War Avatar Card Simulator - Results & Discussion

Arawin - Raging Tide · April 2014

Sooooo,

I think many people who are still playing this game are interested in what it takes to get good war avatar cards and sets. Myself especially, after some pretty bad luck streaks opening war avatar packs, I decided it was time to make a pack opening simulator to determine exactly what I wanted to know. (Basically how many packs on average one would have to open to meet certain requirements, such as having an S card correct for every slot.) I do know there is a forum-bot on here that will open packs for you, in batches up to 10,000 I believe... but I wanted more accurate and specific results, which wouldn't be provided unless I had more control over the simulation and the results. I also wanted to run far larger simulations than one batch of pack opening. I wanted numbers in the hundreds of millions to billions in order to obtain statistically meaningful results.

Anyway the results are below, and I've provided a link to a video explaining and describing them too, for anyone who is interested. I originally intended this only for myself, but some faction mates expressed interest so I shared with them. And now I'm hoping to get some feedback from a larger audience. If others find this data useful or interesting, I may work on / publish more results.

Please let me know what you think. If you have any questions, feel free to ask. If you think my results are rubbish and want contest them, you're also welcome to!

Video link (with extra description of results)

RESULTS

totalSimulationsRun: 10000
totalNumberOfPacksOpened: 7,135,282
MINIMUM Number to get all six S slots filled: 80
MAXIMUM Number to get all six S slots filled: 2778
AVERAGE Number to get all six S slots filled: 713.5282

totalSimulationsRun: 100000
totalNumberOfPacksOpened: 70,944,522
MINIMUM Number to get all six S slots filled: 50
MAXIMUM Number to get all six S slots filled: 4298
AVERAGE Number to get all six S slots filled: 709.4452

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 710,408,745
MINIMUM Number to get all six S slots filled: 38
MAXIMUM Number to get all six S slots filled: 5048
AVERAGE Number to get all six S slots filled: 710.40875

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 288,472,774
MINIMUM Number to get six S cards any slot: 17
MAXIMUM Number to get six S cards any slot: 1181
AVERAGE Number to get six S cards any slot: 288.47278

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 288,661,292
MINIMUM Number to get six S cards any slot: 17
MAXIMUM Number to get six S cards any slot: 1251
AVERAGE Number to get six S cards any slot: 288.6613

totalSimulationsRun: 100000
totalNumberOfPacksOpened: 613,686,690
MINIMUM Number to get all six Neuma Portal Set: 451
MAXIMUM Number to get all six Neuma Portal Set: 36938
AVERAGE Number to get all six Neuma Portal Set: 6136.867

totalSimulationsRun: 100000
totalNumberOfPacksOpened: 610,856,872
MINIMUM Number to get all six Neuma Portal Set: 427
MAXIMUM Number to get all six Neuma Portal Set: 33407
AVERAGE Number to get all six Neuma Portal Set: 6108.569

totalSimulationsRun: 100000
totalNumberOfPacksOpened: 1,362,519,739
MINIMUM Number to get all six double awakened Neuma Portal Set: 3313
MAXIMUM Number to get all six double awakened Neuma Portal Set: 54846
AVERAGE Number to get all six double awakened Neuma Portal Set: 13625.197

Newer results:

Simulations for getting *any* 4-card (60% bonus) S set or better.

totalSimulationsRun: 500000
totalNumberOfPacksOpened: 1497520207
MINIMUM Number: 72 packs
MAXIMUM Number: 13208 packs
AVERAGE Number: 2995 packs

Simulations for getting *any* 3-card (40% bonus) S set or better.

totalSimulationsRun: 500000
totalNumberOfPacksOpened: 978185483
MINIMUM Number: 13 packs
MAXIMUM Number: 8446 packs
AVERAGE Number: 1956 packs

Neodaystar - Sanctuary · April 2014

Thanks for sharing, interesting to know

I heard you mentioned you need "3 copies" of the same card to reawaken it twice (don't you if you mean 1 card + 3 additional copies, or "3 copies" meaning 3 of the same kind).

You actually need 4x of the same card to reawaken it twice.

FaceRolI - Sanctuary · April 2014

cool.

did you design/write the code for your simulations?

i'm sure you will get a lot of requests... but would love to see data on acquiring candlelight soverign set (6x A) from the FSP A packs, and data for getting that set if you already have 3/6 b:thanks

Thanks for sharing.

