MU online--- Item Upgrading of MU online, Applied (go back »)

Let me ask a question first: Can you say, what a pair of +9+12+luck legendary pants cost in terms of bless of MU online? Assume 1 bless = 2 soul and +0+12+luck legendary pants cost 1b.


+Luck Items Of MU online

Let's say you have brought a normal item +0+12+luck for 1b, 1b=2s.
For upgrading it the first time using soul is the cheapest.

+0+12+luck +soul, you'll fail one out of four as:
75% get a +1+12+luck item;
25% get a +0+12+luck item.

Expected cost for a +1+12+luck item:
=1b + 1s*0.75 + 2s*0.25*0.75 + 3s*0.25^2*0.75 +...
=1b + 1.5s
=1.75b


For upgrading +1 to +6, using bless or soul on a +luck item has about the same expected cost, so we will be using blesses for simplicity. We bless the +1+12+luck item 5 times.

Expected cost for a +6+12+luck item:
=1.75b + 5b
=6.75b


From +6 to +7, you use a soul. Since the chance to success is 75% and item level drop only one for cases of failure, you normally get 3 success and 1 fail in a 4-time trial. A +5 item is 1b behind +6, so:
=6.75b+1s*0.75+(1b+2s)*0.25*0.75+(2b+3s)*0.25^2*0.75+...
=6.75b+1b
=7.75b


For upping +8, the expected loss is beginning to rise greatly, that will reflect in it's expected cost. If you failed the item dropped to +0, you'll lose (7.75b-1b)=6.75b. Thus, expected cost for a +8+12+luck:
=7.75b + 1s*0.75 + (6.75b+2s)*0.25*0.75 + (2*6.75b+3s)*0.25*0.25*0.75 +...
=7.75b + 0.5*0.75b + (6.75+1)*0.25*0.75b + (2*6.75+1.5)*(0.25^2)*0.75b +...
=(7.75 + 0.75*( 0.5 + (0.5*2+6.75)*0.25 + (0.5*3+6.75*2)*0.25^2 +...))b
=(7.75 + 0.75*( 0.5*( 1 + 2*0.25 + 3*0.25^2+...) + 6.75*( 0.25 + 2*0.25^2 +...) )b
=(7.75 + 0.75*(( 0.5*1/(1-0.25)^2 ) + ( 6.75*0.25/(1-0.25)^2 )))b
=(10 + 2/3)b
=10.67b


+9, repeat the above calculation process similarly. This time you lose (9-2/3)b if you fail:
=( (10 + 2/3) + 0.75*(0.5*1/(1-0.25)^2 + (9+2/3)*0.25/(1-0.25)^2) )b
=(14 + 5/9)b
=14.55b
Around 14b 1s.

+10 you will lost your item if fail. With the upgrade requirement increased to 1b1s This time you lose (14 + 5/9)b if you fail, ignore zen and chaos cost for simplicity:
=( (14 + 5/9) + 0.75*(1.5*1/(1-0.25)^2 + (14+5/9)*0.25/(1-0.25)^2) )b
=(21 + 11/27)b
=21.41b
Around 21b 1s.

+11 require 2b2s = 3b for combination. Chance of success decreased to 70% and lost (21 + 11/27)b if failed. Expected cost:
=( (21 + 11/27) + 0.7*(3*1/(1-0.3)^2 + (21 + 11/27)*0.3/(1-0.3)^2) )b
=(34 + 164/189)b
=34.86b
Around 35b.

+12 require 3b3s = 4.5b for combination. Chance of success keep at 70%. Lose (34 + 164/189)b if failed. Expected cost:
=( (34 + 164/189) + 0.7*(4.5*1/(1-0.3)^2 + (34 + 164/189)*0.3/(1-0.3)^2) )b
=(56.2396...)b
Around 56b.

+13 require 4b4s = 6b for combination. Chance of success keep at 70%. Lose 56.2396b if failed. Expected cost:
=( (56.2396) + 0.7*(6*1/(1-0.3)^2 + (56.2396)*0.3/(1-0.3)^2) )b
=(88.9137...)b
Around 89b.


