tl;dr: Cost to enchant a Hair Accessory with the exact 3 stats of your choice? $9,709.20 USD per Hair Accessory. Do you want specifically HP, SP, and Crit Damage all at perfect rolls? $5,126,457.60 USD per Hair Accessory. If you only care about getting AOE Defense Ratio, regardless of any other stat on the item, it is only about $13.68. If you only care about a perfect PATK, and don't mind anything else, it would be $327.60 USD.
Update: AOE Attack Ratio +1 and Move Speed +1 have been confirmed in our roll tables but, because of their apparent rarity, are likely to have a different weighting against receiving them. In addition it has also been seen in-game via multiple sources that single stat rolls appear most frequently which may be an issue of unknown weighting which could dramatically decrease our chances of a favorable triple stat roll.
Edit: Post is for educational purposes only. I can’t really take one side or the other anymore because the existence of the item may open pandora’s box, or it may end here in its current form. I don’t know. Hopefully this helps in your decision about how you feel about Magic Scrolls and the possibility of other RNG benefits IMC may introduce. All RNG formulated with an assumed (until proven otherwise) equal weighting. nizidr helped me realize there are multiple attribute types dealing with elemental damage, and possibly defense, that can stack on the same item. All odds updated from base 1:19 stats to 1:31 (1-17 stats remain the same, 18 Attribute Defense updated to 18-Holy 19-Dark 20-Fire 21-Lightning 22-Earth 23-Ice 24-Poison, 25 Attribute attack split into 25-Holy 26-Dark 27-Fire 28-Lightning 29-Earth 30-Ice 31-Poison) due to previous stats allowing multiple rolls from the same pool of options for those stats only. Appending the 1:19 values at the end for reference.
Firstly, as per IMC, 100TP = approx $9.00. From that we can discern that 1 TP = approx 9 cents and 8 TP (cost of Magic Scroll) = approx 72 cents.
So… want to see the odds of getting the perfect 3 stats on your hair accessory using the Magic Scroll that IMC talked about?
In KToS there are 19 possible stats. Yes, this could change, but since they have confirmed the scroll coming to IToS we’ll just have to use these numbers from KToS for now.
19 total stats to choose from and each scroll use has a chance to enchant either 1 stat, 2 stats, or 3 stats. However stat 18 and 19 have 7 sub-rolls each to account for Elemental Attack and Elemental Defense to a specific element. It also appears that while multiple elements can be rolled on to the same piece that no piece displayed thus far has two of the same elemental properties (i.e. a hat may have +Fire Attack, +Ice Attack, +Holy Attack, but not +Fire Attack, +Fire Attack, +Fire Attack) so this is incorporated into the equations at 1:31.
To get our wanted 3 stat types we’d take 313029=26970, but, that is for sequential odds, and our stat order doesn’t matter (HP,SP,CRIT is the same as CRIT, HP, SP for instance). If we give each of the three stats a number we’ll see there are 6 combinations:
123
132
213
231
312
321
So we’re taking 26970/6 to give us 1:4495, but since we can either roll a single stat, 2 stats, or 3 stats we multiply 4495 by 3 to get the final odds of achieving our ideal 3 stat types on our item at 1:13485.
For our costs we will simulate a faux 100% chance by saying if you rolled it that many times you will have been guaranteed the roll you want (even if we know this is not the case and you could re-roll hundreds of millions of times and still not get lucky).
So for a 1:13485 chance, just to get your 3 stat types, not including if the stat values are even high, you’re looking at approximately $9,709.20 USD For one piece. $29,127.60 USD for all three pieces.
Going forward…
Most stats have a variance in what their values can be. For instance, PATK has a range between 21 and 45. 45-21=24, so there are a total of 24 different possibilities for the PATK stat to be. In this example, we’ll say you don’t even care what value the other two stats are and all that matters to you is having those stats plus a perfect PATK roll.
1:13485 for the 3 stats you want, but we’re going to multiply that by 24 since 1:13485 is just the odds of getting all three stats at any random value. So to get a perf PATK and any value for the 2 other stats you want it is 1:323640.
Or, in translation, that roll is worth $233,020.80 USD in the cost of Magic Scrolls.
Now, a step further. What if you didn’t care about the other stats at all and only want a perfect PATK value? This accounts for any random stats that accompany your wanted perfect stat of PATK, but also accepts the possibility you may not have any other stats on the item at all. To get this we first accept that the odds of getting PATK on a single stat roll are 1:31, but the odds for getting it on a double stat item are twice as good at 1:31/2 because there are now two possible stats on the item either of which that could be our PATK, and 1:31/3 for a triple stat item. PATK has a variance of 24 so we are looking at (1:3124 + 1:3124/2 + 1:31*24/3)/3 or (1:744 + 1:372 + 1:248)/3 which gives us 1:455, or $327.60 USD. Sounds more reasonable, possibly scarily so.
And if you only want, say, AOE Defense Ratio? Well, that stat has no variance, and is locked at 1, so you are very likely to get it on your item with (1:311 + 1:311/2 + 1:31*1/3)/3 giving us roughly 1:19 or approximately $13.68 USD. The chances of getting AOE Defense Ratio, that is always by default locked at its perfect value, is very high.
Please note that while AOE Attack Ratio and Movement Speed also share a default perfect value of 1, there do appear to be weighting issues against rolling those stats. Currently this is an unknown that does mix things up a bit, but, if you have one of those stats on your item you are best to not re-roll it given their alarming rarity at the moment.
However, as per the example I listed in the other thread, let’s say I want HP, SP, and Crit Damage, since these three stats have the highest possible variances. What are the odds of rolling perfect stats on all 3 of those on a single piece?
HP: 383 to 803, 420 possible values
SP: 76 to 150, 74 possible values
Crit Damage: 32 to 66, 34 possible values
Getting all 3 of those stat types is 1:13485, getting all 3 stat types with perfect HP is 1:5663700, with SP would be 1:997890, with Crit Damage 1:458490… add those 3 since each is already its own perfect roll, so…
1:7,120,080…
That’s roughly half chance of winning the lottery.
You’re more than 7 times as likely to be struck by lightning this year at 1:960,000.
Neat.
The cost of that perfect enchant? $5,126,457.60. Yep, that’s over 5 million dollars in case you didn’t know IMC, just a heads up lol
And since we have 3 pieces we need to enchant… better make sure they are all perfect yeah? I mean it will only cost you $15,379,372.80 USD.
(Clarification edit: Please note the above figures are only for HP + SP + Crit Damage, as an example, because these three stats have the highest pool of potential values. This means this is the most difficult set of perfect stats to obtain. If you want, for example, a perfect PATK + a specific perfect Element attack + AOE Ratio, the odds would be 1:579,855 or $417,495.60 USD. Not that either cost is something we can realistically afford but it is important to note that the odds of getting your perfect 3 stat combination, all with perfect rolls, is highly dependent on the number of possible values that each stat can inherently have. The more values it can have the harder, and more expensive, it will be to get the best one.)
@Staff_Julie @STAFF_Ethan @STAFF_Shawn @STAFF_J @STAFF_John @STAFF_Ines
Old assumption of only 19 possible rolls that didn’t account for elemental properties on attack and defense: 191817=5814, 5814/6 =1:969, 969*3 gives us 1:2907, 2907(multiple stat variance here i.e. PATK variance would be 24)=chance of getting the perfect highest roll, do that for each perfect stat and add the three values together for the item’s final perfect chance. HP+SP+Crit Damage has the highest variances for the values of their stats so the worst odds in the 1:19 stats to get those perfect is 1:1,534,896 or approximately $1,105,125.12 USD.