Arawin - Raging Tide · April 2014

Neodaystar - Sanctuary wrote: »

Thanks for sharing, interesting to know I heard you mentioned you need "3 copies" of the same card to reawaken it twice (don't you if you mean 1 card + 3 additional copies, or "3 copies" meaning 3 of the same kind).

You actually need 4x of the same card to reawaken it twice.

Is this verified somewhere? I have no proof myself, but I was told by a friend you only needed 1 card to rebirth. Therefore, 1 original. 1 for 1st rebirth. 1 for second rebirth. Equals 3. Unless the second rebirth has two slots for cards? If so it would indeed be 4. The simulation results for getting 3 would still be correct for getting three. But if you need four, that's another story.

If four are indeed needed I could run some simulations for 4, though the costs are already absurd for just 3 lol.

FaceRolI - Sanctuary wrote: »

cool.

did you design/write the code for your simulations?

i'm sure you will get a lot of requests... but would love to see data on acquiring candlelight soverign set (6x A) from the FSP A packs, and data for getting that set if you already have 3/6 b:thanks

Thanks for sharing.

Yeah. I designed and coded the simulations myself. That gives me the most control over showing exactly what results I want to see. They're written in java. I actually added some percentile data in the newer versions (since the video) to show how many packs like 80% of people need in order to get a certain set. (Rather than just showing the average...) The average is of course useful, but knowing some percentiles can also help too. I usually try to hope for better than average, or at least average, but try to prepare for the bad percentiles (80% or 90%)...

I can run both those simulations and get the results. I'll post up later when I have them. I did some partial set simulations already, but only with 1 card obtained. (And sadly found that having one card of a set doesn't really give you much of an advantage over someone who has none. Perhaps 3 of 6 will be a little better though.)

Neodaystar - Sanctuary · April 2014

Arawin - Raging Tide wrote: »

Is this verified somewhere? I have no proof myself, but I was told by a friend you only needed 1 card to rebirth. Therefore, 1 original. 1 for 1st rebirth. 1 for second rebirth. Equals 3. Unless the second rebirth has two slots for cards? If so it would indeed be 4. The simulation results for getting 3 would still be correct for getting three. But if you need four, that's another story.

If four are indeed needed I could run some simulations for 4, though the costs are already absurd for just 3 lol.

I had tried to awaken a C-card 2 times back in December, so yes- you do need a total of 4 cards of the same kind to awaken it twice. After having awaken a card once, you need another card of the same status to awaken it again for the second time. Meaning the card you have to use must also have been awakened once. That brings you to a total of 4 of the same card for 2 awakenings.

I tried to find the card I had awakened 2 times, but don't remember which toon it is on xD But the npc instructions in this ss also states that not only do you need a card of the same type, but also the same number of awakening.

http://postimg.org/image/8v7dsv0y9/

So if you have a card that is awakened once, you can't use a card of the same name that has not been awaken itself to awaken the awaken card a 2nd time. Anyone who has a bunch of C cards laying around can easily try this..

Socqar - Lost City · April 2014

FaceRolI - Sanctuary wrote: »

cool.

did you design/write the code for your simulations?

i'm sure you will get a lot of requests... but would love to see data on acquiring candlelight soverign set (6x A) from the FSP A packs, and data for getting that set if you already have 3/6 b:thanks

Thanks for sharing.

I like that idea :P

Arawin - Raging Tide · April 2014

Neodaystar - Sanctuary wrote: »

I had tried to awaken a C-card 2 times back in December, so yes- you do need a total of 4 cards of the same kind to awaken it twice. After having awaken a card once, you need another card of the same status to awaken it again for the second time. Meaning the card you have to use must also have been awakened once. That brings you to a total of 4 of the same card for 2 awakenings.

I tried to find the card I had awakened 2 times, but don't remember which toon it is on xD But the npc instructions in this ss also states that not only do you need a card of the same type, but also the same number of awakening.

http://postimg.org/image/8v7dsv0y9/

So if you have a card that is awakened once, you can't use a card of the same name that has not been awaken itself to awaken the awaken card a 2nd time. Anyone who has a bunch of C cards laying around can easily try this..

Okay I think I understand now. Thanks for the explanation /screenshot.

Since you've actually successfully reawakened a card, how do you actually do it? If I try to put *any* card into the re-awakening menu it gives an error about having the card in the bag. Do you actually need to have the proper cards in your bag somewhere to even begin?

