My favourite is the “guess the pattern” dice game where you roll out a handful of dice, you need 5 or 6 die for this to work well. You then use the dice to think of a number, the other person has to guess your number. If they get it wrong, you roll another handful, all you tell them is whether their guess was too high, or two low, they don’t get to make another guess on this roll though. Keep re-rolling until they figure out your pattern for producing the number.
This can take about half an hour, and I’m not going to explain the game rules, because that would be stealing from James Bach who I believe invented the game. But the short of it is that it’s a very good game for paying attention to detail, applying logic and a bit of math and can be quite frustrating. So it shows up a lot of what the players are like as people, because you can give hints, or you can choose not to give clues. I like the dice game so much I have a bag of multicoloured dice in my desk drawer.