Maybe not exactly what you're looking for, but the Monty Hall problem is famously counterintuitive.

There are three doors. One conceals a car, and the other two goats. You select one door. The host opens another door, and it has a goat. By changing your choice to the other closed door, you double your odds of choosing the car.

Many readers of Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong...Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.

https://en.wikipedia.org/wiki/Monty_Hall_problem

Maybe not exactly what you're looking for, but the Monty Hall problem is famously counterintuitive.

There are three doors. One conceals a car, and the other two goats. You select one door. The host opens another door, and it has a goat. By changing your choice to the other closed door, you double your odds of choosing the car, compared to keeping your original choice.

Many readers of Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong...Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.

https://en.wikipedia.org/wiki/Monty_Hall_problem

Maybe not exactly what you're looking for, but the Monty Hall problem is famously counterintuitive.

There are three doors. One conceals a car, and the other two goats. You select one door. The gameshow host chooses opens a different demonstrates that it has a goat. By changing your choice to the other closed door, you double your odds of choosing the car.

Many readers of Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong...Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.

https://en.wikipedia.org/wiki/Monty_Hall_problem

Maybe not exactly what you're looking for, but the Monty Hall problem is famously counterintuitive.

There are three doors. One conceals a car, and the other two goats. You select one door. The host opens another door, and it has a goat. By changing your choice to the other closed door, you double your odds of choosing the car.

Many readers of Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong...Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.

https://en.wikipedia.org/wiki/Monty_Hall_problem