Raphxelion - Raging Tide · April 2014

thanks for sharing, finally have an idea of about how much is needed to get full s set. should get stickied!
Hopefully its cheaper since u can get a free S card from 6 A cards.

Socqar - Lost City · April 2014

Raphxelion - Raging Tide wrote: »

thanks for sharing, finally have an idea of about how much is needed to get full s set. should get stickied!
Hopefully its cheaper since u can get a free S card from 6 A cards.

From 10 A cards, and only once so... not much difference anyway

FaceRolI - Sanctuary · April 2014

Arawin - Raging Tide wrote: »

I can run both those simulations and get the results. I'll post up later when I have them.

Thank you b:thanks

XXHotXx - Morai · April 2014

seen this numbers

we should need at least Supply Tokens to S packs exchange option b:surrender

Neodaystar - Sanctuary · April 2014

Arawin - Raging Tide wrote: »

Okay I think I understand now. Thanks for the explanation /screenshot.

Since you've actually successfully reawakened a card, how do you actually do it? If I try to put *any* card into the re-awakening menu it gives an error about having the card in the bag. Do you actually need to have the proper cards in your bag somewhere to even begin?

How to awake a card
https://www.youtube.com/watch?v=aiBRwK-QG48&amp=&feature=youtube_gdata_player&noredirect=1

CapnK - Sanctuary · April 2014

I noticed the card xp stayed at 214, so you didn't get any xp from the card used to reawaken. If this is the same for the second reawaken, this means you're going to lose a lot of xp (from your second card that you have to reawaken once).

Neodaystar - Sanctuary · April 2014

CapnK - Sanctuary wrote: »

I noticed the card xp stayed at 214, so you didn't get any xp from the card used to reawaken. If this is the same for the second reawaken, this means you're going to lose a lot of xp (from your second card that you have to reawaken once).

I would think so, when you want to awaken it a 2nd time, you will have to waste another awaken card to meet the requirement. That additional awakened card you use will be gone, but it does not have to be max leveled.

Arawin - Raging Tide · April 2014

Neodaystar - Sanctuary wrote: »

How to awake a card
https://www.youtube.com/watch?v=aiBRwK-QG48&amp=&feature=youtube_gdata_player&noredirect=1

Wow super informative. Thanks. And you already have 6 S cards. So pro!

I'll have to try myself once I get some cards ready to rebirth.

And yeah it kinda stinks you lose the XP from the 'fodder' card. Though even if you kept it, I can't imagine many cases where you will be wanting to devour re-awakened cards (at least good ones.)

Asterelle - Sanctuary · April 2014

Neodaystar - Sanctuary wrote: »

How to awake a card
https://www.youtube.com/watch?v=aiBRwK-QG48&amp=&feature=youtube_gdata_player&noredirect=1

Uhh did you really have to use the EXACT same card or would any B card have worked? I thought you only need to have the same grade and awakening count.

Also what are the stats you get if you put the awakened B card in a mismatched slot? Is it the lvl1 base stats for a normal B card or an awakened B card?

BTW the avatar pack payouts in PWDB are somewhat inaccurate due to rounding.

Arawin - Raging Tide · April 2014

Asterelle - Sanctuary wrote: »

Uhh did you really have to use the EXACT same card or would any B card have worked? I thought you only need to have the same grade and awakening count.

Also what are the stats you get if you put the awakened B card in a mismatched slot? Is it the lvl1 base stats for a normal B card or an awakened B card?

BTW the avatar pack payouts in PWDB are somewhat inaccurate due to rounding.

Hmmmm, .03846156% is a bit lower than .04%. I could use that in future experiments. Basically that means it's even HARDER than it seems to get cards. Simply grand.

And I think you need the EXACT same card. I have two lifeprime S cards, one 80/80, one 1/80, and I can't rebirth, so I assume it's exact. Unless someone else can confirm otherwise.

Clergywoman - Raging Tide · April 2014

i can confirm that you need the same card, not just the card type, to reincarnate.

*brb tt. farming 1 TRILLION coins to get fully reincarnated nuema set*

Arawin - Raging Tide · April 2014

FaceRolI - Sanctuary wrote: »

i'm sure you will get a lot of requests... but would love to see data on acquiring candlelight soverign set (6x A) from the FSP A packs, and data for getting that set if you already have 3/6 b:thanks

Thanks for sharing.

