That obvious trick relies on that we will only verify its prediction for strategies that it recommends. Here’s a protocol that doesn’t fail to it: A known number of gems are distributed among boxes, we can only open one box and want many gems. Ask for the distribution, select one gem at random from the answer and open its box. For every gem it hides elsewhere, selecting it reveals deception.
That obvious trick relies on that we will only verify its prediction for strategies that it recommends. Here’s a protocol that doesn’t fail to it: A known number of gems are distributed among boxes, we can only open one box and want many gems. Ask for the distribution, select one gem at random from the answer and open its box. For every gem it hides elsewhere, selecting it reveals deception.