The real price of loadouts (Edited with a real statistics analysis)


(Izzy) #1

For those who were wondering the price of a loadout card, I have done some maths.
Let’s assumed to begin with that we will buy everything (cases included) and that we will always receive lead cards. We will lose this assumption later on in this same message.

So here is what it looks like:

Cobalt = 6gold + 10 000 Cred = 1 186 000 Cred (864 cases)
gold = 4
silver + 4 000 Cred = 196 000 Cred (144 cases)
Silver = 4bronze + 2 000 Cred = 48 000 Cred (36 cases)
bronre = 3
iron + 1 000 Cred = 11 500 Cred (9 cases)
iron = 3*lead + 500 Cred = 3 500 Cred (3 cases)
lead = 1 000 Cred = 1 000 Cred (1 case)

If you aim at gold and cobalt and if you buy all cases, expect to have:

gold

0.144 cobalt loadout
0.576 gold loadout (1 chance over two to get a gold loadout from a case while digging for gold)
2.16 silver loadout
4.32 bronze loadout
21.6 iron loadout
115.2 lead loadout

colbat

0.864 cobalt loadout (almost 1 chance to get a cobalt loadout from a case while digging for cobalt)
3.456 gold loadout
12.96 silver loadout
25.92 bronze loadout
129.6 iron loadout
691.2 lead loadout

It is now tricky to figure out how much credits you will save by earning a higher tier loadout simply because it depends on your set. Every combination will lead to different saving, e.g: whether you gain the gold cards in the really last or really first cards.

A simple way to do that would be to create a Python script that mimic a player, i.e., algorithmically:

  1. Get a card
  2. if you can make a higher tier card with this card, do it, compute cost and goto 1, else goto 1

do this model say N times and check the stats.

If there is enough demands and if these thread go sticky, I can do this script and post the results. Let me know.
Note that I might edit this post accordingly.

First EDIT: copy paste of a message I wrote below.

http://i.imgur.com/UKn58YB.png

So I did the python script to compute the real price of a cobalt loadout card of the merc of your choice. I assumed that we will always buy the initial case (1000 cred). But I took into account the fact that you could earn higher tier loadouts than lead ones.

The results are in the image (the x-axis unit is the credit, my bad, and the y-axis is to have it normed, don’t look at the number).

Finally, the cost of a loadout card is in average about 500000 credits, half the price we would have if we could get only lead cases.

Meanwhile, by doing so, you will earn in average 0.316 spare cobalt card (of an unwanted merc).

For those who are interested, here is the python script (Edit, of course, indent doesn’t work here… I ll find a way later). Note that the code is absolutely not optimized and written in a way that people with no coding experience can read it.
[spoiler]
import random as ra
import numpy as np
import pylab as py

cost_list = []
second_cobalt_list = []
for i in range(1000):
cost = 0
second_cobalt = 0
cobalt = 0
gold = 0
silver = 0
bronze = 0
lead = 0
iron = 0
ra.seed(i)

while cobalt == 0:
new_loadout = ra.randint(1,1000)
cost = cost + 1000

if new_loadout == 1:
  second_cobalt = second_cobalt + 1
elif new_loadout >= 2 and new_loadout <= 5:
  gold = gold + 1
elif new_loadout >= 6 and new_loadout <= 21:
  silver = silver + 1
elif new_loadout >= 22 and new_loadout <= 52:
  bronze = bronze + 1
elif new_loadout >= 53 and new_loadout <= 203:
  iron = iron + 1
else:
  lead = lead + 1

if lead == 3:
  lead = 0
  iron = iron + 1
  cost = cost + 500
if iron == 3:
  iron = 0
  bronze = bronze + 1
  cost = cost + 1000
if bronze == 4:
  bronze = 0
  silver = silver + 1
  cost = cost + 2000
if silver == 4:
  silver = 0
  gold = gold + 1
  cost = cost + 4000
if gold == 6:
  gold = 0
  cobalt = cobalt + 1
  cost = cost + 10000

cost_list.append(cost)
second_cobalt_list.append(second_cobalt)

print(‘In average, you will earn’,np.mean(second_cobalt_list),‘spare cobalt cards’)
n, bins, patches = py.hist(cost_list, bins=100, normed=1, histtype=‘stepfilled’)
py.xlabel(“Cobalt loadout cost”)
py.ylabel(“Probability”)
[/spoiler]


(Thai-San) #2

Thanks for doing the math and everything but I disagree with lead being the same price as a case. For me every 3rd-5th card is Iron and sometimes even better so lead should be a little cheaper then a case.