Six Candleflame Sovereigns (0/6)

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 1290455005 packs
MINIMUM Number: 55 packs
MAXIMUM Number: 8917 packs
AVERAGE Number: 1290.4551 packs
15th percentile requires: 689 packs
75th percentile requires: 1611 packs
80th percentile requires: 1741 packs
90th percentile requires: 2132 packs

Six Candleflame Sovereigns (3/6)

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 964328313 packs
MINIMUM Number: 7 packs
MAXIMUM Number: 7509 packs
AVERAGE Number: 964.3283 packs
15th percentile requires: 399 packs
75th percentile requires: 1258 packs
80th percentile requires: 1386 packs
90th percentile requires: 1770 packs

Socqar - Lost City · April 2014

Arawin - Raging Tide wrote: »

Six Candleflame Sovereigns (0/6)
totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 1290455005 packs
MINIMUM Number: 55 packs
MAXIMUM Number: 8917 packs
AVERAGE Number: 1290.4551 packs
15th percentile requires: 689 packs
75th percentile requires: 1611 packs
80th percentile requires: 1741 packs
90th percentile requires: 2132 packs

Six Candleflame Sovereigns (3/6)
totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 964328313 packs
MINIMUM Number: 7 packs
MAXIMUM Number: 7509 packs
AVERAGE Number: 964.3283 packs
15th percentile requires: 399 packs
75th percentile requires: 1258 packs
80th percentile requires: 1386 packs
90th percentile requires: 1770 packs

2 years doing daily FS on 3 accounts (main + 2 alts) for average full Sic Candleflame Sovereigns... not that bad /sarcasm

I'll just stick to doing FS on 20 alts so I can get it in less than a year O.o

Just wondering but... This set bonus give a boost before being 6/6 anyway?

Arawin - Raging Tide · April 2014

Socqar - Lost City wrote: »

2 years doing daily FS on 3 accounts (main + 2 alts) for average full Sic Candleflame Sovereigns... not that bad /sarcasm

I'll just stick to doing FS on 20 alts so I can get it in less than a year O.o

Just wondering but... This set bonus give a boost before being 6/6 anyway?

No, sadly you need *every* card in the set before the bonus activates.

Socqar - Lost City · April 2014

Arawin - Raging Tide wrote: »

No, sadly you need *every* card in the set before the bonus activates.

Will stick to my almost goten Skynet set... 3/4 from 7 A cards... got pretty lucky there... Praying for the 4th and ** it xD

THanks for fast reply ^^

Neodaystar - Sanctuary · April 2014

Asterelle - Sanctuary wrote: »

Uhh did you really have to use the EXACT same card or would any B card have worked? I thought you only need to have the same grade and awakening count.

Also what are the stats you get if you put the awakened B card in a mismatched slot? Is it the lvl1 base stats for a normal B card or an awakened B card?

I think I had tested it out using C cards some months back when I didn't have a variety of duplicated cards to choose from. It does have to be a card of the same name, or you will get an error message.

If you place an awakened card in a non-corresponding slot, it will still obtain the benefits of the base white stats indicated by the awakened card. Like normally, it will still not receive benefits from the blue stats on the card, nor will it trigger a set bonus benefit if placed in the wrong slot.

FaceRolI - Sanctuary · April 2014

Thanks b:thanks

Arawin - Raging Tide · May 2014

I added some more results. Hope maybe they're useful to some! If any other requests, let me know.

These simulations are for meeting specific conditions. Such as getting any 3-card set or better. That means pretty much if you get a 3-card set, or something better (a 4-card or 6-card set), the simulation is satisfied and begins the next simulation. That is to say, if you get a Neuma set, you're probably not gonna care to continue working towards your 3-card set as you already have something better.

Simulations for getting *any* 4-card (60% bonus) S set or better.

totalSimulationsRun: 500000
totalNumberOfPacksOpened: 1497520207
MINIMUM Number: 72 packs
MAXIMUM Number: 13208 packs
AVERAGE Number: 2995 packs

Simulations for getting *any* 3-card (40% bonus) S set or better.

totalSimulationsRun: 500000
totalNumberOfPacksOpened: 978185483
MINIMUM Number: 13 packs
MAXIMUM Number: 8446 packs
AVERAGE Number: 1956 packs

Jaabg - Sanctuary · May 2014

Hi, quick question on the interpretation of things, slightly confused.

totalSimulationsRun: how many simulations you did?
totalNumberOfPacksOpened: total packs opened in all the simulations?
MINIMUM Number: minimum number of packs opened to meet the objective? (good luck)
MAXIMUM Number: Maximum number of packs opened to meet the objective? (bad luck)
AVERAGE Number: on average how many packs need to be opened to meet the objective? (ok luck)

Is that how the above can be interpreted, or did you mean things to be different. Thanks for your help.

