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Playing with the Averages - A simplistic approach
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<blockquote data-quote="77IM" data-source="post: 7579698" data-attributes="member: 12377"><p>As a good approximation, a reroll on a polyhedral die (but you have to take the second roll) is worth about +1 per die.</p><ul> <li data-xf-list-type="ul">Rerolling is worth a smidge less for low dice (d4 it is only worth +0.5) and a smidge more for large dice (for d12 it's +1.5) but I find that +1 is close enough and makes the math very quick. On a d20 it's worth +2.5!</li> <li data-xf-list-type="ul">This also assumes that you can choose when to re-roll, and you choose to re-roll anything less than the average, on the grounds that you are likely to do better on the second roll. (For example, the sorcerer's empowered spell metamagic -- it's worth approximately +Cha mod, assuming you are rolling at least 2x Cha mod dice.) </li> <li data-xf-list-type="ul">If you can only reroll 1-2 (like greatweapon fighting style) or only reroll 1 (like Elemental Adept feat) it's worth a bit less, but not as much less as you might think. For most die sizes, rerolling 1s is worth just shy of +0.5 (the d4 is only +0.375 and the d20 is +0.475), and rerolling 1-2 is worth +0.5 or a bit more (the d4 gets +0.5 and the d20 gets +1; the d12 is +0.83333...). For most purposes, I would just call both reroll 1 and reroll 1-2 an increase of +0.5 and be done with it.</li> <li data-xf-list-type="ul">If you get to roll both dice at once and THEN pick which one you take (like with advantage), it's worth considerably more, usually around 25% of the average.</li> </ul></blockquote><p></p>
[QUOTE="77IM, post: 7579698, member: 12377"] As a good approximation, a reroll on a polyhedral die (but you have to take the second roll) is worth about +1 per die. [list][*]Rerolling is worth a smidge less for low dice (d4 it is only worth +0.5) and a smidge more for large dice (for d12 it's +1.5) but I find that +1 is close enough and makes the math very quick. On a d20 it's worth +2.5! [*]This also assumes that you can choose when to re-roll, and you choose to re-roll anything less than the average, on the grounds that you are likely to do better on the second roll. (For example, the sorcerer's empowered spell metamagic -- it's worth approximately +Cha mod, assuming you are rolling at least 2x Cha mod dice.) [*]If you can only reroll 1-2 (like greatweapon fighting style) or only reroll 1 (like Elemental Adept feat) it's worth a bit less, but not as much less as you might think. For most die sizes, rerolling 1s is worth just shy of +0.5 (the d4 is only +0.375 and the d20 is +0.475), and rerolling 1-2 is worth +0.5 or a bit more (the d4 gets +0.5 and the d20 gets +1; the d12 is +0.83333...). For most purposes, I would just call both reroll 1 and reroll 1-2 an increase of +0.5 and be done with it. [*]If you get to roll both dice at once and THEN pick which one you take (like with advantage), it's worth considerably more, usually around 25% of the average.[/list] [/QUOTE]
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