What if there are 50 tickets left and someone puts in an order to purchase 51 - this code will say it is sold out when

TICKET_PRICE = 10

tickets_remaining = 100  

while tickets_remaining >= 1:
    if tickets_remaining > 1:
        verb = "are"
        remaining_s = "s"
    else:
        verb = "is"
        remaining_s = ""
    print("There {} {} ticket{} remaning (at $10.00 per ticket).".format(verb, tickets_remaining, remaining_s))
    valid = False
    while valid != True:
        client_name = input("What is your name? ")
        if (len(client_name) == 0):
            print("*** INVALID SELECTION ***")
        else:
            try:
                val = int(client_name)
            except ValueError:
                valid = True
            else:
                print("*** INVALID SELECTION ***")
    valid = False
    while valid != True:
        num_ticket = input("{}, how many tickets do you want to purchase? ".format(client_name))
        try:
            val = int(num_ticket)
        except ValueError:
            print("*** INVALID SELECTION ***")
            continue
        if val <= tickets_remaining:
            valid = True
        else:
            print("*** ERROR ***: There {} only {} ticket{} remaining. Try again.".format(verb, tickets_remaining, remaining_s))
    num_ticket = int(num_ticket)
    if num_ticket > 1:
        num_s = "s"
    else:
        num_s = ""
    amount_due = num_ticket * TICKET_PRICE
    print("The total amout due is ${}.00 for {} ticket{}.".format(amount_due, num_ticket, num_s))
    user_info = input("Do you want to procced Y/N? ").lower()
    if user_info == "y":
        print("SOLD!!!")
        tickets_remaining -= num_ticket
    else :
        print("Thanks anyways, {}".format(client_name))
print("Tickets soldout! :( ")