I think the second table is more clear than the first, since it shows that Monty Hall's choice depends on your choice. The main nuance to this problem is that Monty Hall is not picking randomly. There's always some unpicked door with a goat, and he'll pick that one to reveal. So if your original choice is door #1, then when deciding to stay or switch, you're really deciding whether go with door #1 or with the better of doors #2 and #3 (since the worse of the two doors has already been shown to you).