Business schools spend weeks teaching expected value, risk appetite and the discipline of exiting a position. A compact digital format now condenses all three into a five by five grid. Bitz, which operates a mines game, released aggregate play data showing where users actually stop revealing tiles, and the pattern will look familiar to anyone who has studied how managers handle troubled projects: most people stop too late, and the ones who stop early rarely trust the math that told them to.
The mechanics take one sentence to explain. A number of mines, commonly three, hide under 25 tiles, each safe tile you reveal grows a multiplier, and hitting a mine erases the round’s winnings.
The arithmetic nobody feels
Start with the numbers, because they are checkable by hand. With 3 mines under 25 tiles, the first pick is safe with probability 22/25, or 88 percent. Survive five picks in a row and the compound probability is roughly 49.6 percent, almost exactly a coin flip. A fair payout for that coin flip would slightly exceed 2x the stake. Any commercial grid game pays a touch below the fair figure at every step, and that persistent gap is the house margin, the same way a market maker’s spread compounds across trades.
This is precisely the structure of a staged investment decision. Each additional tile is a go or no-go gate: the marginal upside is visible, the marginal blow-up risk is known, and the rational move is defined by expected value, not by how the last three tiles felt. The educational value is that the grid produces in thirty seconds what a capital budgeting committee produces in three years.
Why people still stop in the wrong place
Prospect theory predicts the failure mode. In their 1979 Econometrica paper, Kahneman and Tversky showed that losses loom larger than equivalent gains and that people become risk seeking precisely when they are trying to escape a loss. Translated to the grid: a player who is down for the session keeps revealing tiles at exactly the moment the numbers say to bank, because a small certain win feels insufficient against the memory of earlier losses.
Organizational scholars know the corporate version as escalation of commitment, documented by Barry Staw in 1976: decision makers who feel responsible for a losing course of action allocate more resources to it, not fewer. Every executive who has watched a doomed project absorb one more budget cycle has seen a mine field played badly.
Position sizing, the forgotten lever
The second lesson is about stake size rather than stopping point. In 1956, Bell Labs researcher John Kelly derived the growth-optimal fraction of a bankroll to commit to a favorable repeated bet. The inconvenient corollary for casino formats is that when the edge is negative, the Kelly-optimal stake is zero. Teaching students to run that calculation and accept its answer is arguably the most transferable skill the grid offers: sizing decisions by edge and variance, not by conviction.
There is a defensible reason to play anyway, and honesty requires naming it. People pay for entertainment with negative expected value constantly, from cinema tickets to theme parks. The intellectually consistent frame is to price a session as consumption, cap it like a consumption budget, and never confuse it with investing.
A classroom exercise that works
For instructors: give one group the raw probabilities and require a written stopping rule before play, and let a second group decide in the moment. In our experience running this comparison informally, the pre-committed group banks smaller but dramatically more consistent outcomes, a live demonstration of why investment committees write exit criteria into the original memo rather than debating them mid-crisis. The exercise costs nothing when run on paper with simulated tiles, and the debrief writes itself.
Who should skip the real-money version entirely: anyone under legal age, anyone with a history of problem gambling, and any student who catches themselves believing a revealed tile changes what sits under the next one. That belief has a name in the literature, and no MBA elective can price it out of a person in one semester.
The grid will not make anyone rich. As a decision laboratory, though, it compresses prospect theory, optimal stopping and position sizing into a format a seminar can run before the coffee goes cold, and that is more than most case studies manage.