The Math Behind Cases + The Cost of a single Cobalt Card

[Solid_Stache_NaC]

So I decided to figure out the fractions to get which card you would want from a regular case as well as an elite case. I only did bronze and up since those are sought after the most. My math is a bit rusty, so if I made an error, let me know and I will correct it ASAP.

I also threw in the costs for a single cobalt card credit wise, and it is quite insane… I know Sagan on Roids did the math on gold cards and lower.

so there are 13 characters currently, hence the first fraction, and each character has 9 load out cards, hence the second, while the third is the fraction of the percentage chance to get that specific type of card.

All of these percentages assume that you are looking for a specific load out card.

Normal Cases
Bronze
(1/13)(1/9)(1/33) = 1/3,861

Silver
(1/13)(1/9)(1/66) = 1/7,722

Gold
(1/13)(1/9)(1/250) = 1/29,250

Cobalt
(1/13)(1/9)(1/1,000) = 1/117,000

Elite
Silver
(1/13)(1/9)(4/5) = 4/585

Gold
(1/13)(1/9)(3/20)= 1/780

Cobalt
(1/13)(1/9)(1/20)=1/2,340

For just a specific Character…

Normal

Bronze
(1/13)(1/33) = 1/429

Silver
(1/13)(1/66) = 1/858

Gold
(1/13)(1/250) = 1/3,250

Cobalt
(1/13)(1/1,000) = 1/13,000

Elite Cases

Silver
(1/13)(4/5) = 4/65 (approximately 6%)

Gold
(1/13)(3/20) = 3/260 (approximately 1%)

Cobalt
(1/13)(1/20) = 1/260 (approximately .3%)

Now, the cost of a single Cobalt card…

To figure that out, we must figure out the price for each lower tiered card, which is as follows.

Iron = 3,500 credits

Iron = 3Lead +500 combine costs.

We assume Leads are worth 1k due to cases costing that much.

Bronze = 11,500 credits

Bronze = 3 Iron + 1k combine cost

Silver = 48,000 credits

Silver = 4 bronze + 2k combine cost

Gold = 196,000 credits

Gold = 4 silver +4k combine cost

Cobalt = 1,186,000 credits

Cobalt = 6 gold + 10k combine cost

So to get the single cobalt card of a character of your choice with the load out you want is 1/9, which is around 11%. You are spending 1.2 million credits for an opportunity of a choice card.

Multiply that by 9 for the worst scenario to get the card you want, which is a whopping 10,674,000 credits.

So my question is, is there going to be a breakdown card option for a premium cost? I would rather spend 20k credits or even 30k to break down a cobalt card to try for the one I want. You’ll still spend around 500,000 credits if the break down cost is that much…

what are the plans for the cases? It would be extremely neat to see some specialty ones of a specific class of characters which would raise the chances of a card you want. Be it a rare drop of the case or having to spend money.

[lemonLugnut]

Lowe Chance, higher Income in Elitecases for Higher Chance. Keep that chance also low but not as low so people would deny it -> to acutally sell the Cases.
It’s just fashion and people like it.
So you have to keep the Rate low. If there would be like 10% A lot of people would be at Cobalt fast enough to not spend the money they like on it.

[ThatRandomGuy]

Im not a fan of cobalt… infact i am not a fan of GOLD… I wanted a gold card with bling-bling…and now i have 3 golds… ALL WITH FRIGGING BAMBOO CRAP…I give up… I think bronzes are better…

To hell with chances, if you want a specific card (bronze), click marketplace ->loadout->buy it , end of story…
and if you have more than enough money, then start spending on RNG…

and in reality,(relative to your math) it doesnt cost that much everytime, the cost depends on RNG(once again), if you are lucky a lot of cases could drop…(RNG again) and could drop any from iron to gold (cobalt is too damn rare)…
I have had streak of 3/3 rounds dropping cases (once).

[Solid_Stache_NaC]

For buying an elite case, you have 50 times the chance to get a cobalt. If you are looking for a specific character, card for that fancy clothing, and the augments, that’s when the odds are getting crazy. Especially when more and more characters will be coming out, it will make the cases have an even slimmer chance to get the one you want…

Now if the normal elite cases were 2.50, that would be an excellent price. Now throw in character specific cases, like an assault case, price them at 5 bucks, that would be way more reasonable. Even 7.49 for such a case would be worth it, since the fraction would be much smaller.

For such a hypothetical case, the percentages would be so.

elite case character archetype, 4 characters total with specific card as well.

