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<blockquote data-quote="Nim" data-source="post: 2620282" data-attributes="member: 5684">Interesting. I thought you were wrong, Borlon, but looking at it more closely, I figured out why it looked wrong to me even though you were logically correct. If the game is 'roll this d20 until you roll a 1, and count the number of times you roll', then your mean result WILL be 20.The mode (most commonly occuring single result) is 1.The median (the point at which half of the results are lower and half of the results are higher) is between 13 and 14 - a fractional result wouldn't make sense, since you can't make a fractional roll <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile&nbsp; &nbsp; :)"&nbsp; data-smilie="1"data-shortname=":)" />So, if you do this 10000 times and average the results, you'll come up with something near 20. But half (51.23%) of your results will be 14 or less. Very long stretches without a 1 (say, 100 rolls or more) are very unlikely, but they're possible...and because the numbers involved are big, that moves the mean pretty far from the median.</blockquote>

[QUOTE="Nim, post: 2620282, member: 5684"] Interesting. I thought you were wrong, Borlon, but looking at it more closely, I figured out why it looked wrong to me even though you were logically correct. If the game is 'roll this d20 until you roll a 1, and count the number of times you roll', then your mean result WILL be 20. The mode (most commonly occuring single result) is 1. The median (the point at which half of the results are lower and half of the results are higher) is between 13 and 14 - a fractional result wouldn't make sense, since you can't make a fractional roll :) So, if you do this 10000 times and average the results, you'll come up with something near 20. But half (51.23%) of your results will be 14 or less. Very long stretches without a 1 (say, 100 rolls or more) are very unlikely, but they're possible...and because the numbers involved are big, that moves the mean pretty far from the median. [/QUOTE]

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