexity so that it’s not easy for players to solve.

    Compare Chess to Tic-Tac-Toe. Both are perfect-information (the whole gamestate is known to all players) fully-deterministic (no random elements) abstract games. Tic-Tac-Toe is considerably less complex than Chess – with a little bit of effort, you can see that perfect play by both players means the game always ends in a draw, at which point it stops being interesting. Chess is theoretically the same, but because the game has a lot more actions available on each turn, and there are considerably more turns in the game, it’s impossible for humans to solve completely (even with robot assistance). Each game is therefore a battle over who has the best approximation of a perfect strategy from any given board state, which will nearly always differ from game to game.

    Randomness is a way to shortcut this without making a game overly complex. Take another (fantastic) abstract game, Hey, That’s My Fish. Once the game starts, it’s also perfect-information and fully-deterministic, but the starting board configuration is different every time you play, giving you a new puzzle to solve. Similarly, classic card games like Bridge and collectible card games like Netrunner use shuffled decks to make each round unique, even with the same cards used every session.

  • Randomness increases accessibility
    I need to quickly define some more terms. Let “complexity” refer to the amount of mental effort needed to (a) understand the rules of a game, and (b) understand a typical game state in full (i.e. what actions are available to all players right now, and their immediate consequences). Let “depth” refer to the amount of mental effort needed to play the game perfectly (i.e. evaluating the full long-term implications of each of these actions).

    Complexity is (usually) a negative quality, as it makes your game harder to learn and play. Depth is (usually) a positive quality, as it rewards experienced players by giving them an edge in gameplay, as they can learn which actions (or chains of actions) are generally more optimal.

    These qualities are linked – it’s relatively easy to increase depth by increasing complexity (i.e. adding more rules / things to track). But ideally we’d like to get as much depth for as little complexity as possible. Mark Rosewater, head designer of Magic: The Gathering, refers to this as “lenticular design”. (If you’d like a scrappier, amateurish perspective, I also wrote another long article about it here and here)

    What does this have to do with randomness? From observing the differences between new players and experienced players, Rosewater noted that new players basically ignore depth. They’re still figuring out how everything works right now, and not how things are going to look a turn or so later. This means that they tend to play reactively; adapting to new information as it appears, not anticipating what new information could appear. This effectively means that they’ll stop thinking ahead as soon as a random event occurs – why waste time planning when anything could happen?

    Experienced players, on the other hand, have mastered the “now” and have mental resources to spare to plan for the future. Random events still have a reasonably well-defined set of outcomes; you just don’t know in advance which outcome will come to pass. By concentrating on the most likely or significant of these outcomes, you can gain an edge. For example, consider Texas-Hold-‘Em Poker – experienced players gain an edge by balancing the likelihood and impact of the unknown cards (opponents’ cards, future community cards) relative to their known cards (their hand, revealed community cards), and bet accordingly.

    Adding randomness to your game can reward experienced players with extra strategic decision making, while not putting newer players at too much of a disadvantage. 

 

  • Randomness increases tension
    Great games keep the winning player or team uncertain until the very end.

    As soon as the outcome to some process is known, it stops being exciting, and just becomes a chore. For games (and sports, and books, and film/TV, and life), we need the constant possibility of a reversal of fortune to keep us interested. We just want to know how it ends!

    The more a game relies on skill over luck, the more important it is to have players of a roughly equivalent skill level in order to keep things interesting. If there’s a significant skill imbalance, without randomness there’s no real way for a less-skilled player to win, and the game’s outcome is essentially locked in from the start. However, the more random elements there are (and the higher the variance in those random events), the greater the chance that a low-skill player could get lucky and beat a high-skill player. This gives more hope to the underdog, more fear to the veteran, and more excitement to any spectators.

  • Randomness protects player ego
    If I lose to another player, and the game had no randomness in it, then I know that the loss was my fault. This doesn’t feel great, and makes me less willing to play the game again, especially against the same opponent.

