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[3.5] Tumble
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<blockquote data-quote="iwatt" data-source="post: 1023423" data-attributes="member: 11085"><p>In this <a href="http://enworld.cyberstreet.com/showthread.php?s=&threadid=57073" target="_blank">thread</a> there was some discussion going about the pros and cons of using multiple rolls (as per the new rules) or using a single roll to determine success. </p><p></p><p>The general consensus was that a single roll was better than using multiple rolls (mathematically speaking). This comment had me troubled, until I realized that we were only taking into acount the case in which al AoO were avoided. In this case the multiple rolls will always provide a far smaller chance to avoid all AoO. Let's illustrate this with an example: tumbler with +10 to his check, trying to tumble PAST 4 opponents. Tumbling each opponent past the first rises the tumble DC by +2 </p><p></p><p>Tumble +10</p><p></p><p>One Roll: +10 v/s DC 21-----> 50% of no AoO</p><p>4 Rolls: +10 vs DC 15/17/19/21----> 0.8*0.7*0.6*0.5=16.8%</p><p></p><p>Clearly in this case it's quite harder fort the tumbler to avoid ALL AoO.</p><p></p><p>Let's take the case of a far superior tumbler (+17)</p><p>One Roll: +17 v/s DC 21-----> 85% of no AoO</p><p>4 Rolls: +10 vs DC 15/17/19/21---->1*1*0.95*0.85=80.75%</p><p></p><p>In this case, the single roll is till superior, but not excesively so.</p><p></p><p>But remeber, we are basing our decision of "better" on the success chance on not causing any AoO. I believe the question is wether avoiding all but one or all but two is a better indicator. Therefore, I've analyzed the above example (tumbling past 4 opponents, for the following tumble modifiers: +5/+10/+15. </p><p></p><p>+5</p><p>#AoO___One Roll___4 Rolls</p><p>__0______25%_____2.2%</p><p>__1______75%_____14.9%</p><p>__2______65%_____35.7%</p><p>__3______55%_____35,1%</p><p>__4______45%_____12.1%</p><p></p><p></p><p>+10</p><p>#AoO___One Roll___4 Rolls</p><p>__0______50%_____16.8%</p><p>__1______50%_____39.4%</p><p>__2______40%_____32.0%</p><p>__3______30%_____10.6%</p><p>__4______20%_____1.2%</p><p></p><p>+15</p><p>#AoO___One Roll___4 Rolls</p><p>__0______75%_____60.6%</p><p>__1______25%_____34.1%</p><p>__2______15%_____5.2%</p><p>__3_______5%_____0.2%</p><p>__4_______0%_____0%</p><p></p><p>Now if your decision is to avoid at least half of the AoOs, using multiple rolls is a lot better in all cases. </p><p></p><p>In any case, I'm partial towards a single roll (less time consuming), and this at least makes me feel both options are slightly more balanced. A single roll makes it more likely to avoid all AoO, but does add risk (one bad roll and you're up shi.. creek). Multiple rolls diminih your chance of avoiding all AoO, but also diminishes the chances of getting beat up by every single dude you're trying to avoid.</p></blockquote><p></p>
[QUOTE="iwatt, post: 1023423, member: 11085"] In this [URL=http://enworld.cyberstreet.com/showthread.php?s=&threadid=57073]thread[/URL] there was some discussion going about the pros and cons of using multiple rolls (as per the new rules) or using a single roll to determine success. The general consensus was that a single roll was better than using multiple rolls (mathematically speaking). This comment had me troubled, until I realized that we were only taking into acount the case in which al AoO were avoided. In this case the multiple rolls will always provide a far smaller chance to avoid all AoO. Let's illustrate this with an example: tumbler with +10 to his check, trying to tumble PAST 4 opponents. Tumbling each opponent past the first rises the tumble DC by +2 Tumble +10 One Roll: +10 v/s DC 21-----> 50% of no AoO 4 Rolls: +10 vs DC 15/17/19/21----> 0.8*0.7*0.6*0.5=16.8% Clearly in this case it's quite harder fort the tumbler to avoid ALL AoO. Let's take the case of a far superior tumbler (+17) One Roll: +17 v/s DC 21-----> 85% of no AoO 4 Rolls: +10 vs DC 15/17/19/21---->1*1*0.95*0.85=80.75% In this case, the single roll is till superior, but not excesively so. But remeber, we are basing our decision of "better" on the success chance on not causing any AoO. I believe the question is wether avoiding all but one or all but two is a better indicator. Therefore, I've analyzed the above example (tumbling past 4 opponents, for the following tumble modifiers: +5/+10/+15. +5 #AoO___One Roll___4 Rolls __0______25%_____2.2% __1______75%_____14.9% __2______65%_____35.7% __3______55%_____35,1% __4______45%_____12.1% +10 #AoO___One Roll___4 Rolls __0______50%_____16.8% __1______50%_____39.4% __2______40%_____32.0% __3______30%_____10.6% __4______20%_____1.2% +15 #AoO___One Roll___4 Rolls __0______75%_____60.6% __1______25%_____34.1% __2______15%_____5.2% __3_______5%_____0.2% __4_______0%_____0% Now if your decision is to avoid at least half of the AoOs, using multiple rolls is a lot better in all cases. In any case, I'm partial towards a single roll (less time consuming), and this at least makes me feel both options are slightly more balanced. A single roll makes it more likely to avoid all AoO, but does add risk (one bad roll and you're up shi.. creek). Multiple rolls diminih your chance of avoiding all AoO, but also diminishes the chances of getting beat up by every single dude you're trying to avoid. [/QUOTE]
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