Lord_Kami_Sama - Profile

By far the best AI personality I've seen so far. I like how she also has her job to do and isn't just a backseat critic.

Now to go into some detail. the average stats per crystal is 1,35 (a number I'll use a lot). you get this number from 1 Stat * 70% + 2 Stats * 25% + 3 Stats * 5% = 0,7 Stats + 0,5 Stats + 0,15 Stats = 1,35 You can do the same thing with 1 stat point invested in 2 Stats bringing that to 50% and then you get an average of 1,57. You get an additional 0,217 by investing 1 fate point. If you repeat the process for investing 2 points you get 1,78 and for 3 points you get 2 (100% chance of getting 2 stats). 1,78 is 1,57 + 0,217 and 2 is 1,78 + 0,217 so the pattern of getting 0,217 is repeated and there is no ideal amount you should invest. This is also true for investing in the 3 Stats category but you get only 0,087 stats per invested point with the averages being : 1,35, 1,44, 1,52, 1,61, ... , 2,91 and 3. The only advantage in the 3 stat cat is that you can invest much more fate points into it but you would need to invest at least 8 points to take that into account (8 points invested gives you 2,04 on average which is more that the 2 you get from investing 3 points into 2 Stats). When investing into Drop Rates you first take into account what the average stats per crystal is (1,35). Then you can calculate the average stats you get per goblin without investing fate points. 1,35 Stats * 20% = 0,27. when you invest 1 fate point the chance doubles so 1,35 Stats * 40% = 0,54 and you gain 0,27 stats for every fate point invested with a maximum of 4 fate points you can invest. This is better than investing into 2 stats per crystal both in gains and in maximum investment. and when the Drop rate goes up the gains increase even more (but maximum investment drops at 50% drop rate you can only invest 1 fate point). The gains for a specific drop rate can be calculated as : Drop Rate * 1,35. For 20% this is 0,27 ,for 30 % it's 0,405 for 40% it's 0,54 and for 50% it's 0,675. Above 50% things change since the chance of an event can't go above 100%. at 60% investing a fate point increases chances by 40% and therefore has the same gains as investing into a drop rate of 40%, 70% is the same as 30%, etc. changing the formula into Drop Rate = Avg Stats / 1,35 can calculate d-you the drop rate where investing into 2 Stats is better. 0,2167 / 1,35 = 16,05% (0,2167 is the Stats per fate point in 2 Stats per crystal). Some interesting combinations when hunting goblins with 20% Drop Rate: 1 point invested into 2 Stats per Crystal and 1 point into Drop Rate costs 1,4 per goblin and gives you 0,628 Stats per goblin or 0,256 stats per fate point. 2 points invested into 2 Stats per Crystal and 2 points into Drop Rate costs 3,2 per goblin and gives you 1,068 Stats per goblin or 0,249 stats per fate point. 3 points invested into 2 Stats per Crystal and 4 points into Drop Rate costs 7 per goblin and gives you 2 Stats per goblin or 0,247 stats per fate point. For the ideal drop rate of 50% it would be: 3 points invested into 2 Stats per Crystal and 1 points into Drop Rate costs 4 per goblin and gives you 2 Stats per goblin or 0,5 stats per fate point.

I enjoyed the book so I decided to do some math. The first time I wrote this comment it was far to long so I'll put the details in a reply. Every point invested in the 2 Stats per Crystal Category gives you 0,217 stats on average while every point in 3 Stats gives you 0,087 stats. Thus investing in 2 Stats per crystal is better. Since the drop rate of Goblins is 20% every point invested in the crystal being dropped gives you 0,27 stats. This is higher that the 0,217 in the 2 Stats category gives you and this will be higher as long as the monsters drop rates are between 16,05% and 83,95% with the peak being 50% drop rate and getting 0,675 stats per fate point.

I enjoyed the book so I began to do some math. Any Crystal has 70% chance of 1 stat, 25% chance of 2 stats and 5% of 3 stats. So the average is 1,35. When you invest 1 point in the 2 stats category the average goes up to 1,57, with 2 points it is 1,78 and with 3 points it's 2,0. This means you get 0,217 stats per fate point and it doesn't matter how many you invest. When you decide to invest points in the 3 stats category you only gain 0,087 stats for every fate point. The averages are : 1,35, 1,44, 1,52, 1,61, ..., 2,91, 3. But should you invest in gaining crystals or getting stats from crystals? When he was hunting goblins the stat crystal drop rate was 20% (although I don't know if you can get multiple crystals like the snobby kid). This drop rate and an average stats per crystal of 1,35 means you get 0,27 stats per goblin normally. when you invest a fate point the drop rate goes to 40% and the avg stats go to 0,54. This gets you 0,27 stats per fate point (more than the 0,217 of the 2 Stat cat). However not every creature gives you the same drop rate, so when is the critical point? The formula of calculating the Stats per point for a specific drop rate is : Drop rate * 1,35 The formula of calculating the drop rate that has x stats per points is : Stats per point / 1,35 So a monster with 16,05% drop rate (=0,2167/1,35) gives the same stats per point as the points invested in the 2 Stats category. Quick other numbers if you combine monster drop rates and stat chances: 1 point invested in 2 Stats and 1 point in goblin drop rate costs 1,4 points per goblin, gives 0,628 stats per goblin and 0,256 stats per point 2 points invested in 2 Stats and 2 points in goblin drop rate costs 3,2 points per goblin, gives 1,068 stats per goblin and 0,249 stats per point 3 points invested in 2 Stats and 4 points in goblin drop rate costs 7 points per goblin, gives 2 stats per goblin and 0,247 stats per point