Yes, this also means the expected cost to make a normal set (5 piece) on your own at: (For your reference)
+7+12+luck: 39b
+9+12+luck: 72b 1s
+10+12+luck: 107b 1s
+11+12+luck: 175b
+12+12+luck: 280b
+13+12+luck: 445b

Of course if you can buy a +3+12+luck piece at 1b1s for example, the cost of making a +7+12 set will be decreased to 27.5b. Others should have lower cost too, but we will consider that kind of abbreviated cost is a result of trade profit.


No Luck Items MU online

The market price of a +3+12 non-luck high armor item is around 1s. This may change but we'll take 1s as the cost of a +3+12 item for upgrading. I'd assume +0+12 item have no resale value for simplicity.

No-risk upgrade to +6+12 require:
=1s+3b
=3.5b

Upgrade to +7+12, if failed need 1b back to +6. expected cost:
=( 3.5 + 0.5*(0.5*1/(1-0.5)^2 + 1*0.5/(1-0.5)^2) )b
=5.5b

Now the crazy part is beginning...
Upgrade to +8+12, if failed need 5.5b to make a new +7+12 item for next trial. Expected cost:
=( 5.5 + 0.5*(0.5*1/(1-0.5)^2 + 5.5*0.5/(1-0.5)^2) )b
=12b

Upgrade to +9+12, if failed need 12b to make a new +8+12 for next trial. Expected cost:
=( 12 + 0.5*(0.5*1/(1-0.5)^2 + 12*0.5/(1-0.5)^2) )b
=25b

Upgrade to +10+12, if failed lose item worth 25b to make. Need 1b1s=1.5b for combination. Expected cost:
=( 25 + 0.5*(1.5*1/(1-0.5)^2 + 25*0.5/(1-0.5)^2) )b
=53b

Upgrade to +11+12, if failed lose item worth 53b to make. Need 2b2s=3b for combination. Chance decreased to 45%. Expected cost:
=( 53 + 0.45*(3*1/(1-0.55)^2 + 53*0.55/(1-0.55)^2) )b
=(124 + 4/9)b
=124.44b
Around 124b 1s.

Upgrade to +12+12, if failed lose item worth (124 + 4/9)b to make. Need 3b3s=4.5b for combination. Chance to success keep at 45%. Expected cost:
=( (124 + 4/9) + 0.45*(4.5*1/(1-0.55)^2 + (124 + 4/9)*0.55/(1-0.55)^2) )b
=(286.5432...)b
=286.54b
Around 286b 1s.

Upgrade to +13+12, if failed lose item worth 286.5432b to make. Need 4b4s=6b for combination. Chance to success keep at 45%. Expected cost:
=( 286.5432 + 0.45*(6*1/(1-0.55)^2 + 286.5432*0.55/(1-0.55)^2) )b
=(650.0960...)b
=650b
Around 650b.

Hey, it's still POSSIBLE! GOOD LUCK MAKING YOUR +13 NO LUCK ITEM!


Jewel of Life of MU online
Jewel of life of MU online always have 50% chance +luck or not. If failed drop to +0. Expected cost to make an item with four times option(max option) is:

1st time: ( 0 + 0.5*(1*1/(1-0.5)^2 + 0*0.5/(1-0.5)^2) )JoL = 2JoL
2nd time: ( 2 + 0.5*(1*1/(1-0.5)^2 + 2*0.5/(1-0.5)^2) )JoL = 6JoL
3rd time: ( 6 + 0.5*(1*1/(1-0.5)^2 + 6*0.5/(1-0.5)^2) )JoL = 14JoL
4th time: ( 14 + 0.5*(1*1/(1-0.5)^2 + 14*0.5/(1-0.5)^2) )JoL = 30 JoL

That is, normally there will be one 4 consecutive success in 30 trials. Maybe more or less but the average number is 30. Upgrading from +12 (4x) option is easier but if failed it's quite hard to get back to +12 option. It'd be best to up this option to max from an +x+12 item before upping above +7. If not you'll need a huge number of JoL later...



Hope I cleared out some misconceptions. Do not up a no luck item above +7 it just make no sense.
And hope you legit ppl can make your own set. Good luck