single booster value

madwren

Out of curiosity, would anyone pay any number of crystals for a regular, plain ol' 5-card Kaladesh booster?

I could see paying 1. But maybe I'm underrating how others perceive their value.

Mainloop25

For an extra 6th card that is a guaranteed non-dupe uncommon, I'd pay 40. This supposes that I still have the same chance to get a rare or mythic.

majincob

Well, back when I thought that a BB had an expected value of 1 mythic, with a small chance of the extra rare being upgraded to a mythic, I would buy a BB whenever I got above 2600 to chase missing mythics and rares.

But the expected value of mythics / BB is actually closer to 0.5 so the cost was actually double what I'd pay.

Basically I'd pay ~300 :crystal: for a random mythic as long as I'd get 1-3 random rares with it.

Since they don't post odds of getting rares/mythics it's hard to say what the actual value to me is. If I had to guess I'd say at most 1 pack is worth 30 to me assuming that it is part of the Premium pack with it's non-upgrade-able guaranteed rare. And if it's just a single pack by itself I'd put it closer to 15-20 .

madwren

Thanks. I appreciate the maths so I could follow the thought process.

Certainly I've gotten the surprise mythic or rare from them--in fact, I opened 7 boosters today and got 5 rares and a mythic, though they were dupes. However, judging by reports, that's the exception rather than the rule, and I was the beneficiary of some RNG luck.

However, since prior to this point the chances of getting a rare or mythic from a 5-card booster are indeed very low, I value them as essentially junk, because it's always wiser to save for a big box.

AngelForge

I saw a statistic in some post done by users. If I remember correctly the chance to get a mythic is less than one percent.
So, you can assume to get a mythic every 5 super packs (or 25 single booster) you open.

bk1234

Don't we consistently advise new and mid level players not to do this?

The value for new and mid level players is in PW and boxes or whatever the heck they are called now.

High level players generally have most if not all the commons and uncommons and so there's absolutely no use in buying a single pack.

However if single packs went back to costing runes I would probably buy the heck out of them just to have something to spend my runes on.

AngelForge

But now thinks have quite changed because you don't get extra boosters anymore by buying bigger packs.
Still, you get one extra rare card, which makes buying super packs more efficient than buying booster packs.

So, the advice still kind of stays the same.

"Listen boy, don't spend 60 crystals for a booster. And don't try to sneak around that by entering "pay 2 participate" events!" ^^

Ohboy

madwren wrote:

Thanks. I appreciate the maths so I could follow the thought process.

Certainly I've gotten the surprise mythic or rare from them--in fact, I opened 7 boosters today and got 5 rares and a mythic, though they were dupes. However, judging by reports, that's the exception rather than the rule, and I was the beneficiary of some RNG luck.

However, since prior to this point the chances of getting a rare or mythic from a 5-card booster are indeed very low, I value them as essentially junk, because it's always wiser to save for a big box.

Let's do some actual math :

We'll use old boosters as reference to avoid distracting arguments about how bad new boosters are.

Let's put the value of a guaranteed rare as R.

Value of each booster in a big box = (600-R)/14 = 42.85 - R/14.

Value of R approaches 0 as your rare collection fills up. For a hypothetical elite player I'm just going to assume his R value is 0.

In other words, as of 24 hours ago, his best value for crystals was to buy packs at 42.85 crystals each. Let's say he will buy these packs at no more than 20 crystals each, and is a rational actor. He will never come close to being tempted to open boosters in any form.

What if his R wasn't 0? Working backwards, we know that for him 42.85-R/14 = 20. So he values a random guaranteed rare at about 320 crystals.

Taking it a step further, let's assume he will pay about 300 for a pack with a guaranteed mythic and 1-3 rares. Let's average that to a mythic and 2 rares. Going back to our equation with M=crystals he will pay for mythics :

M+2R = 300
M = 300-(320X2)
M = -340

Not bad! 340 is pretty close to the 350 guaranteed mythic pack price we got at Chris... Wait is that a negative sign?

Anyway all jokes aside, unless you're lacking a lot of rares, the price of a booster is close to 40. So the conclusion to draw in regards to the new event is(for platinum), if you can max out progression, you're paying 60 crystals for:

A booster pack (35-40)
Mana jewel rewards(15J)
Final reward(10)

So each jewel costs about 1 Crystal or slightly less. Of course we're gonna lose some games, so let's assume we lose half our games. That's about a cost of 3-4 crystals per jewel. That's if you lose half your games. Every game you win more than half decreases the cost of a jewel by quite a bit.

