The Big Idea

When rolling with two dice instead of one using The Big Idea’s second printed ability, treat the two dice as saperate die rolls, and calculate their results independently. The effect that instructed you to roll the die treats the total of the results for its result. For everything else treated the individual rolls’ results separately.

Note that the replacement effects from The Big Idea’s second printed ability do not expire once the current turn has ended. They last indefinitely, regardless of whether The Big Idea is on the battlefield, until you are instructed to roll a six-sided die.

If you activate The Big Idea’s second printed ability multiple times, there will be several instances of that replacement effect. As the replacement looks for six-sided die rolls and replaces them with further six-sided die rolls, all instances will be spent ‘boosting’ the next die you are instructed to roll.
For example, say there are five instances of the effect. Painiac‘s ability triggers instructing you to roll a six-sided die and give Painiac +X/+0 until end of turn equal to the result. The first instance of the replacement effect replaces the die with two dice to roll. The second and third instances replace both of these dice, leading to four dice to roll. The fourth and fifth instances replace two of those dice with four more dice, leaving six dice to roll. There are no more instances of the replacement effect, so you roll the six dice simultaneously and determine each of their results. The results, after all result-changing effects are applied, are 2, 3, 4, 3, 1 and 6. Then, total the results, and use that value instead for the effect. Painiac gets +19/+0 until end of turn.