Enhancing and enchanting, or: Statistics and you

[BuzzardJoe]

I just had the good fortune to craft 15 +4 gilgamesh robes, so I thought I would try out enhancing. My previous crafting had created a single +4, so I had a total of 16 of them. My enhancing pattern went:

+4 -> +5  =  6/16
+5 -> +6  =  3/6
+6 -> +7  =  3/3
+7 -> +8  =  0/2  (stopped before losing all.)

Not the results I was hoping for. So, now I am curious about the mathematics. Given the debate over the true enhancing success rate, I calculated the binomial probability rates using both 50% and 55% success rates.

     0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
50%  0  0  0  1  3  7 12 17 20 17 12  7  3  1  0  0  0
55%  0  0  0  0  1  3  8 13 18 20 17 11  6  2  1  0  0

     0  1  2  3  4  5  6
50%  2  9 23 31 23  9  2
55%  1  6 19 30 28 14  3

     0  1  2  3
50% 13 38 38 13
55%  9 33 41 17

     0  1  2
50% 25 50 25
55% 20 50 30

Getting exactly 6/16 was a 8-12% chance.
Getting exactly 3/6 was a 30-31% chance.
Getting exactly 3/3 was a 13-17% chance.
Getting exactly 0/2 was a 20-25% chance.

Nothing stands out as being unusual. I modified my previously posted calculator to include a column showing the probability for enhancing a set of items. Using the new calculator, I found the probabilities of enhancing at least one item to the various grades...

      enchant  enhance
     50%  55%
 +5 100% 100%   100%
 +6  99% 100%   100%
 +7  88%  95%   100%
 +8  64%  78%   100%
 +9  40%  56%     0%
+10  22%  36%     0%

Since those are cumulative numbers, I found the probabilities of each individual grade...

      enhance  enchant
     50%  55%
 +5   1%   0%     0%
 +6  11%   5%     0%
 +7  24%  17%     0%
 +8  24%  22%   100%
 +9  18%  20%     0%
+10  22%  36%     0%

I want to compare enhancing to enchanting, so I revise the table one last time...

      enhance  enchant
     50%  55%
<+8  36%  22%     0%
 +8  24%  22%   100%
>+8  40%  56%     0%

I had a 22-24% chance of getting the same result, a 22-36% chance of doing worse, and a 40-56% chance of doing better. I had the misfortune to land in the “worse” bucket.

I can also more clearly see the affect of having just a 5% higher enhancement probability. The 50% odds show an even chance of doing better or worse. The 55% odds show more than twice as likely to do better than worse. It is unfortunate that we don't have any good data as to what the actual number is.

How did this scenario work out for me financially?

costs:
            Enhancement Enchantment
+4 robes            16          16
Stones             153          86
gold/stone      11,000      65,000
total        1,683,000   5,590,000

results:
            Enhancement Enchantment
              +7 robe     +8 robe

I saved 3,907,000 gold on stones, but gave up a guaranteed +8 robe for a +7, which is a loss of about 60,000,00 at current market on Argos.

This entire analysis was interesting to me. The previous one focused on the cost/reward comparison before I obtained/crafted the items. This one started because I already had a set of items and needed to know what to do with them. Until better data becomes available on the actual enhancement probability value, I will not be enhancing again. At the low end of the 50-55% range, there is no average difference between enhancing and enchanting. At the high end, the chance of doing better than enchanting is good, but there was still a 22% chance of doing worse in my scenario.

My revised calculator is attached. I welcome your feedback on both the calculator and the math I used here.

[NeoZiKa]

nice guide ...thnx alot

[esgaroth]

Had some time to kill earlier, made a program to calculate enchanting and enhancing with a dynamic success rate on enhance(i.e you can set it yourself and default is 50). Might be some exception bugs there, havent tested alot but it should work fine aslong as you put numbers and not !#%!&!#¤& in the textboxes. Let me know if you miss something in the program, might add things if I have more time to kill! Enjoy.


http://hem.bredband.net/anderashaggl...icaEnchSim.rar

[poipoi]

Hi all! Just started playing Atlantica.
I've read the entire thread and all I can is it's nicely done.

