3 ms·

Every value being equally likely does not mean we expect every value to appear only once. Throw a d6 seven times and we expect a configuration to come up twice

• thaumasiotes 3y ago
  Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice. A better example wouldn't involve a probability that can achieve 1; maybe ask about the probability of rolling a 3, or of rolling another 3 given you've already observed one 3. None of those will match the comment above; it isn't well posed.
  • yreg 3y ago
    Throw a d6 six times and you probably won't see each value exactly once.
    • thaumasiotes 3y ago
      Yes, I mentioned that in my comment, unless you believe that after seeing five rolls including a duplicate, adding a sixth might bring the total to six rolls with no duplicates.
      • yreg 3y ago
        I refactored your comment. :)
  • saghm 3y ago
    > Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice Even that isn't as strong as you could make it; rolling a die 5 times is basically the birthday paradox but instead of asking 30 people their birthdays to find a duplicate, you're asking 300. In the case of life supporting planets though, it feels like we're trying to talk about the likelihood of rolling a given value when we haven't even determined whether the die has unique values on each face or not. If you're assuming that only one of the sides has a 3 on it, the interesting part is already over.
• Kichererbsen 3y ago
  why you guys all rolling d6? d20 is the queen of dice!