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<blockquote data-quote="Thanee" data-source="post: 1998047" data-attributes="member: 478">Ok, a little comparison should make that clear, I hope. <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=":)" />We use the standard re-rolling method. You can re-roll once, but have to keep the new roll.It's obvious, that your method, where you take the highest from the two rolls is better than that, because either the second roll is equal or higher, then the result will be the same, or the first roll was higher, then your method yields the better result. It's always equal or better, there is no way you can come out worse.But we'll stick to the weaker version, since it's easier to compare.When you roll the HD you can expect to gain the average of the die roll. It can be lower or higher, but on average it is exactly the average. On a d8, this is 4.5, for example.So, if we can re-roll once, we'll always choose to re-roll, if we rolled lower than 4.5, because then we can expect to gain more hp (of course, you could get higher even on a 6 or 7, but usually you won't).So, if we roll a 1, 2, 3, or 4 we'll re-roll, otherwise the result stands.With the re-roll we replace our result (1, 2, 3, or 4) with 4.5, basically, which is the average of the second roll, so on average, every roll below 5 becomes 4.5.With my method, every such roll becomes 4, which is .5 lower.Therefore the re-roll once method is always equal or better than the half HD minimum method.The take highest from two rolls is always equal or better than the re-roll once method, so obviously also as the half HD minimum method.ByeThanee</blockquote>

[QUOTE="Thanee, post: 1998047, member: 478"] Ok, a little comparison should make that clear, I hope. :) We use the standard re-rolling method. You can re-roll once, but have to keep the new roll. It's obvious, that your method, where you take the highest from the two rolls is better than that, because either the second roll is equal or higher, then the result will be the same, or the first roll was higher, then your method yields the better result. It's always equal or better, there is no way you can come out worse. But we'll stick to the weaker version, since it's easier to compare. When you roll the HD you can expect to gain the average of the die roll. It can be lower or higher, but on average it is exactly the average. On a d8, this is 4.5, for example. So, if we can re-roll once, we'll always choose to re-roll, if we rolled lower than 4.5, because then we can expect to gain more hp (of course, you [i]could[/i] get higher even on a 6 or 7, but usually you won't). So, if we roll a 1, 2, 3, or 4 we'll re-roll, otherwise the result stands. With the re-roll we replace our result (1, 2, 3, or 4) with 4.5, basically, which is the average of the second roll, so on average, every roll below 5 becomes 4.5. With my method, every such roll becomes 4, which is .5 lower. Therefore the re-roll once method is always equal or better than the half HD minimum method. The take highest from two rolls is always equal or better than the re-roll once method, so obviously also as the half HD minimum method. Bye Thanee [/QUOTE]

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