WannaBM - Archosaur · May 2014

holy cows, needing 4 the same cards to reawaken. b:shocked

I wonder what their plans are really because this is just total bull**** right now of course. Youd need to spend very roughly:

1500 USD to get all slots filled with S cards.

25.000 USD to get a set of S cards.

100.000 USD* to get that set of S cards x4 for reawakening them all twice. (useless to do that with a non-set as youd still need roughly the same amount of total cards before you have them 4x)

And in addition you'd need to do 25.000 FSP runs so you can use the good boxes. Else it doubles to 200.000 USD.

So did they include stuff in the game that really noone is ever going to get, or are they gonna make them tradable in the future after all ? (although that would actually make it kinda too easy to get an OP set and reawaken them)

The OPness of it is also pretty scary of course. I already am pretty near to quiting PWI because there is nothing remotely challenging in PvE and im only R9+8 with cheap chards and A cards. If youd ever get a set of reawakened S cards, the level 100+ content would be like BH19 is now for lvl 100+ toons.
Sure its all for PvP, but PvP alone is not really that interesting is it ? (certainly not with only a few events per week that are at 5AM for half the population)

*counting only the needed Scards, not the exp.

Arawin - Raging Tide · May 2014

Jaabg - Sanctuary wrote: »

Hi, quick question on the interpretation of things, slightly confused.

totalSimulationsRun: how many simulations you did?
totalNumberOfPacksOpened: total packs opened in all the simulations?
MINIMUM Number: minimum number of packs opened to meet the objective? (good luck)
MAXIMUM Number: Maximum number of packs opened to meet the objective? (bad luck)
AVERAGE Number: on average how many packs need to be opened to meet the objective? (ok luck)

Is that how the above can be interpreted, or did you mean things to be different. Thanks for your help.

Yeah, that's an accurate interpretation. I include the total number of packs opened to give a better feel for how accurate the results are. (Say if you only tested with 20,000 packs, said results are far less meaningful than simulating over 500 million packs.)

WannaBM - Archosaur · May 2014

I want to add something to the correct interpretation.

You see a tremendous difference between max and min amount. While of course both extremes are possible, chance things like this can be represented in a bell curve. (google that if you dont know what it is) This curve shows a high chance for values near the average and declining chances for values further from the average. The chances far from the average are tiny. But if you take a huge sample size (as is done here) they will show up sometime and thus cause such extreme outcomes. If you take an even bigger sample size, you will eventually get 6 as the outcome for minimum for it is theoretically possible to get the 6 set cards out of 6 packs. And if you run the simulation enough times, it will happen. Similarly, the max will eventually go towards infinity if you make your sample size large enough. So while normally in statistics large sample sizes are a good thing, i do not agree with arawins statement above here that these numbers are more meaningful with a larger sample size. On the contrary. (Now dont start thinking there are cases in statistics where you dont want large sample sizes. You do. But you arent really interested in min and max results those are not things you should look at in a statistical analysis. Standard deviation is normally used instead)

totalSimulationsRun: 1000000
totalNumberOfPacksOpened: 710,408,745
MINIMUM Number to get all six S slots filled: 38
MAXIMUM Number to get all six S slots filled: 5048
AVERAGE Number to get all six S slots filled: 710.40875

The actuall math is pretty complicated and i dont feel like looking it all up now, but rest assured that those extremes are extremely unlikely. If you expect to need between half and double the average, (between 350 and 1400) i think you are already reasonably safe.
Still even though that is a whole different picture than painted by the extremes in these simulations, i still think such a range is not reasonable for a 1000s of dollars investment. Playing a lotery for a few pennies can be fun, but this is like buying a car with a random price between 10.000 and 50.000 USD and youll only know it after signing the contract.

PS: Arawin, please dont take this as negative criticism towards your work. I appreciate it your contribution very much.

PPS: You dont need to calculate standard deviation, there is actually and easier and more accurate method to get the info you want. (more accurate because the curve wont be symetrical in a situation like this) If you can store the results of your simulations in an ordered list, you can just scrap the top and bottom 2.5% of your results and then look at your max and min of the remaining list for a 95% certainty interval. And now in this case you do want the biggest possible sample size.

War Avatar Card Simulator - Results & Discussion

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