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Inspiration & Hero Points Math
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<blockquote data-quote="guachi" data-source="post: 7422652" data-attributes="member: 6785802"><p>Simple example:</p><p></p><p>You succeed on the task 50% of the time. There are four possible outcomes, each of which has the same chance of occurring.</p><p></p><p>Succeed/Succeed</p><p>Succeed/Fail</p><p>Fail/Succeed</p><p>Fail/Fail</p><p></p><p>If you must use Inspiration beforehand, it is useful 1 of 4 times used. That being the case where you Fail/Succeed.</p><p></p><p>If you use Inspiration only after you Fail then you will only use it in the last two instances. In this event, your Inspiration is useful 1 of 2 times it's used.</p><p></p><p>You'll use Inspiration 1/2 as often but it will be 2x as useful.</p><p></p><p>An extreme example where you must have a 20 to succeed. The possible outcomes are still </p><p></p><p>Succeed/Succeed</p><p>Succeed/Fail</p><p>Fail/Succeed</p><p>Fail/Fail</p><p></p><p>However, the chances of each occurring are not the same. The chances of each of the four possibilities occurring are</p><p></p><p>1/20 x 1/20 = 1/400</p><p>1/20 x 19/20 = 19/400</p><p>19/20 x 1/20 = 19/400</p><p>19/20 x 19/20 = 361/400</p><p></p><p>You will use your Inspiration 19/20 times as that's how often you'll fail but it will only benefit you 1/20 times. The net result is that you'll use the die a lot but benefit little, 4.75% of the time.</p><p></p><p>Choosing to use Inspiration after the first die is thrown will always be better than choosing beforehand. "Better" in the sense that you'll never waste a die on an already successful roll rather than "better" in the sense of having a higher chance to succeed on that particular attempt. Overall you'll have a higher success rate as you get to save dice for later.</p></blockquote><p></p>
[QUOTE="guachi, post: 7422652, member: 6785802"] Simple example: You succeed on the task 50% of the time. There are four possible outcomes, each of which has the same chance of occurring. Succeed/Succeed Succeed/Fail Fail/Succeed Fail/Fail If you must use Inspiration beforehand, it is useful 1 of 4 times used. That being the case where you Fail/Succeed. If you use Inspiration only after you Fail then you will only use it in the last two instances. In this event, your Inspiration is useful 1 of 2 times it's used. You'll use Inspiration 1/2 as often but it will be 2x as useful. An extreme example where you must have a 20 to succeed. The possible outcomes are still Succeed/Succeed Succeed/Fail Fail/Succeed Fail/Fail However, the chances of each occurring are not the same. The chances of each of the four possibilities occurring are 1/20 x 1/20 = 1/400 1/20 x 19/20 = 19/400 19/20 x 1/20 = 19/400 19/20 x 19/20 = 361/400 You will use your Inspiration 19/20 times as that's how often you'll fail but it will only benefit you 1/20 times. The net result is that you'll use the die a lot but benefit little, 4.75% of the time. Choosing to use Inspiration after the first die is thrown will always be better than choosing beforehand. "Better" in the sense that you'll never waste a die on an already successful roll rather than "better" in the sense of having a higher chance to succeed on that particular attempt. Overall you'll have a higher success rate as you get to save dice for later. [/QUOTE]
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