Refinement lvl Chance of success Compund probability BE needed BE returned for failure
1.................................100.00%......................100.00%..................0.............................0 2.................................100.00%......................100.00%..................0.............................0 3..................................90.00%........................90.00%..................1.............................0 4..................................80.00%........................72.00%..................2.............................1 5..................................80.00%........................57.60%..................4.............................2
6..................................70.00%........................40.32%..................7.............................3 7..................................50.00%.........................20.16%..................10...........................4 8..................................40.00%..........................8.06%..................15...........................5 9..................................40.00%..........................3.23%..................20...........................6

Adapted from
http://phpbb.acclaim.com/9dragons/viewtopic.php?t=85639&postdays=0&postorder=asc&highlight=reece&start=15

This post shall be fairly technical, but I hope it will be of help to those who read it.

Expected Cost of A Refined Weapon

I shall first draw up a general formula for calculating the price associated with a weapon of a particular refinement level:

You go to the refiner with your weapon, the refinement material and pay some gold, and there are 2 possible outcomes:
1. You get a weapon of the next refinement level with chance c.
2. You fail and get some BE returned, if any, with a chance (1-c).

Let W be the price of the unrefined weapon,
and B be the price of BE,
M(n) be the number of BE associated with the material required to refine from n to n+1,
Br(n+1) be the number of BE returned upon failure in refining from n to n+1,
Pr(n) be the expected cost of a weapon of a particular refinement level
and R(n) be the amount of gold you have to pay to the refiner to refine it from n to n+1.

Pr(n) + R(n)+ M(n) = cPr(n+1) + (1-c)Br(n+1)

Rearranging, we derive a recursive formula for calculating the expected cost associated with a weapon of refinement n+1.
Pr(n+1) = 1/c[Pr(n) + R(n) + M(n) - (1-c)Br(n+1)]

Pr(1) = W + 1100 + 1000 = W +2100
Pr(2) = Pr(1) + 3300 + 3000 = W + 8400
Pr(3) = 1/0.9[Pr(2) + 5000 + B] = 1.11W + 14889 + 1.11B
Pr(4) = 1/0.8[Pr(3) + 10000 + 2B - 0.2B] = 1.39W+ 31111 + 3.64B
Pr(5) = 1/0.8[Pr(4) + 20000 + 4B - 0.4B] = 1.74W + 63889 + 9.05B
Pr(6) = 1/0.7[Pr(5) + 35000 + 7B - 0.9B] = 2.48W + 141270 + 21.64B
Pr(7) = 1/0.5[Pr(6) + 50000 + 10B - 2B] = 4.96W + 382540 + 59.28B
Pr(8) = 1/0.4[Pr(7) + 75000 + 15B - 3B] = 12.40W + 1143849 + 178.20B
Pr(9) = 1/0.4[Pr(8) + 100000 + 20B - 3.6B] = 31.00W + 3109623 + 486.51B

Interpreting the Results

By looking at the coefficient of W, you can find out how many weapons on average it will take in order to refine a weapon from +0 to +n. You can also find out how many weapons on average it will take you to refine from +n to +(n+k) by dividing the coefficient of W for line Pr(n+k) by the coefficient of W for line Pr(n).

By looking at the coefficient of B, you can find out how many BEs on average it will take in order to refine a weapon from +0 to +n.

Buying vs Refining

As shown from the results of the calculation, the cost associated with refining a weapon can become amazingly high at the higher refinement levels, it more than doubles from one refinement level to the next (assuming you are refining a normal weapon).

When deciding whether it worthwhile to buy a weapon from a stand, simply refer to the above results and substitute appropriate values for the variables. Chances are, it is better to buy than refine a weapon. The above results can be also used as a tool for comparing two weapons of the same type of different refinement levels. For example, you might find a +5 weapon at price x and a +6 weapon of the same type at price x+c. By using the line Pr(6), substituting Pr(5) with x and using a suitable value for B, you can determine if it would be better for you to get the +5 weapon and refine it to +6 or to buy that +6 weapon.

If you decide to refine a weapon, you can be sure that you will not be able to recover the value associated with a refined weapon of that level - that is, the price you can expect to receive from selling a refined weapon will be lower than the expected cost in refining it to that level, Pr(n). Take a +9 weapon for example, you will never be able to get a price of 487BE for it. Hence, if you are concerned about breaking even, you should exercise great caution when it comes to refining - the odds are greatly weighted against you, not just by the probabilities of success, but also by market forces.


I hope this post has provided with a rigorous basis for your decision as to whether to refine a weapon or otherwise. Take your time with the math, and weigh for yourself the risks against the potential gain.