    Instead, if I lose to another player and the game does have a reasonable amount of randomness in it, I can blame the randomness for my loss – even if it was still entirely my fault. This might be frustrating, but it’s not a reason to stop playing the game – after all, I’m still great, it’s just the game that caused me to lose, and I’ll do better next time.

    Conversely, if I beat another (objectively better) player entirely due to luck: no, it wasn’t luck, it was skill, and I can feel good about myself for being such a great player.

 

CRITICAL FUMBLE

Unfortunately, we can’t just add a fistful of dice to everything and call it a day. There are also downsides to randomness:

  • Bad luck feels unfair
    If you invest a lot of time learning and improving at a game, you expect to be rewarded for your investment with a greater win rate. If that game contains random elements, then there will be times when those act in your favour, and times when they go against you, and in most sessions they’ll usually balance out.

    But sometimes the heart of the cards isn’t with you, and no matter how well you play, you can draw ten lands in a row and lose to Jeff’s lone goblin beatdown. These situations are less likely, but they do happen, and you’re more likely to remember when they do. Especially because humans underestimate the odds of regular patterns occurring in a random sequence (HTHHT feels like a more random sequence of coin flips than HHHHH, even though they have the same chance of appearing).

    We can take steps to minimize this by reducing the variance of random effects. For example, we can take a game that relies on drawing a balanced mix of action cards and resource cards (Magic: The Gathering) and turn it into one with only action cards (Hearthstone). However, this reduces all the positive effects of randomness listed above – I believe this is why Hearthstone leans heavily on random gameplay effects despite having a predictable resource system.
  • Randomness reduces the effect of skill
    Players enjoy games in different ways. A lot of players place a high emphasis on mastery – that is, learning how to play the game better than your opponents to increase your win rate.

    Randomness gets in the way of this. The added depth can make games harder to master (a good thing!), but it can also make it very frustrating when all the time you’ve invested is cancelled out by a bad roll of the dice.

    If you want to make a serious competitive game, then it can’t feel too random, otherwise mastery-driven players get a low return on their time investment and will look elsewhere for their kicks.

 

FULL HOUSE

It seems that randomness is a useful tool to make games more engaging, as long as we’re careful not to make things too chaotic for our target audience. How can we make our games less predictable?

Here are some of the main archetypes, along with example methods, advantages, disadvantages, and any relevant mathematical concepts you may (optionally!) need for theorizing / balancing:

FIXED-PROBABILITY RANDOM EVENTS

Methods: Rolling dice, flipping coins, spinning spinners, picking a tile/token (with immediate replacement), drawing a card from a deck (with immediate replacement)

Relevant Math: Independent Probability, Binomial Distribution, Multinomial Distribution, Central Limit Theorem, The Gambler’s Fallacy

Advantages: Dice require zero preparation time (no need to assemble or shuffle a deck), and the fixed set of independent outcomes makes them straightforward to reason with. The more of them you roll, the more likely you are to have a “normal”, non-extreme result.

Disadvantages: Humans are really susceptible to the Gambler’s Fallacy, which is a mistaken belief that independent probabilities are self-correcting (i.e. if you initially roll a lot of 1s, you’re less likely to roll a 1 in future). The annoying thing is that this can apply even if you know about the Fallacy – we have really hardwired notions of sequences that look random (e.g. “13524”) and things that don’t (e.g. “11313”). It’s a hard bias to shake. (Early Sub Terra II fell into this trap, as I’ll explain later)

It’s also hard to fit much information onto a die face – you’re limited to either numbers/dots for threshold checks (“4+”) and magnitude (“D6 damage”), or special symbols that require some lookup table.

