Wondering if we need to buy train tickets in advance or can we wait until we get to Italy. We arrive in Milan from Paris August 9 by air and will train to Monterosso the 10th. Our hotel is near the rail station. We return to Milan the 17th by rail and fly out the 18th. What are the chances of sold out trains?
Nearly zero chances of sold out trains. It is possible they might sell out the 2nd class fare in August on the IC train (peak tourist time), but you can always find the ticket in first class for €9 more (unless you want to wait for a later train).
You can buy tickets in advance if you want to secure a discounted fare (which tend to run out as you get closer to the time of departure). But no chance of selling out all seats.
Be aware that discounted tickets come with restrictions on the possibility of getting a refund or changing the time of departure, in case you change your mind later.
It is not whether the trains sell out, but what price you want to pay, and can you commit to a nonrefundable non changeable ticket.
For instance, for August 10 you can buy SuperEconomy tickets now for 18.90 EUR, whereas the Base fare is 28.50 EUR. Not that big a deal, but why pay more and chance it. August is vacation time in Italy.