Silver
(1/4)(1/9)(4/5) = 1/45

Gold
(1/4)(1/9)(3/20) = 1/240

Cobalt
(1/4)(1/9)(1/20) = 1/720

Approximately a third of the original. 7.49 would be the best price for such a case.

[ThatRandomGuy]

Buying cases would actually make sense if they drop ONLY CARDS FOR MERCS THAT YOU OWN !

[Ardez1]

Your math is slightly flawed. The trade up fee from lead to iron is 500 credits.

Also, basing your price on the value of a case is a poor decision. Most people do not purchase cases and just get the ones for free from drops. Not to mention basing your math on buying crates + the trade up system without taking into account variable drops. Somebody might just buy a single case and get a bronze. Does that mean his bronze is worth less because it only cost him 1,000 credits? His sample size means that must be what they are worth. You are basing your math on a sample size of 1 case with the result being lead.

I have tried to do this math before, but without knowledge of the variables(in this scenario case opening results) you will find it had to make a prediction of value. Best way to do this is to actually get a sample size based on a # of cases to calculate value rather than assign a blanket value based on the minimum you might pay.

These variables were released to us but I never went back to look at the math again until now.

Let us pretend that the odds are PERFECT and you open 1,000 cases. This cost you 1,000,000 credits.

There are 6 different levels of rarity. Divide 1,000,000 by 6 to get 166,667 value per tier. Then divide that number by the number of cards received for that rarity to determine how much each card is worth.

You received:
1 Cobalt = 166,667 Credits
4 Gold = 41,667 Credits Each
15 Silver = 11,111 Credits Each
30 Bronze = 5,556 Credits Each
150 Iron = 1,111 Credits Each
800 Lead = 208 Credits Each

[ThatRandomGuy]

@Ardez

I would say MATH based on RNG is false, everytime, every damn time…
Why?
We are not talking about continues probability / chance, you could get 1 million LEAD cards out of 1 million boxes…

[Ardez1]

[quote=“peppyFarmer;33667”]@Ardez

I would say MATH based on RNG is false, everytime, every damn time…
Why?
We are not talking about continues probability / chance, you could get 1 million LEAD cards out of 1 million boxes…[/quote]

Yes. And the moment you show me that video I will change my math. Hell, you give me a sample size of 100 cases and I will change my math in an instant to suite it. Just let me know when you upload that video. I will believe the given statistics until I am proven differently.

[ThatRandomGuy]

[quote=“Ardez;33668”][quote=“peppyFarmer;33667”]@Ardez

I would say MATH based on RNG is false, everytime, every damn time…
Why?
We are not talking about continues probability / chance, you could get 1 million LEAD cards out of 1 million boxes…[/quote]

Yes. And the moment you show me that video I will change my math. Hell, you give me a sample size of 100 cases and I will change my math in an instant to suite it. Just let me know when you upload that video. I will believe the given statistics until I am proven differently.[/quote]

GIMME DEM MONIES N I WILL DO IT :lol:

[Solid_Stache_NaC]

[quote=“Ardez;33665”]Your math is slightly flawed. The trade up fee from lead to iron is 500 credits.

Also, basing your price on the value of a case is a poor decision. Most people do not purchase cases and just get the ones for free from drops. Not to mention basing your math on buying crates + the trade up system without taking into account variable drops. Somebody might just buy a single case and get a bronze. Does that mean his bronze is worth less because it only cost him 1,000 credits? His sample size means that must be what they are worth. You are basing your math on a sample size of 1 case with the result being lead.

I have tried to do this math before, but without knowledge of the variables(in this scenario case opening results) you will find it had to make a prediction of value. Best way to do this is to actually get a sample size based on a # of cases to calculate value rather than assign a blanket value based on the minimum you might pay.

These variables were released to us but I never went back to look at the math again until now.

Let us pretend that the odds are PERFECT and you open 1,000 cases. This cost you 1,000,000 credits.

There are 6 different levels of rarity. Divide 1,000,000 by 6 to get 166,667 value per tier. Then divide that number by the number of cards received for that rarity to determine how much each card is worth.

You received:
1 Cobalt = 166,667 Credits
4 Gold = 41,667 Credits Each
15 Silver = 11,111 Credits Each
30 Bronze = 5,556 Credits Each
150 Iron = 1,111 Credits Each
800 Lead = 208 Credits Each

[/quote]

I merely went with the worst case scenario with everything, as it would give somewhat of an idea for what would happen if you have the worst luck. I over looked the lead to iron stuff, I’ll change that up.