SELF-CORRECTING RANDOM EVENTS

Methods: Drawing a card from a shuffled deck, picking a tile/token (without replacement), cube towers

Relevant Math: Conditional Probability, Hypergeometric Distribution

Advantages: As long as you draw most of the deck, the total number of a certain card type you draw will tend towards the total number of that card type in the deck. This is admittedly a very trivial statement, but if compared to independently random dice (above) this matches our gambler’s-fallacy-based human intuition better: if you draw a lot of Spades, you’re less likely to draw Spades in future. Cards are therefore very useful at providing a “fair” or “balanced” spread of random outcomes across almost any distribution of probabilities.

You can also fit a lot of information onto a single card – a huge part of the tabletop industry is built around this.

Disadvantages: If you don’t draw most of the deck, this suffers from the same these-sequences-don’t-look-random problem as dice. I worked on Magic Duels, which implemented a mathematically perfect shuffle (I checked), and there were still endless online conspiracy theories about the shuffler being broken when players drew too many resource cards early in the game.

If you do draw most of the deck, the last few draws can become very predictable, which might remove some tension from the end of your game. A number of games put “end-the-game” cards at a roughly known position in the deck, to remove certainty over when the game will end and what cards will be available (e.g. Coloretto).

Additionally, shuffling a deck fairly can take a reasonable amount of time. Magic has been moving away from effects that shuffle your deck over the years because of this, favouring effects that look at the top few cards of your deck instead. Bags of tiles or tokens get around this, though they’re harder to search through.

 

SIMULTANEOUS ACTIONS

Methods: Each player makes a hidden choice then reveals it simultaneously (cards, tokens, amount of tokens, hand signals, writing something down)

Relevant Math: Payoff Matrices, Dominant Strategies, Mixed-strategy Nash equilibria (solver here)

Advantages: Let’s play Rock-Paper-Scissors! Your opponent has three equally valid actions, and you have no real way of knowing what they’re going to pick. Regardless of what you pick, you have a ⅓ chance of winning, ⅓ chance of losing, and ⅓ chance of a draw.

If the actions are symmetric (like Rock-Paper-Scissors), this is just a more theatric way to flip a coin. If the actions are more asymmetric (e.g. RPS, but winning with Rock is worth double), then the “correct” probabilities to maximise your score also shift, but it’s usually not easy to figure out what they should be (here, it’s apparently correct to play Paper ½ the time, and Rock/Scissors ¼ the time, but I couldn’t have told you that without working it out).

Whole games have been built on the back of complex simultaneous choices (Libertalia, Revolution!) – the appeal is trying to predict what your opponents are going to do, then picking something to counter it, even though the outcome is likely to be highly chaotic.

Disadvantages: Solving these can get complicated, fast. They’re probably not suitable if you want players to reason with the probabilities to gain an edge, but are great for providing lots of unpredictable chaos.

You also need to watch out for dominant strategies – that is, actions that are correct no matter what, as this makes the outcome predictable unless someone playing irrationally. As a silly example, consider Rock-Paper-Scissors-Gun, where Gun beats everything except another Gun. It never makes sense to pick anything other than Gun, so the game should always end in a draw.

 

MULTIPLAYER COMPETITION

Methods: “Winner-takes-all” scoring and 3+ competing players

Relevant Math: Game Theory, Extensive-form games

Description: In a two-player competitive game, every change in game state is either good for you, bad for you, or neutral – there is only one winner, and you want to be it. If you add more players, though, things get a little murkier. If each player has a score at the end of the game, then it’s easy enough to define the winner as the player with the highest score, but what about the remaining players? Are they trying to get the highest score possible, or the highest rank possible? Are they actually indifferent to all outcomes other than winning outright? Each of these motives changes how they should play, and because most games don’t specify which is “correct”, it’s up to each player to privately figure out.

Advantages: This helps keep multiplayer games interesting! You can get some of the benefits of randomness without having any overtly random mechanisms in your game, just a lot of politics and negotiation as you try to guess how much your opponents value second place.

Disadvantages: A lot of people really don’t like political interactions in their games – a lot of eurogames restrict direct player interaction, and I think this is a plausible reason why. It’s unsatisfying to have a losing player arbitrarily choose which other player wins the game.