Maybe like 900-800.


(Izzy) #3

[quote=“ThaiSan;107299”]Thanks for doing the math and everything but I disagree with lead being the same price as a case. For me every 3rd-5th card is Iron and sometimes even better so lead should be a little cheaper then a case.

Maybe like 900-800.[/quote]

What do you mean? that’s the price at which you buy it, I can’t change that. However, as I said, the total price of a card, gold or cobalt will be less thanks to the proba of getting higher tiers cards, but then, you ll need more complex method to investigate the impact of this, like doing the proper proba calculation or using monte-carlo analysis.


(Ardez1) #4

You might find this old thread interesting.
http://forums.dirtybomb.nexon.net/discussion/comment/34098/

Just a snippet of that overall discussion there.

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


(DB Genome editor) #5

@Ardez I’m not following how you got to this conclusion:

This assumes that what you get at each level of rarity has the same value, but I don’t see a justification for this. Also, the resulting values don’t seem to hold up when you look at Bronze vs Iron: as per you figures, a completely random Bronze (random merc and loadout) is worth 5 completely random Irons, but you can get a merc-specific Bronze for a little less than 4 Iron (3 Irons@1,111 Cr + 1,000 Cr trade-up fee). More value (less random) for less cost…

All we have to establish relative value between rarity levels are the trade-up formulas, but those can’t apply directly to completely random drops like those from cases because trade-ups convert fully-random cards into merc-specific ones. We know the value of a random Bronze has to be less than 3 random Irons + 1000 Cr (i.e. the value of a merc-specific card), but how much less?


(watsyurdeal) #6

Personally I feel like anything more than 5000 credits and 3 cards for a trade up is absurd. 6 gold cards is literally 24000 credits, just for the trade ups.

Imo, here’s how it should be

Trade ups

Iron - 3 lead + 500 credit charge
Bronze - 3 Iron + 1000 credit charge
Silver - 3 Bronze + 2000 credit charge
Gold - 3 Silver + 4000 credit charge
Cobalt - 3 Gold + 8000 credit charge

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.


(ImSploosh) #7

[quote=“Watsyurdeal;107395”]Personally I feel like anything more than 5000 credits and 3 cards for a trade up is absurd. 6 gold cards is literally 24000 credits, just for the trade ups.

Imo, here’s how it should be

Trade ups

Iron - 3 lead + 500 credit charge
Bronze - 3 Iron + 1000 credit charge
Silver - 3 Bronze + 2000 credit charge
Gold - 3 Silver + 4000 credit charge
Cobalt - 3 Gold + 8000 credit charge

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.
[/quote]

I’ve read in multiple threads that the trade-in/up system will be reworked entirely or will be changed in some ways in the future. What makes no sense to me personally is the trade-in system. 3 cards for a card of the same rarity? It’s pointless. I’d rather keep the cards.

Not to mention you can trade in 3 iron cards for a bronze, so why trade in 3 irons for another iron? Who in their right mind would trade 3 Cobalts for 1 Cobalt? Even if they’re Cobalts you don’t like or wouldn’t use. Just seems a bit absurd to me.

Maybe 1 card+some credits for the trade-in? That would be much better and make a bit more sense in my opinion.


(Armuh) #8

With the trade-ins are you assuming that you can choose what card you get?
Cos imo 3 cobalts traded in just for another random cobalt isn’t worth it no matter how cheap the credit cost is.


(watsyurdeal) #9

[quote=“Armuhsin;107451”][quote=“Watsyurdeal;107395”]

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.
[/quote]

With the trade-ins are you assuming that you can choose what card you get?
Cos imo 3 cobalts traded in just for another random cobalt isn’t worth it no matter how cheap the credit cost is.[/quote]

Well if you guys prefer, there could be a system like this

3 cobalt fraggers = 1 cobalt fragger of your choice

So, imagine the store, with the bronze loadouts, same thing. But instead you trade in cobalts for a specific one of your choice.


