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). 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
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings? Moving to General Math
The only thing that I can add is that my 14.44% result is not holding up under further investigation. What I did to try and confirm the 14.44% was create a simple computer program to simulate rolling a d20 10,000,000 times and have found that Exploit Weakness is on average about a 10.9% increase. My current thoughts are that something is wrong with the statement bellow. I think I'm taking something to be an independent event when its not?