 

SKILL-BASED MECHANICS

Methods: Dexterity (accuracy, balancing objects, steady hands, reflexes), Knowledge (trivia, spelling, definitions), Computation (arithmetic, estimation, anagrams, pattern matching) etc.

Relevant Math: Classical Mechanics? Chaos Theory?

 

Advantages: With skill-based mechanics you have some control over the outcome, but you can’t always be certain you or other players will perform the required action perfectly. This leads to uncertain pseudo-random outcomes in countless different ways (sports, word games, party games…), and is definitely worth an article in its own right. However, in this particular context, it makes sense to group them all together.

Disadvantages: Skillful players will have an advantage over less skilled players, which might be undesirable if you want randomness to be an equaliser.

 

MEMORY MECHANICS

Methods: Overwhelming players with trackable information, then concealing it.

Advantages: This is another skill-based mechanic, but is used frequently enough that I wanted to discuss it separately. A reasonable number of games use this mechanic to make endgame scoring more uncertain (e.g. Citrus, Solenia, Smallworld; anything with a victory-point token that you acquire face up and can turn face down). The random element comes from not knowing for sure what different objects players possess, so you have to approximate. This can speed up games where an overwhelming amount of visible information would slow down play while That Guy painstakingly goes through all the options.

Disadvantages: Full disclosure: I hate this mechanic, because the smartphone era of information-on-tap has rotted my brain. Thankfully, it’s easy enough to convert most games that use it into games that don’t by insisting that information can’t be hidden once revealed. I don’t think it’s unfair to say that it’s polarizing – if you use it, make sure it’s an essential pillar of your game, otherwise I’m begging you to remove it and use some other form of randomness instead.

 

HIDDEN RULES

Methods: Gamesmasters (GMs / DMs), app integration, locked content, forbidden books

Advantages: This one’s interesting. Every other random mechanic listed provides either a mathematical problem to solve, a skill-based action to complete, or a way to gauge the mental state of other players. By adding new information or rules to the game while it’s in progress, anything can happen, and your only way of anticipating this is by somehow guessing what madness the designers could come up with.

Betrayal at House on the Hill uses this as its core premise. You’re exploring a spooky house, then about halfway through the game you turn to a random page in a special book and suddenly everything changes in a way that’s only fully known to a single player. The same is true for tabletop role-playing games with a gamesmaster/director role, or for anything with digital integration (the app hides information).

At a less involved level, you should be able to achieve the same result with a deck of mostly unknown cards (Dead of Winter’s crossroads deck), or a legacy/campaign game that adds in new components every time you play (Pandemic Legacy, Fortress).

Disadvantages: Cost, mainly. You need a bunch of additional components and rules that you need to keep hidden from the players, and that you barely use any of in any given session. All of which needs testing. Not to mention the effort required to build a companion app or (*winces*) a full-sized video game.

Having said that, if you’re making a tabletop-like video game anyway, then this is fantastic design space to explore (Into the Breach).

 

—————————————————————————————–

 

TEMPTING FATE

 

So how did Sub Terra use randomness, and how does Sub Terra II try to improve things?

 

Sub Terra used three main random mechanics:

 

  • Shuffled stack of tiles
    This was essentially a deck of cards, which had to be almost fully depleted before it became possible to win the game. This meant that almost every tile got played every game, and the various threats/obstacles/connectivity all broadly balanced out.

    However, the large size of the stack (65 tiles) meant that early game exploration was often radically different. This was good in terms of adding variety / replayability, but outlier starts where you only had one hyper-dangerous route to explore out from could feel unfair. The large stack was also a bit awkward to shuffle.

  • Shuffled deck of hazard cards
    This was a difficulty-balanced set of dangerous cards, with a small number of cards randomly returned to the box so the deck was an appropriate size for the number of players. This allowed the deck contents to remain uncertain even when it was nearly empty.

