I think you guys need to study Bayesian math.

Like with Deal or No Deal, if you get to the last case, it's ALWAYS better to switch the cases. You would think that the chances are 50/50. But based on Bayesian math, the chances are actually around 60-70%.

It would be too complex to explain it here, but essentially, they lead you to believe that it's not the case you picked so you'll miss it.