Same average, different feel
Two games can have exactly the same expected result per play and feel nothing alike. One hands out small outcomes often. The other is quiet most of the time and occasionally produces something large. The first is called low volatility, the second high volatility. In statistical terms, volatility is variance: how widely results scatter around the average.
Designers of games of chance, loot systems and reward schedules choose volatility deliberately, because it shapes the experience even when the average is fixed.
Two illustrative games
These are made-up games for illustration, not descriptions of any real product. In both, a play costs one unit, and the figures below are net results per play.
Game A (low volatility): win 1 unit with probability 0.45, lose 1 unit with probability 0.55.
- Expected result: 0.45 x 1 + 0.55 x (-1) = -0.10 units.
- Average of squares: 1. Variance: 1 - 0.01 = 0.99. Standard deviation: about 1.0.
Game B (high volatility): win 9 units with probability 0.09, lose 1 unit with probability 0.91.
- Expected result: 0.09 x 9 + 0.91 x (-1) = 0.81 - 0.91 = -0.10 units.
- Average of squares: 0.09 x 81 + 0.91 x 1 = 7.29 + 0.91 = 8.20. Variance: 8.20 - 0.01 = 8.19. Standard deviation: about 2.86.
Both games have the same expected result of -0.10 per play, so the same long-run cost. Yet B has a spread nearly three times larger.
What it looks like over 100 plays
For independent plays, the expected total after 100 plays is -10 units for both. The standard deviation of the total is about 10 for Game A (the square root of 99) and about 28.6 for Game B (the square root of 819).
- In Game A, results cluster fairly close to -10, and a typical session drifts down steadily.
- In Game B, a typical session is also expected to lose, but the range is far wider. Some sessions end well ahead thanks to one or two large wins, while many end well behind.
Game B also has long dry spells. The chance of no win at all in 20 plays is 0.91 to the power of 20, about 15%. In Game A, the chance of no win in 20 plays is 0.55 to the power of 20, which is tiny (under one in a hundred thousand). A player of Game B therefore sees “nothing happens” far more often, then occasional jumps.
Hit frequency and size
Two numbers describe the shape well: how often something pays (the hit frequency) and how big the payouts are relative to the stake. At a fixed average, more frequent hits must be smaller, and larger payouts must be rarer. Volatility is largely the tuning of that trade-off.
Low volatility means smoother results and slower swings in either direction. High volatility means longer droughts and a wider range of session results.
Why designers choose different volatility
In game design, the same ideas show up in many places.
- Reward schedules and loot systems can mix frequent minor rewards with rare big ones to keep play interesting. Systems such as weighted random tables and pity timers adjust how rare outcomes arrive.
- A high-variance contest creates more upsets and drama; a low-variance one is more predictable and favours the stronger side more consistently. This is part of the balance of luck versus skill in a design.
- Critical hits in video games are a small-scale example: a high chance of a modest bonus versus a low chance of a huge one can have the same average damage but very different feel.
Volatility in chance-based gambling
For real-money games, volatility changes how quickly a budget moves in either direction, but it does not change the sign of the expected result. A game with a negative expected value is expected to cost the player over time regardless of whether it is volatile. Higher volatility can make a short session look better or worse than the average, which can mislead people into reading a lucky stretch as skill or a game becoming “hot”.
The pattern of rare large wins among frequent small losses is also tied to variable rewards, which can make play feel compelling. A long dry spell does not make a win more likely next; each play is independent.
Takeaways
- Volatility is variance: the spread of results around the same average.
- Equal averages can hide very different experiences.
- A volatile game needs a bigger buffer to ride out dry spells, but this does not alter the long-run expected cost.
- Short results say little about the true average.
Nothing here is a way to beat a house edge. Outcomes are uncertain, and gambling can be harmful. Set limits you can afford, and contact a local support service if play is becoming difficult to control.