Rolling Singles or Pools?

        In the context of rolling for a success, do you prefer a single dice determine your fate or a pool? I've known people who insisted on rolling 2d10 in place of a d20 because statistics. That being said, I recommended a player switch away from his "lucky" d20 after it rolled 4 for the umpteenth time. Then there is that case of a GM stipulating the player can only pass this next check with a roll of 20, or PC has bad things happen. So, he digs out his secret weapon magic die .... and it rolls a 20, ftw ...
        Now there are questions of die quality, the option of game science dice and other arguments that fall under this umbrella, but do pools really take a bit of die chicanery out of the mix? I'm no statistician ...