I have a question though and no one mentioned it here. Since it's part of enchanting/enhancing, how much difference does a +0 to +1 to +2...and so on mean? Is it that big and a must to do? For weapons, how much damage does it improve?

Thanks y'all. Sorry for a noob question.

[Cheesecake]

Originally Posted by poipoi

Hi all! Just started playing Atlantica.
I've read the entire thread and all I can is it's nicely done.

I have a question though and no one mentioned it here. Since it's part of enchanting/enhancing, how much difference does a +0 to +1 to +2...and so on mean? Is it that big and a must to do? For weapons, how much damage does it improve?

Thanks y'all. Sorry for a noob question.

For all equipment, from +0 to +4 or so, each + adds about 20% to the equipments power (stats, defence, atk, all that stuff), from +5 to +6, each + is about 30%, from +7 to +10, each + adds 40%. This ends up with a +10 being 4x stronger then a +0 weapon. In the early lvls, no enchanting weapon is not neccesary, but it speeds things up a bit. Later on though, you will want to start enhancing(70+), once you get late game(95+), its basically a neccessity to have enchanted equipment thats updated.

[poipoi]

Originally Posted by Cheesecake

For all equipment, from +0 to +4 or so, each + adds about 20% to the equipments power (stats, defence, atk, all that stuff), from +5 to +6, each + is about 30%, from +7 to +10, each + adds 40%. This ends up with a +10 being 4x stronger then a +0 weapon. In the early lvls, no enchanting weapon is not neccesary, but it speeds things up a bit. Later on though, you will want to start enhancing(70+), once you get late game(95+), its basically a neccessity to have enchanted equipment thats updated.

Wow 20% that's huge!
I also read somewhere that using Sea King, Ocean and Red Soul to +3 will make it useful til 35. Am I on the right track?

Thanks man for the quick response!

[Cheesecake]

Originally Posted by poipoi

Wow 20% that's huge!
I also read somewhere that using Sea King, Ocean and Red Soul to +3 will make it useful til 35. Am I on the right track?

Thanks man for the quick response!

Thats fine, nothing wrong with being a bit under/over geared in the early levels. It doesn't affect you too much. My first char, i was VERY undergeared and still made it to 97 before starting over and making a new char :P. Just an example..on my first GunM....my viking was using a +5 lvl 35 top at lvl 89, main was 97.

[Habile]

Very, very new to the game, but enchanting has been one of the more enjoyable parts for me so far.

Not sure if you're still around, but your formula for enhancement is a little wonky. I'm not too familiar with probability and statistics myself, so if someone else could correct me where I'm wrong.

You're essentially using the same formula for enhancing that you're using for enchanting, in that 1 in every 1.818181 WILL be successful, just as 1 in every 2 will be successful for enchanting (100% success, 2 items used).

Instead, 1-(0.55)^10 will get you a 99.7467% chance to fail in getting to +10 at some point in the enhancing process.

The 395 items that you're assuming will get a +10 only get you to that 63.28% of the time:
1-(0.997467)^395 = 0.632777

However, we can use logs to find a better approximation of items required. For instance, to find the number of items required for +10 from +0 at a 95% success rate, we can use the following formula:
log[1-0.95] / log[0.997467] = 1181.21 items.

Or at 99.99% success rate:
log[1-0.9999] / log[0.997467] = 3631.6 items.

------

Now for the average number of enhance stones necessary. Obviously, failing at +1 every time except the last will use far fewer stones than always failing at +10.

So, the chance to fail at +1 enhancement is 45%. The chance to fail at +2 is ALSO 45%. However, because it requires not failing at +1, +2 actually has less of an impact on stones used. In other words (or numbers), 0.45*0.55 = 24.75% of your failures will be at +2 enhancement. 0.45*0.55^2 = 13.61% of your failures will be at +3.

To calculate how many stones used per failed item, we can use a summation:
SUM[0.45*0.55^x, in terms of x from 0 to 9] = 2.19126 stones per item.

So, back to our previous numbers of items used:
95% success rate with 1181.21 items = 2588.33 enhance stones.
99.99% success rate with 3631.6 items = 7957.8 enhance stones.

50% success rate with 273 items = 598.884 enhance stones.

Aaand finally:
63.28% success rate with 395 items = 865.549 enhance stones.


Again, correct me if I'm mistaken anywhere.