Fifth-grade students’ fairness judgments through probabilistic ideas: Maintaining and refining reasoning across two game contexts

Long before children learn the formal rules of mathematics, they are already making complex judgments about what is right, what is just, and what is fair. In the world of childhood, fairness often means getting an equal share or having the same rules as everyone else. But when games involve chance—like rolling a die or flipping a coin—fairness becomes a trickier concept. It is no longer just about who gets the first turn; it is about whether the game itself gives everyone an equal shot at winning, even if the outcome feels random. This is where the science of probability begins to take root in the human mind. Researchers have long wondered how children navigate this gap between their everyday sense of justice and the hidden mathematical structures that govern chance. Do they simply guess, or do they possess an intuitive understanding of how likely different outcomes are, even without a teacher explaining the numbers?

A recent study set out to explore this very question by watching how eleven-year-old students in Turkey judged the fairness of two different games. The researchers, led by Gamze Kurt at Mersin University, were not looking for children who could calculate odds on paper. Instead, they wanted to see what ideas children used spontaneously when asked if a game was fair, and how those ideas changed after they actually played. The study focused on two specific scenarios: a familiar game of rock-paper-scissors and a custom-made game using a weighted die. In the first game, the rules were perfectly balanced, with both players having the exact same options and the same chance to win. In the second, the die was secretly rigged; it had four sides marked with one symbol and only two sides marked with another, giving one player a distinct advantage over the other. The goal was to see if the children could spot the unfairness in the rigged game and how their reasoning evolved as they experienced the results of playing.

The researchers gathered sixty-eight fifth-grade students and asked them to work in pairs. Before they touched any game pieces, the children were asked to write down whether they thought the game was fair and why. Then, they played ten rounds of each game, recording who won each time. After the playing was done, they were asked to judge the fairness of the game again and explain their reasoning. The results revealed that children are far more sophisticated in their thinking than the study anticipated. In the game with the weighted die, every single pair of students immediately identified it as unfair before they even rolled the die once. They did not need to count the sides or do any math to know this. Instead, they looked at the physical object and saw that one player had more winning symbols than the other. They described the game as "rigged" or noted that one player had "more chances" to win. This suggests that even without formal instruction, children possess a strong, intuitive grasp of how unequal opportunities create unfairness.

What was perhaps more surprising was how the children handled the game of rock-paper-scissors. Because this game relies on the players' choices rather than a random object like a die, the structure of fairness was invisible. Here, the children's reasoning was much more varied. Some focused on the rules, stating that the game was fair because both players had the same rights and followed the same procedures. Others looked at the players themselves, arguing that the game was fair because the winner was determined by skill, strategy, or who could guess the other person's move better. A few children even argued that the game was unfair simply because it involved luck, believing that a game cannot be fair if the outcome is not entirely under a player's control. This contrast showed that children do not rely on a single definition of fairness; instead, they shift their thinking depending on whether the game feels like a test of skill or a roll of the dice.

The study also tracked how the children's minds changed after they played. The researchers found that playing the game rarely caused a child to completely flip their opinion. If a child thought the weighted die game was unfair before playing, they almost always thought it was unfair afterward, even if they happened to lose a few times or if the game ended in a tie. However, the experience of playing did refine their thinking. Children who initially said the die game was unfair because "one side had more shapes" began to use more precise language after playing, talking about "winning opportunities" or "probabilities" rather than just the shapes themselves. In the rock-paper-scissors game, playing helped some children realize that their initial fears about luck were misplaced; they saw that even though the outcome was uncertain, the rules still gave both players an equal footing. The act of playing did not usually change the verdict of fair or unfair, but it did sharpen the reasons behind that verdict.

The findings suggest that fairness is a powerful tool for teaching probability, not just a moral concept. Children enter the classroom with a rich set of informal ideas about chance, opportunity, and advantage. They can distinguish between a game that is structurally rigged and one that is balanced, and they can coordinate these ideas with their own experiences of winning and losing. The study indicates that educators do not need to wait for students to learn formal math to start discussing these concepts. By using games as a context, teachers can help children articulate and refine the intuitive reasoning they already possess. The children in this study showed that they are capable of seeing the hidden structure of a game, understanding that a few lucky wins do not make an unfair game fair, and recognizing that fairness is about the setup of the game, not just the result of a single round. This research highlights that the seeds of mathematical reasoning are already growing in the minds of young children, waiting to be nurtured through the simple, universal experience of playing a fair game.