So those numbers are for a perfect RNG, so if we average the values that we created it would come up with more realistic numbers. I’ll take the time to go about that later tonight.

[giftedStatue]

Well, let’s see… In a perfect world, if you bought 1,000 cases you would get 4 gold cards, 15 silver cards, 30 bronze cards, 150 iron cards, and 801 lead cards (well, 800 lead and 1 cobalt actually, but getting a cobalt outright would defeat the purpose of this post, so we’re just going to ignore that possibility for now o:)).

Combining the haul above as far as you can get, you would end up with 3 cobalt cards, a silver card, and a bronze card. Numerically, this is just about 3.0520833 cobalt cards. So, it goes to reason that the statistical on-average cost of a cobalt card should be 3.0520833 times less than the total cost of buying and combining those 1000 loadouts.

So, let’s do the math here. 1000 cases means a million credits, right off the bat.
Then, we can turn the 801 lead cards into 267 iron cards at 500 credits each. Total cost: 133,500 credits.
Next, we can turn our new sum of 417 iron cards into 139 bronze cards at 1000 credits each. Total cost: 139,000 credits.
Our 169 bronze cards can be turned into 42 silver cards at 2000 each, with one bronze card being left over. Total cost: 84,000 credits.
Our 57 silver cards can be turned into 14 gold cards at 4000 each, with one silver card being left over. Total cost: 56,000 credits.
Finally, we can use our 18 gold cards to create 3 cobalt cards at 10,000 each. Total cost: 30,000 credits

GRAND TOTAL

1000 cases = 1,000,000 credits
Combining costs = 442,500 credits
Total cost of crafting 3.0520833 cobalt cards: 1,442,500 credits

Now, the moment you’ve all been waiting for…

1,442,500 / 3.0520833 = … drum roll please …

472,628 credits.

I’m going to go to bed now.

[CabeRawit]

[quote=“giftedStatue;33756”]stuff
[/quote]
Or you could just include the extra cobalt from cases and add them to the divisor, since we’re talking about the average cost (1,442,500 / 4.0520833 and I couldn’t be bothered changing the calculation from the additional lead card), which results to about 350k-ish creds.

Also maybe another calculation that counts all cases acquired (not bought), though I doubt anyone would actually collect that much cases from matches.

tl;dr:
Ask Rhino about statistics. I hear he’s good with it.

[_Sniff]

Mind if I ask you to do the math for Elite cases? How much money + credits it would take to trade up?

[Ardez1]

Mind if I ask you to do the math for Elite cases? How much money + credits it would take to trade up?

Not sure who you are asking, but I will use the same math I used above.

Pretending you buy 100 Elite Cases at $350

Three possible tiers of rarity. $116.67 value per tier.

5 Cobalt = $23.33 Each
15 Gold = $7.78 Each
80 Silver = $1.46 Each

Pretending you buy 100 Elite Cases at $500(DON’T DO THIS!!!)

166.67 value per tier.

5 Cobalt = $33.34
15 Gold = $11.11
80 Silver = $2.08

If we combine this information with the supposed credit values from above we can determine a relative value.

1 Cobalt = 166,667 Credits
4 Gold = 41,667 Credits Each
15 Silver = 11,111 Credits Each
30 Bronze = 5,556 Credits Each
150 Iron = 1,111 Credits Each
800 Lead = 208 Credits Each

Based on Nexon’s math 5,000 credits = $1

Cobalt = $23.33 = 116,650 credits
Cobalt = $33.34 = 166,700 credits

Gold = $7.78 = 38,900 credits
Gold = $11.11= 55,550 credits

Silver = $1.46 = 7,300 credits
Silver = $2.08 = 10,400 credits

Shockingly the value based on the $5 cases is quite close to the credit value I determined them to have based on 1,000 normal cases.

P.S. 1,000,000 credits = $200. This means $350 of Elite Cases, in a perfect world, should generate 1,750,000 credits worth of loadouts.