I value a guaranteed mythic from a selectable pool of just 5 to be greater than 1k crystals. That's why I'm not complaining about this.

Basically this deal gets sweeter the more rares and mythics you already own. You can put it in a spreadsheet and figure out where you stand.

losdamianos

madwren wrote:

Out of curiosity, would anyone pay any number of crystals for a regular, plain ol' 5-card Kaladesh booster?

I could see paying 1. But maybe I'm underrating how others perceive their value.

ahhahahhahahhahah
why would I pay 60 crystals for single boosters when I used to get 14 packs for 600 which is 42 crystals each pack plus higher chance/guaranteed rare
I dont think anyone would perceive 60 crystals per pack as more appealing than the one which costs 42

@up I didnt notice your comment which puts it much more nicely

majincob

Ohboy wrote:

Basically this deal gets sweeter the more rares and mythics you already own. You can put it in a spreadsheet and figure out where you stand.

You are saying the value increases in playing because the relative value of increases as the value of a pack decreases? It doesn't seem that simple to me as the value of the Masterpiece pack decreases the more potential dupes there are to pull.

Ohboy

majincob wrote:

Ohboy wrote:

Basically this deal gets sweeter the more rares and mythics you already own. You can put it in a spreadsheet and figure out where you stand.

You are saying the value increases in playing because the relative value of increases as the value of a pack decreases? It doesn't seem that simple to me as the value of the Masterpiece pack decreases the more potential dupes there are to pull.

Yup, let's go back to the equation.

Let P be the value of a single booster pack. As I've already worked out above,

P = 42.85-R/14 *ammended*, where R is the value of a random guaranteed rare

Assuming a perfect clear in the game, we get:

15J+P+10 = 60, where J is the value of each in a perfect clear

Assuming the worst most people will do in platinum is a half clear, the worst value you should get out of it is

6J+P = 60.

Notice that the value of P goes up as R goes down, and R goes down as the number of rares missing in your collection goes down.

So we can conclude that P is inversely proportional to R. In other words, the value of a pack of boosters increases as you have more unique rares.

The value of J is inversely proportional to the value of P no matter how well you do. So each costs you more the less rares you have.

That's for rares. Let's look at mythics now.

For this, let's assume the pack contains a pool from only 5 mythics from the current expansion. To do this, we must also assume to agree that a chance to hit a random masterpiece is always value added in a booster. But I'm sure we will have no argument there.

Here's the important part. You know exactly what 5 mythics are in the pool, and you're capable of waiting as long as you like for different ones to rotate in.

Let X be the number of mythics in the pool you already own. The Expected Value(EV) by redeeming a pack is:

EV = 400J-(X/5*400J)

Using our previously defined range, J is a max cost of (60-P)/6, and min cost of (50-P)/15. If P =35(which most mid tier players should roughly be at), we get J = 4 (max cost) and J = 1(min cost). That's just for reference since we're already doing the math anyway. It doesn't matter for the final part.

Octal's spreadsheet shows a 0.83% chance of any card being a mythic, which translates to 58% chance of hitting a mythic per big box costing 600.


The expansion roughly has 45 non exclusive cards, give or take. For simplicity, let's just say it has 50. Let's let the number of mythics you already own from this expansion by Y

The expected value by redeeming a big box is thus

EV = 600- (Y/50*600)
EV = 600-12Y

Let's compare the two:

(value in opening a pack)
EV = 400J-(X/5*400J)
As shown before, if you're a really gosu player, J=1. We'll just use J=1 because it's easy.
EV = 400-(X/5*400)
EV = 400-80X

(value in opening a big box)
EV = 600-12Y

Remember X is a number between 0 and 5 that you can theoretically manipulate by waiting, so X can be 0, which means you can theoretically always gain full value for opening a pack, while you'll always lose 12Y by opening a big box.


Remember, you can wait till X is favourable to you, which becomes easier as your value of Y increases. Hence, as Y(the number of mythics in the big box pool you own, in case you've lost track) increases, the greater the comparative value the booster holds.



I might have made some errors above, but the idea should be roughly there.

majincob

Ohboy wrote:

So we can conclude that P is inversely proportional to R. In other words, the value of a pack of boosters increases as you have more unique rares.

False.

Ohboy wrote:

P = 42.85+R/14, where R is the value of a random guaranteed rare

As stated, P is directly proportional to R. As R decreases, P decreases.

Ohboy

majincob wrote:

Ohboy wrote:

So we can conclude that P is inversely proportional to R. In other words, the value of a pack of boosters increases as you have more unique rares.

