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General Tabletop Discussion
*Dungeons & Dragons
Analysis on attack odds and the influence of (some) game elements on said odds
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<blockquote data-quote="Aeloric1976" data-source="post: 7350878" data-attributes="member: 6939509"><p>My preliminary thoughts about your case are the following:</p><p></p><p>The chance of proning an opponent on an unarmed strike (UnStrAtk) equals the chance to get a hit plus the chance to get a crit (that is, the chance to get a non miss on an unarmed strike) (1-MissC/UnStrAtk) times the chance to get a prone (ProneC) on an unarmed strike. In abbreviated terms:</p><p></p><p>ProneC/UnStrAtk = (1-MissC/UnStrAtk) x ProneC</p><p></p><p>Say you score a non miss (hit or crit, it doesn't matter for the proning attempt) 50% of the time and a success on a proning attempt 50% of the time. You'll hit <strong>and</strong> prone your opponent 25% of the time.</p><p></p><p>If you have 2 UnStrAtks and a prone attempt on each hit. <strong>Only the first successful prone attempt matters.</strong> After you successfully prones an opponent you don't have to prone it again. To calculate the chance of getting at least one successful prone in two Unarmed Strikes you have to first calculate the chance of getting no prones in one UnStrAtk, wich is (1 - (ProneC/UnStrAtk)), and then the chance of getting no prones in 2 attack, wich is (1 - (ProneC/UnStrAtk))². Now you determine the chance of getting one prone by subtracting the previous result from 1, in other words, the chance of getting at least one successful prone is 100% minus the chance of getting no prones. In abbreviated terms:</p><p></p><p>1ProneC/2UnStrAtks = 1 - (1 - (ProneC/UnStrAtk))²</p><p></p><p>Knowing your overall chance of getting at least one prone, you must determine the chance of getting the prone either on the first attempt or on the second attempt. </p><p></p><p>On the first is already known: ProneC/UnStrAtk</p><p></p><p>On the second is what's left from (1ProneC/2UnStrAtks) - (ProneC/UnStrAtk)</p><p></p><p>Using the values that I used in the first example above (50% for a non miss and 50% success for a proning check), you get that 1ProneC/2UnStrkAtks = 1 - (1-25%)² = 1 - (75%)² = 1 - 56,25% = 43,75%</p><p></p><p>So, if in 43,75% of the times you get at least one prone, 56,25% you'll get just 2 UnStrAtk and 2 regular attacks (Unarmed or otherwise).</p><p></p><p>The chance of getting a prone on the first UnStrAtk is 25%</p><p></p><p>The chance of getting a prone on the second is 43,75% - 25% = 18,75%</p><p></p><p>My end results:</p><p></p><p>1) 56,25% you'll get just 2 UnStrAtks with no prones and 2 regular attacks (Unarmed or otherwise) (calculate dpr normally for all attack with no Comb Adv)</p><p></p><p>2) 25% of the time you'll get a prone on the first UnStrAtk and 3 attacks with Combat Advantage (1 Unarmed and 2 Unarmed or not) (apply Comb Adv on the last 3 attacks)</p><p></p><p>3) 18,75% of the time you'll get a prone on the second attempt and 2 attacks with Combat Advantage (2 Unarmed or not) (apply Combat Advantage on the last 2 attacks)</p><p></p><p>I think it is correct, please revise my findings and we can correct any mistakes.</p></blockquote><p></p>
[QUOTE="Aeloric1976, post: 7350878, member: 6939509"] My preliminary thoughts about your case are the following: The chance of proning an opponent on an unarmed strike (UnStrAtk) equals the chance to get a hit plus the chance to get a crit (that is, the chance to get a non miss on an unarmed strike) (1-MissC/UnStrAtk) times the chance to get a prone (ProneC) on an unarmed strike. In abbreviated terms: ProneC/UnStrAtk = (1-MissC/UnStrAtk) x ProneC Say you score a non miss (hit or crit, it doesn't matter for the proning attempt) 50% of the time and a success on a proning attempt 50% of the time. You'll hit [B]and[/B] prone your opponent 25% of the time. If you have 2 UnStrAtks and a prone attempt on each hit. [B]Only the first successful prone attempt matters.[/B] After you successfully prones an opponent you don't have to prone it again. To calculate the chance of getting at least one successful prone in two Unarmed Strikes you have to first calculate the chance of getting no prones in one UnStrAtk, wich is (1 - (ProneC/UnStrAtk)), and then the chance of getting no prones in 2 attack, wich is (1 - (ProneC/UnStrAtk))². Now you determine the chance of getting one prone by subtracting the previous result from 1, in other words, the chance of getting at least one successful prone is 100% minus the chance of getting no prones. In abbreviated terms: 1ProneC/2UnStrAtks = 1 - (1 - (ProneC/UnStrAtk))² Knowing your overall chance of getting at least one prone, you must determine the chance of getting the prone either on the first attempt or on the second attempt. On the first is already known: ProneC/UnStrAtk On the second is what's left from (1ProneC/2UnStrAtks) - (ProneC/UnStrAtk) Using the values that I used in the first example above (50% for a non miss and 50% success for a proning check), you get that 1ProneC/2UnStrkAtks = 1 - (1-25%)² = 1 - (75%)² = 1 - 56,25% = 43,75% So, if in 43,75% of the times you get at least one prone, 56,25% you'll get just 2 UnStrAtk and 2 regular attacks (Unarmed or otherwise). The chance of getting a prone on the first UnStrAtk is 25% The chance of getting a prone on the second is 43,75% - 25% = 18,75% My end results: 1) 56,25% you'll get just 2 UnStrAtks with no prones and 2 regular attacks (Unarmed or otherwise) (calculate dpr normally for all attack with no Comb Adv) 2) 25% of the time you'll get a prone on the first UnStrAtk and 3 attacks with Combat Advantage (1 Unarmed and 2 Unarmed or not) (apply Comb Adv on the last 3 attacks) 3) 18,75% of the time you'll get a prone on the second attempt and 2 attacks with Combat Advantage (2 Unarmed or not) (apply Combat Advantage on the last 2 attacks) I think it is correct, please revise my findings and we can correct any mistakes. [/QUOTE]
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