(CCP115) #10

[quote=“Watsyurdeal;107454”][quote=“Armuhsin;107451”][quote=“Watsyurdeal;107395”]

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.
[/quote]

With the trade-ins are you assuming that you can choose what card you get?
Cos imo 3 cobalts traded in just for another random cobalt isn’t worth it no matter how cheap the credit cost is.[/quote]

Well if you guys prefer, there could be a system like this

3 cobalt fraggers = 1 cobalt fragger of your choice

So, imagine the store, with the bronze loadouts, same thing. But instead you trade in cobalts for a specific one of your choice.
[/quote]

I feel as though trade ins should be 1 for 1, but with a ridiculous credit cost, 30k-50k even. Because who wants to trade away 2 cobalts for the change to get another terrible one? With a 1 to 1 system, you could reroll that same card infinitely, but it would be a huge credit setback. The fact that you also can’t buy credits means that you HAVE to play the game to get credits. At which point you could potentially trade up to another cobalt anyway.


(Ctrix) #11

5000 Credits = 1€

Silver Loadout = 9.60€
Gold Loadout = 39.20€
Cobalt Loadout = 235.20€


(Izzy) #12

http://i.imgur.com/UKn58YB.png

So I did the python script to compute the real price of a cobalt loadout card of the merc of your choice. I assumed that we will always buy the initial case (1000 cred). But I took into account the fact that you could earn higher tier loadouts than lead ones.

The results are in the image (the x-axis unit is the credit, my bad, and the y-axis is to have it normed, don’t look at the number).

Finally, the cost of a loadout card is in average about 500000 credits, half the price we would have if we could get only lead cases.

Meanwhile, by doing so, you will earn in average 0.316 spare cobalt card (of an unwanted merc).

For those who are interested, here is the python script (Edit, of course, indent doesn’t work here… I ll find a way later):
[spoiler]
import random as ra
import numpy as np
import pylab as py

cost_list = []
second_cobalt_list = []
for i in range(1000):
cost = 0
second_cobalt = 0
cobalt = 0
gold = 0
silver = 0
bronze = 0
lead = 0
iron = 0
ra.seed(i)

while cobalt == 0:
	new_loadout = ra.randint(1,1000)
	cost = cost + 1000
	
	if new_loadout == 1:
		second_cobalt = second_cobalt + 1
	elif new_loadout >= 2 and new_loadout <= 5:
		gold = gold + 1
	elif new_loadout >= 6 and new_loadout <= 21:
		silver = silver + 1
	elif new_loadout >= 22 and new_loadout <= 52:
		bronze = bronze + 1
	elif new_loadout >= 53 and new_loadout <= 203:
		iron = iron + 1
	else:
		lead = lead + 1
		
	if lead == 3:
		lead = 0
		iron = iron + 1
		cost = cost + 500
	if iron == 3:
		iron = 0
		bronze = bronze + 1
		cost = cost + 1000
	if bronze == 4:
		bronze = 0
		silver = silver + 1
		cost = cost + 2000
	if silver == 4:
		silver = 0
		gold = gold + 1
		cost = cost + 4000
	if gold == 6:
		gold = 0
		cobalt = cobalt + 1
		cost = cost + 10000
cost_list.append(cost)
second_cobalt_list.append(second_cobalt)

print(‘In average, you will earn’,np.mean(second_cobalt_list),‘spare cobalt cards’)
n, bins, patches = py.hist(cost_list, bins=100, normed=1, histtype=‘stepfilled’)
py.xlabel(“Cobalt loadout cost”)
py.ylabel(“Probability”)
py.show()
[/spoiler]

Maybe I should make a new post for that result which is quite interesting I think.
What do you guys think, and what should I compute next?

I have copy pasted this message in my first one.


(B_Montiel) #13

Great work ! The code : “new_loadout = ra.randint(1,1000)” is generating a random number, isn’t it ? (I don’t really know python’s syntax).

In my mind, an interesting next step would be to add the trade-up probability process : The guy is looking for both specific rarity and at least one out of n loadout cards from a specific merc. As an example, what is the average cost to get CR73 or CR42 Sawbonez in gold rarity.

I was searching a bit about getting the probability to get expected loadouts after x numbers of trade-up draws. I can write a sum-up if you want (at least my probability process behind it).


(Izzy) #14

Well, I have been lazy, here’s some explanation.

What I do is to take a random number between 1 and 1000 included:
new_loadout = ra.randint(1,1000)

regarding the number, it either translates to a cobalt, gold or else:
elif new_loadout >= 2 and new_loadout <= 5: …

and if I can make a combination with cards I have, I do it:
if lead == 3:
lead = 0
iron = iron + 1
cost = cost + 500

I end up once I have my cobalt card only and repeat these steps N times with new seeds to ensure some good statistics:
for i in range(1000):
ra.seed(i)

In the end, you end up with this nice illustration of the central limit theorem.

