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[Math] Is the Great Scimitar balanced?
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<blockquote data-quote="Mike Sullivan" data-source="post: 994420" data-attributes="member: 9824"><p>The percentage of hits which are critical hits is always equal to the (effective) crit range of the weapon, divided by 20. So, if you have a weapon which threatens crits only on a 20, 5% of its hits will be critical hits. One that threatens on a 19-20, 10%, 18-20, 15%, etc.</p><p></p><p>Note that that's <em>effective</em> threshhold. If your threshhold is 12-20, and you hit on a 16+, then for that hit, your effective threshhold is 16-20 (25%), not 12-20 (45%).</p><p></p><p>Basically, the reason for that is that to determine whether or not you make a critical hit, you roll two dice. If one is a hit, and the other is in the critical threshold, then you've done a critical hit. Thus, it follows that your odds of making a critical hit with each attack are (your odds of rolling a hit on a d20) * (your odds of rolling into your critical threshold on a d20). Since all of your critical hits are also normal hits, and your odds of hitting at all = (your odds of rolling a hit on a d20), then it follows that (your odds of rolling into your critical threshold on a d20) is the percentage of your hits which are critical hits.</p></blockquote><p></p>
[QUOTE="Mike Sullivan, post: 994420, member: 9824"] The percentage of hits which are critical hits is always equal to the (effective) crit range of the weapon, divided by 20. So, if you have a weapon which threatens crits only on a 20, 5% of its hits will be critical hits. One that threatens on a 19-20, 10%, 18-20, 15%, etc. Note that that's [i]effective[/i] threshhold. If your threshhold is 12-20, and you hit on a 16+, then for that hit, your effective threshhold is 16-20 (25%), not 12-20 (45%). Basically, the reason for that is that to determine whether or not you make a critical hit, you roll two dice. If one is a hit, and the other is in the critical threshold, then you've done a critical hit. Thus, it follows that your odds of making a critical hit with each attack are (your odds of rolling a hit on a d20) * (your odds of rolling into your critical threshold on a d20). Since all of your critical hits are also normal hits, and your odds of hitting at all = (your odds of rolling a hit on a d20), then it follows that (your odds of rolling into your critical threshold on a d20) is the percentage of your hits which are critical hits. [/QUOTE]
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[Math] Is the Great Scimitar balanced?
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