Why Game Designers Bend Randomness So It Feels Fair

A reader wrote to me last spring, quite upset, because the Three of Swords had come up in four of her last six daily pulls. She wanted to know whether the deck was telling her something. A day later, in an unrelated message, a friend complained that Tetris "always" gives him an S piece when he needs a line. Both of them were describing the same thing: a run that felt too unlikely to be chance.

Game designers have spent thirty years dealing with exactly that feeling. Their conclusion, more or less, is that people do not trust true randomness, so many games quietly replace it with something that feels fair instead. Looking at how they do it is one of the clearest ways I know to understand what a random draw can and cannot tell you, whether the draw is a tetromino or a tarot card.

The problem: real randomness clumps

Truly random sequences contain streaks far more often than intuition expects. Flip a fair coin 100 times and the chance of seeing at least one run of six heads or six tails in a row is around 80 percent. Most people, asked to write down a "random" sequence of 100 flips, never include a run longer than four.

Applied to cards, the numbers are similar. With a 78-card deck shuffled fairly every day, any particular card has a 1 in 78 chance of appearing on a given single-card pull. That makes four appearances of one specific card in six days very unlikely. But there are 78 cards that could each produce a run like that, and you would notice whichever one did. Across a year of daily pulls, a few odd-looking clusters are close to guaranteed. I worked through a related case in where the idea of a lucky streak comes from.

Players feel cheated by clumps. So designers adjust.

Four ways games fake fairness

Tetris and the seven-piece bag

Early versions of Tetris picked each piece independently, so long droughts of the straight I piece were possible. Modern Tetris games follow what fans call the 7-bag system: all seven pieces go into a virtual bag, the bag is shuffled, and the pieces are dealt out before a new bag is filled. You can never wait longer than 12 pieces for an I piece, and you can never see more than two of the same piece in a row. It is less random and far more popular.

Dota 2 and pseudo-random criticals

A hero with a 25 percent chance to land a critical hit does not actually roll 25 percent each time. The game uses a pseudo-random distribution: the first attack after a crit has only about an 8.5 percent chance, and each miss adds another 8.5 percent until a crit lands and the counter resets. Over many attacks the average is still 25 percent, but long dry spells and lucky triple-crits both become rare. The approach goes back to Warcraft III, and it exists purely because players hated the streaks.

Fire Emblem and the "true hit"

From the Game Boy Advance era onward, several Fire Emblem games averaged two random numbers instead of one when deciding whether an attack hit. The screen says 70 percent; the real chance is close to 82 percent. Low numbers get pushed down in the same way, so a displayed 30 percent lands less than a fifth of the time. Designers did this because players treated a 70 percent attack as a sure thing and felt robbed every time it missed. Rather than fix the players, they made the screen lie in the players' favour.

Hidden help after a run of misses

Firaxis has been open about bending odds in strategy games. Sid Meier described in a talk at the 2010 Game Developers Conference how players of Civilization Revolution refused to accept losing a battle at displayed 3 to 1 odds, so the team tilted results toward the player. XCOM 2's configuration files, which players can read, include an aim bonus that grows after consecutive misses on the two easier difficulty settings.

Why I do not think tarot should copy them

Every so often someone suggests that readers should "fix" their decks the same way: remove a card for a week after it comes up, or keep pulling until a different card appears. I understand the appeal. If the Three of Swords has shown up four times, a fifth feels like noise.

I disagree, and the games explain why. A designer bends randomness because the goal is enjoyment. A reading is supposed to start from a draw you did not control. Once you begin removing or redrawing cards to keep things feeling even, you are no longer drawing; you are choosing, slowly, with extra steps. The one part of the game designers' thinking that does carry over is the opposite lesson: streaks are normal, and a streak alone is not a message.

That does not mean a repeated card is meaningless. It means the repeat itself is not the evidence. Whether the card speaks to your situation is a separate question, and it should be asked the same way on the fifth appearance as on the first. The same reasoning applies to numbers, which I covered in why lucky numbers are not lucky odds.

The one thing worth checking: your shuffle

Here is where a real problem sometimes hides. Mathematicians Dave Bayer and Persi Diaconis showed in 1992 that a 52-card deck needs about seven riffle shuffles before the order is close to random. The usual rule of thumb scales with deck size, which puts a 78-card tarot deck at roughly eight or nine riffles. The overhand shuffle that most readers use, sliding small packets from hand to hand, is far weaker: estimates for a 52-card deck run into the thousands of overhand passes to reach the same mix.

So if a card keeps appearing, the most likely explanation is ordinary clumping. The second most likely is that you put it back on top or near the top after the last reading and a few gentle overhand passes did not move it far. Neither explanation involves the deck trying to tell you anything, and the second one is entirely fixable. Our explainer on what RNG means in games covers the computer side of the same idea if you want to go further.

For this week: after each daily pull, before you put the card back, write down its position in the deck (top quarter, middle, bottom quarter) and how you shuffled. At the end of seven days, look at whether repeated cards were also cards that went back near the top. If they were, change the shuffle before you change anything else. In my own small test of 40 pulls, that one adjustment made the "favourite card" pattern disappear almost completely.