I could add your process, but I am not sure on how many combination you can make with loadout cards. Are there only the one you can buy for 15000 creds each? I that case, sure, I can do it. For instance, if you want one weapon or one augment specifically, that turns out to be that many cards out of the possible merc cards. But then, you need to introduce trade-in as well as it might be cheaper. That can be done with some recurrence, but I believe this is still premature as trade-in is still broken.


(Eox) #15

[quote=“Watsyurdeal;107454”][quote=“Armuhsin;107451”][quote=“Watsyurdeal;107395”]

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.
[/quote]

With the trade-ins are you assuming that you can choose what card you get?
Cos imo 3 cobalts traded in just for another random cobalt isn’t worth it no matter how cheap the credit cost is.[/quote]

Well if you guys prefer, there could be a system like this

3 cobalt fraggers = 1 cobalt fragger of your choice

So, imagine the store, with the bronze loadouts, same thing. But instead you trade in cobalts for a specific one of your choice.
[/quote]

Feels much better IMO. At least you are assured to beat RNG after the 3rd card rolled.


(B_Montiel) #16

[quote=“Izzy;107763”]
[…]
I could add your process, but I am not sure on how many combination you can make with loadout cards. Are there only the one you can buy for 15000 creds each? I that case, sure, I can do it. For instance, if you want one weapon or one augment specifically, that turns out to be that many cards out of the possible merc cards. But then, you need to introduce trade-in as well as it might be cheaper. That can be done with some recurrence, but I believe this is still premature as trade-in is still broken.[/quote]

The process is quite clear to me then, thank you.
So far, for trade-up, you don’t necessarily need to go this specific : The general target of players is to get one of the loadout they consider acceptable.
Generally I think we could say the player is looking for N acceptable loadouts during a trade up (1 to 3 in most cases).
So, considering your statistical analysis, that’s just adding a “dice roll” with results from 1 to 9 when you get the excepted card rarity if the card is made via trade-ups (N/9 possible loadouts). For random drops, that’s N / (Number of mercs (17 currently) * Number of loadouts (9 for each merc currently)). Rinse and repeat if it fails, etc.


(Izzy) #17

I am sure that the game devs have already done this analysis and probably an even more advanced one (Well, I hope so. The opposite would be insane).

I would be glad to see some of their results and why they made this choice.
I don’t know how but that would be nice if someone could have the game devs attention on this thing to have some more light on this.

They already go quite transparent as they ask us feelings on trade-in, I am sure they wouldn’t mind talking about it.


(retief) #18

[quote=“Eox;107771”][quote=“Watsyurdeal;107454”][quote=“Armuhsin;107451”][quote=“Watsyurdeal;107395”]

Trade ins

Iron - 3 Iron+ 250 credit charge
Bronze - 3 Bronze + 500 credit charge
Silver - 3 Silver + 1000 credit charge
Gold - 3 Gold + 2000 credit charge
Cobalt - 3 Cobalt + 4000 credit charge

That would cut down at least a significant portion of the credit costs.
[/quote]

With the trade-ins are you assuming that you can choose what card you get?
Cos imo 3 cobalts traded in just for another random cobalt isn’t worth it no matter how cheap the credit cost is.[/quote]

Well if you guys prefer, there could be a system like this

3 cobalt fraggers = 1 cobalt fragger of your choice

So, imagine the store, with the bronze loadouts, same thing. But instead you trade in cobalts for a specific one of your choice.
[/quote]

Feels much better IMO. At least you are assured to beat RNG after the 3rd card rolled.[/quote]

Something like this could work, but if it works for bronze cards, they’d need to look at the price for buying specific bronze loadouts. Currently, 3 bronze cards + ~2k credits is a lot cheaper than direct buying the loadout.


(B_Montiel) #19

[quote=“Eox;107771”]
Feels much better IMO. At least you are assured to beat RNG after the 3rd card rolled.[/quote]

Beat the randomness on a casino table, you’ll get kicked out in less than an hour. Sadly, random systems need to stay random through all their aspects to remain profitable for the sellers… Of course a 3 to 1 for a sure trade-in sounds like a fair bet. But it’s a definite straight loss for the seller as you’ll have what you were looking for in a trusty way. Keep in mind, this just defeats the purpose of such systems… Which is trying to keep you in the need as long as possible.


(Matuno) #20

You have a lot of faith for the guys that brought out the Trade In system the way it is now.