3 ms·

> random 0 to 9 mod 4 does not have an even distribution over 0-4. That's true, but only because 4 never appears in the result. The possible results for modulo

by lutusp 12y ago

> random 0 to 9 mod 4 does not have an even distribution over 0-4. That's true, but only because 4 never appears in the result. The possible results for modulo 4 are 0 - 3. The first child is numbered zero. Shall I explain it in more detail? n n % 4 ----------- 0 0 1 1 2 2 3 3 4 0 5 1 6 2 7 3 8 0 9 1 10 2 11 3 12 0 13 1 14 2 15 3 > It's also more difficult to explain to children. And rewarding, unless you want your children to grow up innumerate.

aeosynth 12y ago
if the stopwatch uses base 10, the last digit will be in the range [0, 9], making n >=10 irrelevant. in this range, 0 and 1 appear 3 times; 2 and 3 appear 2 times. if the stopwatch uses hex, then 0-3 will appear equally often in this case
- lutusp 12y ago
  The second digits on my digital watches extend to 59, and if a precocious youngster were to correctly object that a limit of 59 produces a bias, I would extend the range by multiplying the minute digit by 60 and adding it to the seconds (thus reducing the bias). We are, after all, most likely using a calculator to produce the result. > if the stopwatch uses hex ... I think we're safely in the red herring zone now. :) EDIT: Yes, of course -- when confronted by a correct and reasoned reply, downvote it to discourage any such mistakes in the future.
  - aeosynth 12y ago
    i think you're confused on what a 'last digit' is. the seconds digits (plural) contain two digits, which range from 0-59; the last digit (singular) ranges from 0-9
    - lutusp 12y ago
      > i think you're confused on what a 'last digit' is. Digits, not digit, please, and do try to limit the anti-intellectualism and adversarial posture.
valleyer 12y ago
The last digit on the clock can only be 0 through 9. If you truncate your chart accordingly, 0 and 1 are represented more than 2 and 3. Or do you mean “the entire seconds value” (for which this idea would work with four children) instead of “the last digit”?
- lutusp 12y ago
  To avoid confusion, I used the expression "last digits".
  - baddox 12y ago
    It actually doesn't matter how many options are in your random number generator. You only get a normal distribution if the number of children you have divides the number of options in your generator. Even if you're using the seconds of a clock, it doesn't work for 7 children.
    - lutusp 12y ago
      > It actually doesn't matter how many options are in your random number generator. It certainly does -- the larger the random number, the fairer the outcome is. > Even if you're using the seconds of a clock, it doesn't work for 7 children. For a digits range of 0 - 59? Plus the fallback in the face of a precocious child of adding the number of minutes * 60?

by lutusp 12y ago

aeosynth 12y ago

if the stopwatch uses base 10, the last digit will be in the range [0, 9], making n >=10 irrelevant. in this range, 0 and 1 appear 3 times; 2 and 3 appear 2 times. if the stopwatch uses hex, then 0-3 will appear equally often in this case

lutusp 12y ago
The second digits on my digital watches extend to 59, and if a precocious youngster were to correctly object that a limit of 59 produces a bias, I would extend the range by multiplying the minute digit by 60 and adding it to the seconds (thus reducing the bias). We are, after all, most likely using a calculator to produce the result. > if the stopwatch uses hex ... I think we're safely in the red herring zone now. :) EDIT: Yes, of course -- when confronted by a correct and reasoned reply, downvote it to discourage any such mistakes in the future.
- aeosynth 12y ago
  i think you're confused on what a 'last digit' is. the seconds digits (plural) contain two digits, which range from 0-59; the last digit (singular) ranges from 0-9
  - lutusp 12y ago
    > i think you're confused on what a 'last digit' is. Digits, not digit, please, and do try to limit the anti-intellectualism and adversarial posture.

valleyer 12y ago

The last digit on the clock can only be 0 through 9. If you truncate your chart accordingly, 0 and 1 are represented more than 2 and 3. Or do you mean “the entire seconds value” (for which this idea would work with four children) instead of “the last digit”?

lutusp 12y ago
To avoid confusion, I used the expression "last digits".
- baddox 12y ago
  It actually doesn't matter how many options are in your random number generator. You only get a normal distribution if the number of children you have divides the number of options in your generator. Even if you're using the seconds of a clock, it doesn't work for 7 children.
  - lutusp 12y ago
    > It actually doesn't matter how many options are in your random number generator. It certainly does -- the larger the random number, the fairer the outcome is. > Even if you're using the seconds of a clock, it doesn't work for 7 children. For a digits range of 0 - 59? Plus the fallback in the face of a precocious child of adding the number of minutes * 60?