Hi I play a video game (DDO to be specific). In this game I can chose one of 2 options the first (Keen Edge) increases my Critical hit rate by 10% permanently, the second option (Exploit Weakness) increases my critical hit rate by 10% each time I do not make a critical hit (e.g. Attack 1 crits so attack 2 has +0% crit chance, attack 1 and 2 do not crit so attack 3 has +20% chance to crit).(adsbygoogle = window.adsbygoogle || []).push({});

Which option is better and if the second one (Exploit Weakness) by how much?

The game being based on Dungeons and Dragons uses a d20 model for a lot of its probability. So my base Crit range is 15-20 (30%) which leaves 1-14 as a chance to not crit (70%).

My attempt at answering this question was to do the following

How many 13-14 would be critical hits if I take Exploit Weakness. Since a 13 or 14 can only be crits if the previous hit did not crit that means that 70% of 13 and 14 are crits. Further since 10% of my attacks will be rolls of 13 or 14 I have raised my critical hit rate by 7%

So now how many 11-12 will be critical hits. An 11-12 can only be a crit if the previous 2 hit were not crits. The first attack has a 70% chance to not be a crit and the second chance has a 60% chance to not be a crit so = .7*.6 = .42 so 42% of 11 and 12's will be crits for an additional 4.2% to total crit chance.

This train of thought leads to

09-10: 0.7*0.6*0.5 = 0.21 or 21% which is +2.1% critical hits

07-08: 0.7*0.6*0.5*0.4 = 0.084 or 8.4% which is +0.84% critical hits

05-06: 0.7*0.6*0.5*0.4*0.3 = 0.0252 or 2.52% which is +0.21% critical hits

03-04: 0.7*0.6*0.5*0.4*0.3*0.2 = 0.00504 or 0.5% which is +0.0504% critical hits

02: 0.7*0.6*0.5*0.4*0.3*0.2*0.1 = 0.000504/2 or 0.0252% which is +0.00252% critical hits

01: 0 because a 1 is always, and for this example the only time you, miss.

Sum it all up and you get ~14.44% increase to critical hits taking the second option (Exploit Weakness) which is a 4.44% gain over the other option.

Does my logic hold up?

Thank You

--Joe

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# Video Game Math Problem Help?

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