**someone posted this on EUKO forums , i hope it answers your question.**

''The Anvil... revealed
Ok, since I play KO I heard alot different theory about the anvil, somes very weird, somes good and some that I didn't find words to qualify. I decided to really study the anvil back in 2007-2008, and maded a complete theory of how it does really works. For all thoses who know me on Cypher (Bodycult), know my upgrading skills. Just for a bit credibility, here is a list of some thing I maded:

__Cypher__

Tons of +8 (wont enumerate)

Salamander staff +9

Shard +9

Elixir staff +9

Scorching staff +17 rebirth (burnt at +18)

__CWest__

Shard +12reb

Shard +13reb (a different one)

*To reduce calculs, I wont talk here about +1 to +7 upgrades, but rather focus on +8, +9 and +10.*

__Hypothesis__

Chance of sucess +7 to +8 = 5%

Chance of sucess +8 to +9 = 2%

Chance of sucess +9 to +10 = 0.5%

**1) Upgrading with trina**

Saw on official website that trina add 20% sucess rate. There is 2 theory about this statement:

First: you try a +7 to +8 item, you'll have 5% +20% = 25% chance of sucess

Second: it add 20% to the odd you already have, so it would be 5%(1.2) = 6% chance of sucess

With all the data I've got over the past 6 years, the first theory win. If you dont thrust me on that just compile data yourself and do some stats.

2) Burning items.... whats the goal ?!?

Alot find it weird to burn stuff, alot find it very usefull, alot use this technique without knowing why they do that, so let me explain. This is a bad application of a probability law called the geometric law. The main goal of this technique is to increase the odds of getting a sucess after getting some burns. Consider the following outcomes (s as sucess, f as fail)

f s s f f f s f f f f f f f f f f s f s f f s f s f f f f f f s f f f f f

It is true to say that there is more odds of getting a sucess giving the first n burnt. The more you burn, the more sucess rate you got. HOWEVER THIS IS ONLY TRUE IF YOU LOOK THE ENTIRE SEQUENCE. If you throw a piece 9 times and got 9 face, you still got 50% chance of getting a face the next throw. So in reallity, its useless to burn stuff before upgrading.

__3) Upgrading rebirthed items__

Ok here is the most interresting part, since there is alot controversy. I'll give a bit more details on that.

On official site when rebirth system has been installed ingame, we found this very important statement: "Upgrading through the rebirth system give exactlly the same odds as using non rebirth items ".We also can find on website PUS that Tears of Karivdis add 30% chance of sucess. Lets see what thoses two statements means:

Some information

+7 to +8 = +1reb to +5reb (4 upgrades)

+8 to +9 = +5reb to +11reb (6 upgrades)

+9 to +10 = +11reb to +21reb (10 upgrades)

Another usefull information is that the sucess rate is the same for each step I mean:

+1reb -------> +2reb = +2reb -------> +3reb = +3reb -------> +4reb = +4reb -------> +5reb

then we switch to another sucess rate

+5reb -------> +6reb = +6reb -------> +7reb ....... = +10reb -------> +11reb

then we switch to another again

+11reb -------> +12reb = +12reb -------> +13reb ....... = +20reb -------> +21reb

This is not an hypothesis, this is the way it has been programmed to satisfy the official statement. Ok lets start to calculs the sucess rates, based on the top post hypothesis (I'll put hypothesis in green)

To find a sucess rate for +7 to +8, we need to solve the following equation:

0,05 = x^{4}

(0,05)^{1/4} = x

Then x = 0,47287

This mean for each step to +1reb to +5reb, the sucess rate is 47,287% of sucess and this is without Tears of Karivdis. So adding a Tears give 30% + 47,287% = 77,287% chance of sucess

To find a sucess rate for +8 to +9, we need to solve the following equation:

0,02 = x^{6}

(0,02)^{1/6} = x

Then x = 0,521

This mean for each step to +5reb to +11reb, the sucess rate is 52,1% of sucess and this is without Tears of Karivdis. So adding a Tears give 30% + 52,1% = 82,1% chance of sucess

To find a sucess rate for +9 to +10, we need to solve the following equation:

0,005 = x^{10}

(0,005)^{1/10} = x

Then x = 0,5887

This mean for each step to +11reb to +21reb, the sucess rate is 58,87% of sucess and this is without Tears of Karivdis. So adding a Tears give 30% + 58,87% = 88,87% chance of sucess

Alot see this and think its not possible, but the proove is here, and I prooved it just by using the official statements. You find this ratio a bit high ? Then try and you will see. Also if you want, you can change the hypothesis odds (in the top) and adjust the calculs to see what it give, but the hypothesis like that are very realistic. ''

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