For a casual game, where it is assumed no one is cheating, then, unless you're a stickler for tradition, who cares? Your friends are wrong.

Sure, but the "wrong" in this case couldn't be shown to my friends. They perfectly understood probability. The problem wasn't in the math. So where were they wrong?

Another way of saying this:

• The territory said one thing
• Their map said another thing
• Their map understood probability
• Where did their map go wrong?

The answer has nothing to do with me cheating and has nothing to do with misunderstanding probability. There is some other problem here and I don't know what it is.