Why the refine anvils weren't worth the money.
This post may get a little mathheavy. Bear with me, those of you averse to numbers.
Last patch, Ntreev introduced the refine anvils. The Anvils worked like this:
I'm going to take a look at different refines, and see if the anvils really help your refining that much.
In other words, are they worth the money?
Let's assume I'm refining an Ult. Wooden Rod (level 65 equip), which I'll assume falls under the "Craftsman/Teacher" type category. Taking the higher (blue) numbers, we have:
99/81/62/46/33/25/17/12/9% chance of success refining levels 1  > 9.
At level 1, it's obviously a useless proposition to use 1 anvil of either type, as you're wasting 4% or 9% of the increase in probability.
So a few rules:
We're assuming that for each level of refine, you want to get your item to the next level no matter what the cost.
Thus, you have an infinite supply of refine powders.
Refine Powders  2700/5 or 540/powder.
For our example, we have:
Probability r = refine probability, a = additional cost of refining after a break.
a = refine powder + anvil cost for repair/rerefine.
r = refine success probability
102,400 points on average for your level 9 item.
138,300 points per level 9 item.(without anvils :102,400 points on average for your level 9 item). You're saving approximately 36k to not use craftsman's anvils and just use refine powders instead.
p + .1
Average MyShop Cost of Refining an item to level 9:
It costs on average nearly twice as much MyShop to refine an item using anvils. Refining with anvils at lower levels of refine is even more expensive.
The anvils need to be buffed. The price of the anvils needs to be decreased, the refine % increased, or both.
Last patch, Ntreev introduced the refine anvils. The Anvils worked like this:
 When refining from N>N+1, N+1 anvils are required to increase the refine rate. In other words, you need 2 anvils to refine to level 2, and 9 anvils to refine to level 9.
 Anvils can only be used on refines up to level 9.
 Anvils can't be stacked  a 5% or a 10% increase is the maximum allowed for a single refine.
 +5% success rate to refine.
 Cost: 2k for a pack of 5, or 400 points/anvil.
 +10% success rate to refine.
 Cost: 2.5k for a pack of 3, or 833.3 points/anvil. I'll round this down to 800 for simplicity.
Spoiler!
I'm going to take a look at different refines, and see if the anvils really help your refining that much.
In other words, are they worth the money?
Let's assume I'm refining an Ult. Wooden Rod (level 65 equip), which I'll assume falls under the "Craftsman/Teacher" type category. Taking the higher (blue) numbers, we have:
99/81/62/46/33/25/17/12/9% chance of success refining levels 1  > 9.
At level 1, it's obviously a useless proposition to use 1 anvil of either type, as you're wasting 4% or 9% of the increase in probability.
So a few rules:
We're assuming that for each level of refine, you want to get your item to the next level no matter what the cost.
Thus, you have an infinite supply of refine powders.
Refine Powders  2700/5 or 540/powder.
Let's find out what the average cost of refining an item to the next level is!
Quote:
Originally Posted by Adapted from Wikipedia
Note: the average cost of refining an item continually to the next level is rather like a geometric series from math....
The nth term in the series is ar^n (in other words how much additionally it costs to refine after the nth break), and the convergence of the series is a/(1r) [in other words, how much it costs on average to refine to the next level].
The nth term in the series is ar^n (in other words how much additionally it costs to refine after the nth break), and the convergence of the series is a/(1r) [in other words, how much it costs on average to refine to the next level].
Probability r = refine probability, a = additional cost of refining after a break.
0 breaks: Anvil cost.From this, I derived the following expression for the Average Cost to refine an item to the next level (in MyShop points):
1 break: 0 breaks + refine powder + anvil cost
2 breaks: 1 break + refine powder + anvil cost
a = refine powder + anvil cost for repair/rerefine.
r = refine success probability
Average Cost of refining to a level = a/(p)  refine powder cost.The last term comes from the fact that if you succeed on the first refine, you don't need to pay refine powders.
Refining an item without Anvils:
Thus, if you're refining an item with just refine powders, you are paying (on average) per refine:Thus to refine an item to level 9,on average you'd be spending 43680+27720+... orSpoiler!
102,400 points on average for your level 9 item.
Craftsman's Anvils + Refine Powders:
With a craftsman's anvil we have the same deal, but p = p + .05 for all probabilities and now we have an anvil cost to account for (400/anvil)Note:Spoiler!
 It costs more at EVERY LEVEL to refine with anvils than without.
 The amount of increased cost is the greatest at level 2 and the least at level 9.
138,300 points per level 9 item.(without anvils :102,400 points on average for your level 9 item). You're saving approximately 36k to not use craftsman's anvils and just use refine powders instead.
Anvil of Generations
cost per anvil is now 800.p + .1
Spoiler!
Average MyShop Cost of Refining an item to level 9:
With Anvils of Generation:CONCLUSION:
171,757 myshop.
With Craftsman's Anvils:
138,300
Without either:
102,400
It costs on average nearly twice as much MyShop to refine an item using anvils. Refining with anvils at lower levels of refine is even more expensive.
The anvils need to be buffed. The price of the anvils needs to be decreased, the refine % increased, or both.
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