The kind of answer to this problem that I see most frequently uses logical reasoning. I don't think that's the best approach to start with, because it is abstra

The kind of answer to this problem that I see most frequently uses logical reasoning. I don't think that's the best approach to start with, because it is abstract and disconnected from reality. It has a high chance of error. I think people would do better to write a computer simulation of the problem, or, for non-programmers, to design a game with dice that simulates the problem. When you execute the simulation, you pretty quickly realize what's going on. Then you can use logic or formal reasoning to put your intuition into words. A couple people here have said something similar (ctrl-f "simulation" on this page). According to https://www.mwsug.org/proceedings/2010/stats/MWSUG-2010-87.pdf https://www.mwsug.org/proceedings/2010/stats/MWSUG-2010-87.p... , even the great mathematician Paul Erdős wasn't convinced that switching was better until he saw a simulation: > Vazsonyi ran the program 100,000 times. Erdős watched the results of the simulation. The simulation results indicated that by switching, the odds of winning are indeed two out of three. Finally, he was grudgingly convinced that switching was better. He did not like it but seeing was believing. He could not argue with the results.