If you roll a standard 6 sided die and you get paid $1 for every spot it lands on (so if you roll a 5 that would mean $5), what's the average payout for one roll? same game as before, but you can reroll one time and you get paid whatever you get on the final roll (either the first roll or the second, depending if you stop). So, if you roll a 6 you would keep it, but if you roll a 2, you might choose to reroll that and then you could get higher or you could also get stuck with a 1. What values would you reroll, and what values would you keep? now what's your average payout if you play this game, when you can reroll once, 1 time? our cofounder has a dog named fennel. Fennel barks a lot, usually when strangers randomly walk by, and often disrupts a meeting. Let's say, if we have a 1 hour meeting, there's an 84% chance that fennel interrupts the meeting. Interrupts means that he barks at least 1 time. He might bark once, twice, ten times, or 1000 times; but at least once. If we have a 30 min meeting, what's the chance that fennel interrupts the meeting?