Why games contain randomness at all
A game with no randomness and no hidden information is a puzzle that can, in principle, be solved: the better planner wins every time. Designers add chance for several reasons, and it helps to separate them.
- Variety. Randomness makes each play different. Shuffled cards, rolled dice or a generated map mean the same rules give new situations every time.
- Uncertainty and tension. When the outcome is not known, each moment matters. A result that depends partly on chance keeps players engaged to the end.
- Accessibility. Luck narrows the gap between experienced and new players. A beginner can win a game of chance occasionally, which keeps the table friendly.
- Adaptation. Random events force players to respond to circumstances rather than follow a memorised plan.
Chance also has costs. Too much of it makes choices feel pointless, and too little makes a game feel rigid or predictable. Much of design is deciding where on that spectrum a game should sit.
Where randomness comes from
Physical games use dice, cards, spinners, bags of tokens and shuffled tiles. Digital games use code, which usually relies on pseudo-random generators: algorithms that produce sequences that look random but are determined by a starting value. Both can be analysed with the same probability tools. A good starting point is knowing the probability distributions involved: how likely each possible result is, and how those likelihoods combine.
A few basic distributions turn up constantly:
- Uniform. Every outcome is equally likely, as with one fair six-sided die.
- Bell-shaped. Adding several dice makes middle totals more likely than extremes.
- Weighted. Some outcomes are deliberately more likely than others, as in a loot table.
Each produces a different feel, even when the average result is identical.
Two dials: average and spread
Designers tune two properties of any random mechanic. The first is the average outcome. If a combat roll deals damage on average, the expected value tells designers how quickly health totals will fall, how long a typical match will last and how costs and rewards should be priced.
The second is the spread, or volatility. Two mechanics can share an average and differ in how much individual results wander. A single die with a wide range gives dramatic swings; rolling several smaller dice and adding them gives tighter results. High volatility creates memorable moments and comebacks. Low volatility rewards planning and consistency. Neither is better in the abstract, since it depends on the game’s purpose. This idea of game volatility is a central design choice.
Keeping randomness fair, and keeping it feeling fair
There are two separate problems here: whether a system is actually fair, and whether it feels fair.
Real fairness comes from the maths. If an outcome is supposed to occur 10% of the time, a large number of trials should land near 10%. Designers often check this with a simulation, which is far faster than playing thousands of games by hand.
Perceived fairness is different. Human intuition expects randomness to look evenly spread, but true random sequences contain streaks and clusters. A player who misses three 70% chances in a row can feel cheated, even though this happens often enough across a long game. Players also tend to remember bad streaks more clearly than good ones.
Designers respond in different ways:
- Controlled draws. Drawing from a pool without replacement, as with a deck, limits extreme runs, because the pool shrinks and rebalances.
- Adjusted probabilities. Some systems raise the chance after each failure so that long droughts become unlikely. This is a deliberate departure from independent trials, and it should be documented so that it is not mistaken for a bug.
- Visible odds. Telling players the actual chances helps them judge choices and builds trust.
Input and output randomness
A useful distinction is when randomness happens in a player’s turn. Output randomness happens after a decision: you choose to attack, then dice decide the result. Input randomness happens before a decision: a card or tile is revealed and you decide what to do with it. Input randomness tends to preserve skill, since players respond to what appears, while output randomness can make plans feel fragile. Most games use both in some proportion.
Tuning with numbers
Several habits help designers keep randomness under control:
- List every outcome and its chance. Make sure the probabilities add to 100%.
- Calculate the expected value. Check that rewards and costs balance across the game.
- Look at the worst realistic case. What happens to a player who gets an unlucky but plausible run?
- Simulate. Run thousands of trials through a Monte Carlo simulation to confirm that the maths matches the design and to reveal surprises.
- Playtest. Numbers cannot tell you how a streak feels. Watching players confirms whether a mechanic is frustrating or exciting.
A quick sense check on rare events also helps. If something has a 5% chance per attempt, the chance of seeing it at least once in 20 attempts is 1 minus 0.95 to the power 20, about 64%. So roughly one in three players will go through 20 attempts without seeing it, which may or may not be acceptable for the design.
Randomness and responsibility
Games that involve spending real money on random rewards raise different issues. Randomised paid rewards, such as loot boxes, can resemble gambling in how they work, and some players, especially younger ones, can be harmed by them. Responsible design means clear odds, sensible limits and no pressure to spend. As a player, set limits on time and money in advance and be wary of anything that encourages chasing a rare outcome.
The same principle applies to real gambling. Casino games are built so that each bet has a long-run advantage for the operator, and no tuning of randomness changes that for the player. If gambling is causing you or someone you know difficulty, a local support service can help.
Putting it together
Designing with probability means choosing the type of randomness, setting its average and spread, checking that it behaves as intended, and then testing how it feels. The articles in this section take specific parts of that process in turn: dice sums, the balance between luck and skill, controlled draws and weighted tables.