Really annoyed me that the kiddos voted to not switch, and they got the car. Getting children to understand that 1/3 is smaller than 1/2 is hard enough. I’m going to program my own evil version that only wins on switch the first time next time I do this.
The issue is that this isn’t a fraction problem, it’s a statistics problem. You need sample size. You need to teach it with M&Ms or something small, and let the kids choose to switch or not switch and play 20 rounds each with that choice, then compare piles.