    As this was the main “clock” that controlled game length, the whole deck was used in every session, meaning that a roughly even number of each hazard event appeared in every game. Additionally, the game progressed, the probability of each hazard type appearing next could often shift quite dramatically, changing the risk of certain locations. This was a nice reward for more experienced players, who could use this to gain an edge.

     

  • Skill checks (50% success rate die roll)
    This was used in a number of places to deliberately reduce the certainty of actions and events. Because a large number of these checks would occur every session, and they all had roughly the same impact on the game, in general you’d get a reasonably even mix of successes and failures. However, outlier games could still occur, which could easily be frustrating (fail almost every roll) or dull (succeed almost every roll). This variance was useful at giving players hope, though – you could optionally make a skill check to gain a free action every turn, so if things were getting out of hand you could always try to get lucky to eke out a win.

    However, this was also used for situations where players didn’t really have a choice – mainly, Tremors (hazard events that would deal damage on a failed check) and placing ropes (an action that unlocked a specific route, which was sometimes necessary to proceed or regroup). There were ways to mitigate the worst effects of failing these checks (healing, retreating, exploring onwards), but sometimes these weren’t available, making these now-mandatory checks quite frustrating.

Sub Terra II reworks this a bit:

 

  • Bag of tiles
    This is mathematically equivalent to a shuffled stack of tiles, except much easier to set-up and handle. The exit mechanics of the first game prevented this from being an option, as the exit tile had to be in the bottom six tiles of the stack to make placement less predictable/controllable. This time, the double-sided nature of the tiles (one side is “normal”; the other is filled with lava) meant that a bag was essential, so the objective tile is now placed on the board when the bag is empty.

    The consequences of this are similar to the first game, with the caveat that there are considerably fewer tiles in the bag (30). This is still enough for each session to feel reasonably unique, while reducing the chance of extreme outlier cases where players start extremely blocked in.

     

  • Hazard die
    The hazard cards have been replaced with a six-sided “hazard die”, rolled at the end of each player’s turn (i.e. 3-6 times every full round). Each hazard effect is less severe than each of Sub Terra’s hazard cards, but they occur much more frequently. The removal of the deck (both construction and shuffling) significantly shortens set-up time.

    In early design, my initial assumption was that the hazard die would be rolled enough to ensure that the number of each symbol would be roughly similar in any given session. This meant that the original hazard effects were of wildly varying power levels, including one that advanced the volcano track one step (equivalent to robbing each player of an entire turn). This was a terrible idea – it turns out that the number of rolls (~100 per session) was nowhere near enough to ensure the required level of uniformity, which meant that team success was nearly always down to how many “volcano symbols” were rolled on the die. It took me far too long to realise this. After changing the hazard effects to be much closer in magnitude, the game became a lot more consistent and improved dramatically.

    While overall hazard consistency is higher than in the previous game, there’s still a pleasing amount of unpredictability to every turn, as the randomness isn’t self-correcting – consecutive runs of the same result can and do happen, which add some nice texture to each session (e.g. a drought of enemy spawns for a few turns can turn into a horde ambush with little warning).

     

  • Skill checks (50% success rate die roll)
    These were initially removed completely, but were reintroduced in a couple of places to make last-resort actions feel more tense (specifically, moving onto spike traps and for non-combat characters attacking monsters). In both cases, the action is entirely voluntary, and alternatives exist – you can choose to push your luck to gain an advantage, but if you roll badly and mess up you only have yourself to blame. It’s possible to play entire sessions without performing a single check.

     

Overall, these changes make the threat against the team a bit more consistent. This increases the impact of player skill, but removes some of the extremely-high-tension moments of the original game. This was a deliberate shift to fit the heroic-adventure-feel of the new theme.

 

—————————————————————————————–

 

LOST IN THE SHUFFLE

 

I hope you didn’t find this article too predictable. Did I miss anything? Let me know in the comments!

 

Next week I’ll be discussing resonance in games – using visual and thematic elements to reinforce a design.

 

See you then!