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Inspiration & Hero Points Math
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<blockquote data-quote="guachi" data-source="post: 7422667" data-attributes="member: 6785802"><p>As to the d6, it's a bit like Precision on the Battlemaster (just with a d6 instead of a d8).</p><p></p><p>Let's assume you actually do know exactly how much you failed by. Let's assume you have infinite uses of Inspiration so you'll use it whenever you fail by six or less. Let's further assume that you can actually fail a roll by up to six (I mean, it's possible there are rolls where a four will succeed and, therefore, can't fail by any more than three but that makes math messy so we'll skip it).</p><p></p><p>You'll end up with 1 of 20 rolls failed by each of 1, 2, 3, 4, 5, and 6. The chance of succeeding after rolling a d6 if you fail by...</p><p>1: 100% (6/6)</p><p>2: 83.3% (5/6)</p><p>3: 66.7% (4/6)</p><p>4: 50.0% (3/6)</p><p>5: 33.3% (2/6)</p><p>6: 16.7% (1/6)</p><p></p><p>The net result is that with an infinite supply of Inspiration you always use on a roll failed by 1 to 6 your total chance of success increases by 17.5%. (I've skipped a math step here).</p><p></p><p>Let's use our previous example of succeeding 50% of the time (needing an 11+ to succeed). Under the "roll another d20" example you use your Inspiration 50% of the time and your total success rate increases from 50% to 75%. Under the "add a d6" example you use your Inspiration 30% of the time (6/20. You'd never use the die if you succeeded or if you failed by 7+) and increase your success rate from 50% to 67.5%.</p><p></p><p>Let's use our previous example of succeeding 5% of the time (needing a 20 to succeed). Under the "roll another d20" example you use your Inspiration 95% of the time (19/20) and your total success rate increases from 5% to 9.75%. Under the "add a d6" example you use your Inspiration 30% of the time and increase your success rate from 5% to 22.5%.</p><p></p><p>As you can see, the <em>change</em> to your success rate and the use rate of Inspiration<em> varies wildly</em> rolling another d20 but is<em> constant </em>using a d6.</p></blockquote><p></p>
[QUOTE="guachi, post: 7422667, member: 6785802"] As to the d6, it's a bit like Precision on the Battlemaster (just with a d6 instead of a d8). Let's assume you actually do know exactly how much you failed by. Let's assume you have infinite uses of Inspiration so you'll use it whenever you fail by six or less. Let's further assume that you can actually fail a roll by up to six (I mean, it's possible there are rolls where a four will succeed and, therefore, can't fail by any more than three but that makes math messy so we'll skip it). You'll end up with 1 of 20 rolls failed by each of 1, 2, 3, 4, 5, and 6. The chance of succeeding after rolling a d6 if you fail by... 1: 100% (6/6) 2: 83.3% (5/6) 3: 66.7% (4/6) 4: 50.0% (3/6) 5: 33.3% (2/6) 6: 16.7% (1/6) The net result is that with an infinite supply of Inspiration you always use on a roll failed by 1 to 6 your total chance of success increases by 17.5%. (I've skipped a math step here). Let's use our previous example of succeeding 50% of the time (needing an 11+ to succeed). Under the "roll another d20" example you use your Inspiration 50% of the time and your total success rate increases from 50% to 75%. Under the "add a d6" example you use your Inspiration 30% of the time (6/20. You'd never use the die if you succeeded or if you failed by 7+) and increase your success rate from 50% to 67.5%. Let's use our previous example of succeeding 5% of the time (needing a 20 to succeed). Under the "roll another d20" example you use your Inspiration 95% of the time (19/20) and your total success rate increases from 5% to 9.75%. Under the "add a d6" example you use your Inspiration 30% of the time and increase your success rate from 5% to 22.5%. As you can see, the [I]change[/I] to your success rate and the use rate of Inspiration[I] varies wildly[/I] rolling another d20 but is[I] constant [/I]using a d6. [/QUOTE]
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