Total combinations for enchants

[Mine AGK]

I did math and decided to share it with everyone. This was interesting and difficult as it took me nearly 1hr just to complete all of this.

The current amount of cominations of enchants are as follows. These include repeating combinations, but in different orders. I.e, 123/321/231/213 ect. Being in any order and with the same numbers or in this case enchants.

The current amount of total combinations are listed below.


1h weapons: 26,235
2h weapons: 171,700
Armors: 50,115
Shields: 45,759
Amulets: 32,509

These are the total numbers of combinations including the same enchants in different orders.

[Mine AGK]

This thread is also not meant to be a rude assault on anyone at STS. This is just some math that i decided to think up because i got curious.

[Communion]

What are enchants exactly?

[burntoutdex]

what, so to get a +60 enchantment on a level 30 amulet is a 1 in ~16k?

props on the maths, probability is not my strongest suite at all, i am impressed o;

[Mine AGK]

what, so to get a +60 enchantment on a level 30 amulet is a 1 in ~16k?

props on the maths, probability is not my strongest suite at all, i am impressed o;

Id have to do seperate math for that. But i can give you the equation of you want.

nCr= n!śr!(n-r)!

[burntoutdex]

Incorrect information, see further down in thread.

[Dolloway]

I dislike doing math. It's not my strong suit

Can anyone propose a better enchant system based on this kind of math though?

If we took out the absolutely useless enchants like 1 int or 1 dex or 1 str or other obviously useless enchants, the odds would improve significantly, correct?

Can anyone take out the obviously useless enchants and figure out the % it would take to get your desired enchants or how many combinations there would be after taking out those useless enchants from the system? Like I said, math is not my strong suit

[burntoutdex]

I dislike doing math. It's not my strong suit

Can anyone propose a better enchant system based on this kind of math though?

If we took out the absolutely useless enchants like 1 int or 1 dex or 1 str or other obviously useless enchants, the odds would improve significantly, correct?

Can anyone take out the obviously useless enchants and figure out the % it would take to get your desired enchants or how many combinations there would be after taking out those useless enchants from the system? Like I said, math is not my strong suit

note, only calculated for amulets - but you get the idea

Approximated percentages because i more than likely have missed a few enchantments here and there.

removing all additions of dex/str/int:

for one slot, 4.8% chance to roll desired enchantments

for two slots, 0.48% chance to roll desired enchantments

for three slots, 0.08% chance to roll desired enchantments

Didn't bother with total combinations, i feel as if this portrays more effectively the 'gambling' aspect of the game in its current state.

To answer your question, no, removing the insignificant enchantments does not improve your chances of desired rolls all that much.

Hope this helps, Dolloway

[Draebatad]

Very useful facts, mathematics confirms what we've all been experiencing. Sadly, as the math has noted, removing the less desirable enchantments won't provide any realistic relief if we're unable to lock slots as desired. Apparently the only way to win, is not to play the enchantments game. In the end, the best thing for the community would be for this system to be converted into something that isn't actually such a huge gamble, or something entirely different altogether. Thanks for taking the time and interest to run the numbers. It's definitely food for thought.

[yannjoel]

This is a good guide to calculate the prices for perfect enchated sets.

[Mine AGK]

Ah, so after being inspired by this post and enquiring in game, i concluded there are 42 different possible enchantments you can add to an amulet (thanks for your time, xyz). From that, you can have either 1, 2, or 3 slot enchantments. After that, I calculated the probability of getting the desired enchantments on your first attempt, the results are well - laughable.

This is only for amulets, and i think i may have missed a couple enhancements, not 100% i found everything from browsing CS

with 1 enchantment slot, you have a 2.4% chance to get your desired enchantments on your first roll
with 2 enchantment slots, you have a 0.1% chance to get your desired enchantments on your first roll
with 3 enchantment slots, you have a 0.009% (yes, that's correct) to get your desired enchantments on your first roll.

if i made a mistake, please feel free to correct me.

calculations below.

The total number of enchants for amulets for L105 elites. I counted a total of 59. I think you seem to have done me the liberty of getting rid of repeats of enchants in different orders. I believe this isnt how the system works though (reroll no repeats of the same group of enchants)

[Mine AGK]

I dislike doing math. It's not my strong suit

Can anyone propose a better enchant system based on this kind of math though?

If we took out the absolutely useless enchants like 1 int or 1 dex or 1 str or other obviously useless enchants, the odds would improve significantly, correct?

Can anyone take out the obviously useless enchants and figure out the % it would take to get your desired enchants or how many combinations there would be after taking out those useless enchants from the system? Like I said, math is not my strong suit

As for removing the useless enchants thst no one really goes for. That would be easily calculated. Ill do the math today removing enchants that no one deisres. I will also do the math and see what we could keep as enchants.

[burntoutdex]

Thanks for the correction on what i overlooked, AGK

Upon redoing with replacement i found this:

for 1 slot, 1.7% to get desired enchantments
for 2slot, 0.03% to get desired enchantments
for 3slot, 0.0005% to get desired enchantments

redone calculations here: https://i.imgur.com/ozkvIVz.jpg
(as always, correct me if im wrong)

[Mine AGK]

Thanks for the correction on what i overlooked, AGK

Upon redoing with replacement i found this:

for 1 slot, 1.7% to get desired enchantments
for 2slot, 0.03% to get desired enchantments
for 3slot, 0.0005% to get desired enchantments

redone calculations here: https://i.imgur.com/ozkvIVz.jpg
(as always, correct me if im wrong)

Thats crazy if you think about it though, the only thing that has less amounts of enchants is a 1h weapon.

