There's a 20% chance that the volunteer was initially correct. In the 80% case, one of the two remaining cups has the price beneath it, so choosing one of the

There's a 20% chance that the volunteer was initially correct. In the 80% case, one of the two remaining cups has the price beneath it, so choosing one of the remaining cups gets you a 40% chance of payout instead of your initial 20%. Switching doubles your chance of payout. This should be straightforward to anyone who actually understands the Monty Hall problem.