[hanoz]

This is pretty counterintuitive. In the game described you should expect to see one 'wrong way' bus per play on average, not half as you might expect. On the other hand, you have an exactly even chance of catching your own bus before seeing a wrong one, so if your scoring system had been +1 for your bus and -1 for one or more wrong ones, then you would indeed score 0 over time. But with your point per bus scoring system your expected score turns out to be -0.5 per play.