[giftedStatue]

[quote=“Ardez;33927”]
1 Cobalt = 166,667 Credits
4 Gold = 41,667 Credits Each
15 Silver = 11,111 Credits Each
30 Bronze = 5,556 Credits Each
150 Iron = 1,111 Credits Each
800 Lead = 208 Credits Each

Based on Nexon’s math 5,000 credits = $1

Cobalt = $23.33 = 116,650 credits
Cobalt = $33.34 = 166,700 credits

Gold = $7.78 = 38,900 credits
Gold = $11.11= 55,550 credits

Silver = $1.46 = 7,300 credits
Silver = $2.08 = 10,400 credits[/quote]

I think you’re thinking about this in a different way… The way I see “the cost of a cobalt card” is how much you would have to spend to get your hands on one. Which, as it turns out, happens to be a lot more than you suggest.

I’ll give it a try my way, though… In a perfect world, if you bought 20 elite cases you should get 1 cobalt card, 3 gold cards, and 16 silver cards.
You can trade up those silver cards to make 3 gold cards at 4,000 credits, not crafting the last gold card because it wouldn’t get you any more cobalts. Total cost: 12,000.
Then you can use your 6 gold cards to make 1 cobalt card. Total cost: 10,000.
You are left with 2 cobalt cards and 4 silver cards (2.167 cobalt cards).
In total, you spent $35 and 22,000 credits.
$35 / 2.167 = $16.15
22,000 / 2.167 = 10,152

The price of a cobalt card using elite cases instead of normal ones is $16.15 and 10,152 credits.

[Ardez1]

[quote=“giftedStatue;34096”][quote=“Ardez;33927”]
1 Cobalt = 166,667 Credits
4 Gold = 41,667 Credits Each
15 Silver = 11,111 Credits Each
30 Bronze = 5,556 Credits Each
150 Iron = 1,111 Credits Each
800 Lead = 208 Credits Each

Based on Nexon’s math 5,000 credits = $1

Cobalt = $23.33 = 116,650 credits
Cobalt = $33.34 = 166,700 credits

Gold = $7.78 = 38,900 credits
Gold = $11.11= 55,550 credits

Silver = $1.46 = 7,300 credits
Silver = $2.08 = 10,400 credits[/quote]

I think you’re thinking about this in a different way… The way I see “the cost of a cobalt card” is how much you would have to spend to get your hands on one. Which, as it turns out, happens to be a lot more than you suggest.

[/quote]

What you quoted is answering @Sniff about Elite Cases.

Also, basing it entirely on paid cases that cost 1,000 credits each and where you only ever get leads is completely unrealistic as far as determing what it takes to get a cobalt goes. Yes, it is within the realm of possibility, but so is pulling a random cobalt from a normal case. Besides the fact that many people very quickly realize that buying 1,000 credit cases is not worth it at all.

[giftedStatue]

[quote=“Ardez;34098”]
What you quoted is answering @Sniff about Elite Cases.

Also, basing it entirely on paid cases that cost 1,000 credits each and where you only ever get leads is completely unrealistic as far as determing what it takes to get a cobalt goes. Yes, it is within the realm of possibility, but so is pulling a random cobalt from a normal case. Besides the fact that many people very quickly realize that buying 1,000 credit cases is not worth it at all.[/quote]

Well, let’s see… In a perfect world, if you bought 1,000 cases you would get 4 gold cards, 15 silver cards, 30 bronze cards, 150 iron cards, and 801 lead cards

I never said they would all be lead, man. I calculated assuming that what you got would follow the percent chances.

[frolicsomeCrane]

I don’t believe in RNG math either, mainly because I spent 260~ hours in the game, buying regular cases with all the cash I could get and I didn’t get a single cobalt from any case, meanwhile a friend of mine who played the game once for two hours, got a case and bam cobalt.

[XavienX]

Damn, people are serious bout dis.

[Kristin_Cool]

[quote=“Solid Stache ~NaC;33663”]For buying an elite case, you have 50 times the chance to get a cobalt. If you are looking for a specific character, card for that fancy clothing, and the augments, that’s when the odds are getting crazy. Especially when more and more characters will be coming out, it will make the cases have an even slimmer chance to get the one you want…

Now if the normal elite cases were 2.50, that would be an excellent price. Now throw in character specific cases, like an assault case, price them at 5 bucks, that would be way more reasonable. Even 7.49 for such a case would be worth it, since the fraction would be much smaller.

For such a hypothetical case, the percentages would be so.

elite case character archetype, 4 characters total with specific card as well.

Silver
(1/4)(1/9)(4/5) = 1/45

Gold
(1/4)(1/9)(3/20) = 1/240

Cobalt
(1/4)(1/9)(1/20) = 1/720

Approximately a third of the original. 7.49 would be the best price for such a case. [/quote]

how much is the cost approx? if you were to sell them