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<blockquote data-quote="Esker" data-source="post: 7905711" data-attributes="member: 6966824"><p>To me it feels a bit weird to make rolling a 1,2 or 3 lead to a better outcome than rolling higher numbers. Of course, GWF does that already with 1s and 2s compared to the other values that are below average, but at least rolling high values are better than rolling low values.</p><p></p><p>Your math is also off for 2d4 and 2d6. You seem to be assuming a 75% chance of rolling a 3 or below when rolling 2d4 and a 50% chance of rolling 3 or below when rolling 2d6, but since you're rolling two dice you have two chances to trigger a reroll, for a (1 - 0.25^2) = 0.9375 chance of rolling a 3 or below with 2d4, and a (1 - 0.50^2) = 0.75 chance of rolling a 3 or below with 2d6. That makes the expected values of these rolls</p><p></p><p>2d4: 5 -> 7.34 (+2.34)</p><p>2d6: 7 -> 9.63 (+ 2.63)</p><p></p><p>which makes 2d4 better than 1d10, and 2d6 even more better than 1d12 than it already is.</p></blockquote><p></p>
[QUOTE="Esker, post: 7905711, member: 6966824"] To me it feels a bit weird to make rolling a 1,2 or 3 lead to a better outcome than rolling higher numbers. Of course, GWF does that already with 1s and 2s compared to the other values that are below average, but at least rolling high values are better than rolling low values. Your math is also off for 2d4 and 2d6. You seem to be assuming a 75% chance of rolling a 3 or below when rolling 2d4 and a 50% chance of rolling 3 or below when rolling 2d6, but since you're rolling two dice you have two chances to trigger a reroll, for a (1 - 0.25^2) = 0.9375 chance of rolling a 3 or below with 2d4, and a (1 - 0.50^2) = 0.75 chance of rolling a 3 or below with 2d6. That makes the expected values of these rolls 2d4: 5 -> 7.34 (+2.34) 2d6: 7 -> 9.63 (+ 2.63) which makes 2d4 better than 1d10, and 2d6 even more better than 1d12 than it already is. [/QUOTE]
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