The object that Dan is holding is a twenty sided die, or d20 for short. In Dungeons and Dragons players roll a die to determine how well their character performs certain actions- for example, when attempting to lie to another character. If a character rolls a 1, no matter how good their other stats or bonuses are, they will fail... horribly. When a one is rolled archers will accidentally shoot the king instead of the assassin behind the king; a diplomatic translator will think they are complimenting a rival faction's floral arrangements when they actually insulted the rival's mother; a character trying to get rid of a pest who is latched onto their arm will end up punching their own arm off. Every once in a great while a person can be seen to roll a one in the game of life, like when Dan MASTERFULLY bluffed his way through a small lie.
...because, y'know, if I was at the door ALL the way downstairs that would just be WAY too far to go, clearly. That's like a ten mile hike, in a snowstorm, in the blinding sun, uphill both ways. Two feet... okay, MAYBE that's doable, just give me a minute.