2h weapons have 102 different enchants that have a possibility of being repeated alot. Mind sharing the formula used to find the percentages? Ill will update my post with these today

[burntoutdex]

Thats crazy if you think about it though, the only thing that has less amounts of enchants is a 1h weapon.

2h weapons have 102 different enchants that have a possibility of being repeated alot. Mind sharing the formula used to find the percentages? Ill will update my post with these today

Yeah, it's crazy that an amulet is one of the more favorable things for getting good enchants, yet the percentages are still disgustingly low. If you can tell me how many different enchantments there are for things other than amulets, i'll sit down and work out the percentages for desired rolls. i have no way of checking as i have yet to finish the quest which allows you to enchant.

As far as converting to percentage:

the formula c = a^n, where a is the number of enchantments, c is the combinations and n is the number of slots, gives you the possible combinations of what you might roll with replacement (how we believe the system works). Naturally raising this answer to -1, (to give c^-1) will give you the chance of 1 possible combination occurring. This resolves to be a decimal answer.

Of course, decimals are equivalent to percentages, just a different notation, to convert 1/c to a percentage, you simply multiply by 100.

Ex. for 2 slots, you compute 59^2

59^2 = 3481
3481^-1 = 0.0003 (1s.f.)
>this is the chance for one event to occur (eg the desired roll)
0.0003 x 100 = 0.03
0.03 is the percentage equivalent to the decimal chance, of course becoming 0.03%

Hope that makes sense :]

[Mine AGK]

Yeah, it's crazy that an amulet is one of the more favorable things for getting good enchants, yet the percentages are still disgustingly low. If you can tell me how many different enchantments there are for things other than amulets, i'll sit down and work out the percentages for desired rolls. i have no way of checking as i have yet to finish the quest which allows you to enchant.

As far as converting to percentage:

the formula c = a^n, where a is the number of enchantments, c is the combinations and n is the number of slots, gives you the possible combinations of what you might roll with replacement (how we believe the system works). Naturally raising this answer to -1, (to give c^-1) will give you the chance of 1 possible combination occurring. This resolves to be a decimal answer.

Of course, decimals are equivalent to percentages, just a different notation, to convert 1/c to a percentage, you simply multiply by 100.

Ex. for 2 slots, you compute 59^2

59^2 = 3481
3481^-1 = 0.0003 (1s.f.)
>this is the chance for one event to occur (eg the desired roll)
0.0003 x 100 = 0.03
0.03 is the percentage equivalent to the decimal chance, of course becoming 0.03%

Hope that makes sense :]

I can give you all the amount of enchants for all 5 enchantable pieces of L105 elite gear if you want to compare answers.

1h weapons: 56
2h weapons: 102
Armors: 68
Shields: 66
Amulets: 59

[Waug]

Sts ain't interested to change this enchantment system sadly, devs stated that many times. While everyone noticing this incredible luck based system now, I kept saying it since beginning lel about the astounding rng/luck factor & suggested many improvements even including slight and small possible improvement but the only thing that was accepted was the enchanted event for 1/5th of it's value.

[burntoutdex]

I can give you all the amount of enchants for all 5 enchantable pieces of L105 elite gear if you want to compare answers.

1h weapons: 56
2h weapons: 102
Armors: 68
Shields: 66
Amulets: 59

Thanks, i'll finish the calcs later this morning (1am atm cant be bothered)

ill let you know what i find :]

[Jensmage]

I did math and decided to share it with everyone. This was interesting and difficult as it took me nearly 1hr just to complete all of this.

The current amount of cominations of enchants are as follows. These include repeating combinations, but in different orders. I.e, 123/321/231/213 ect. Being in any order and with the same numbers or in this case enchants.

The current amount of total combinations are listed below.


1h weapons: 26,235
2h weapons: 171,700
Armors: 50,115
Shields: 45,759
Amulets: 32,509

These are the total numbers of combinations including the same enchants in different orders.

Armors: 50,116 <------Correct value
Shields: 47905 <------Correct value

Should the enchant system be left as is because the previous players have enchanted and spent quite a lot?
Should some players buy plat and invest in these weapons and PL? Some will say no.
The odds of receiving a high stat during the enchant event was high. Extremely high.

I recommend to buy plat and enchant :P

[Jensmage]

Thanks for the correction on what i overlooked, AGK

Upon redoing with replacement i found this:

for 1 slot, 1.7% to get desired enchantments
for 2slot, 0.03% to get desired enchantments
for 3slot, 0.0005% to get desired enchantments

redone calculations here: https://i.imgur.com/ozkvIVz.jpg
(as always, correct me if im wrong)

What is the desired enchant?
LOl ill be happy if I got 240-260 for armor.
Wand..ill be happy if it it was 135 dmg
shield...ill be happy if it was 130 armor
Amulet...

Enchant helps a little in the game but I think proc will determine the winning battle.