False.

Ohboy wrote:

P = 42.85+R/14, where R is the value of a random guaranteed rare

As stated, P is directly proportional to R. As R decreases, P decreases.

You're right. I got confused. I'll ammend it. the equation is P=42.85-R/14.

I copied it wrong.

majincob

Ohboy wrote:

You're right. I got confused. I'll ammend it. the equation is P=42.85-R/14.

I copied it wrong.

Making the equation a false statement doesn't help

The value of a pack is the sum of the expected value of the cards inside.

Vp = (Vx*X + Vm*M + Vr*R + Vu*U + Vc*C)*5

Where Vp is the value of the pack, Vx-Vc are the value of the respective card types and X,M,R,U,C are the probabilities of pulling Masterpieces, Mythics, Rares, Uncommons, and Commons respectively. And times 5 because there are 5 pulls per pack.

The value of the card types can be expressed as follows:

Vn = $n * P(n)

$n : price customer is willing to pay for a non-dupe rarity n
P(n) probability of a random card of rarity n not being a duplicate

The probability of a a random card of rarity n not being a duplicate, P(n) is inversely proportional to the number of cards of that type I have:

P(n) = (total cards - cards I already have)/(total cards)

Now that I have all the formulas spelled out, let's use my collection and calculate my expected value from a pack.

First I'm going to use span_argoman's calculated drop rate as it's the largest sampling I'm aware of.

C: 53.72% - adjusted see X below.
U: 41.16%
R: 04.16%
M: 00.87%
X: unknown - but less than M to be sure, let's give it an arbitrary number like 0.08% (1 Masterpiece for every 10 mythics) and shave that off the Commons %

Next I'm going to assume this is an imaginary 5-card pack that can pull any card from any set to average the generic price across all the sets.

The third assumption I'm making is the value of non-dupe cards. I'll set it at $29.99 for a mythic and $4.99 for a rare based on the special offers we have gotten in the past. I will even be generous and assume all the extras are bonus and don't add to the value of those offers. I will also use the worst rate of purchase: 100 for $4.99. So a non-dupe mythic is worth 600 and a non-dupe rare is worth 100 . Uncommons and Commons are harder to price, but let's again be generous and assume they are both worth about the same at 20 . Masterpieces can be calculated by assuming you have a 3/8 chance of getting one from the new packs which cost 400 .

550 + 2000 = $99.99 = 3000 .
550 = 1000
400 = 727
$x = 8/3 * 727 = 1940

The last piece is my collection:

C: 322/322
U: 351/355
R: 198/229
M: 88/134
X: 0/19

So for me the value is:

C: 20 * 0 * 0.5372 = 0.0000
U: 20 * (355-351)/355 * 0.4116 = 0.0928
R: 100 * (229-198)/229 * 0.0416 = 0.5631
M: 600 * (134-88)/134 * 0.0087 = 1.7919
X: 1940 * 1 * .0008 = 1.552

Vp = 5*∑($n*P(n)*N) = 5 * 3.9998 = 19.999

The expected value of a 60 pack to me is 20

Note that almost all the value from the pack comes from mythics and masterpieces because I am missing a good number of them combined with their higher worth.

So in Platinum with the event, the 60 get's me 20 worth of expected value of cards, 10 and 15 which are worth 27.26 so I would turn 60 into 67.26 with a perfect record and 57.26 with just one loss.

Additionally, my personal value may differ from the set value. For instance I wouldn't pay 1940 for a non-dupe Masterpiece, maybe 800 if I'm feeling generous, but the truth is I'd rather get many missing mythics over masterpieces. In fact if you just used P(n) to express the probability of getting a card I want of rarity n, the expected value of the pack plummets making the event a clear loser in terms of prize/price value.

span_argoman

Majincob, while I think the equations work out, however I would like to point out that we should compare it to your next best alternative for spending crystals. I think we commonly assume that to be the Big Box of pre-1.10.2, so I were to use your values for a Big Box (ignoring the percentage chance for the guaranteed rare to be upgraded to a mythic), you would be getting an expected value of
(With Vr being 100 * (229-198)/229 = 13.5371 )
70 * 3.9998 + 13.5371 = 293.5 for 600

In which case then converting 60 for 57.26 to 67.26 worth of your utility would be a much superior trade.


Btw I noticed you used the numbers for 1.6 - 1.8.1 so here's the latest set of numbers I have (it's at the end of the survey in my signature):
1.6 - 1.10.1
1.6 - 1.10.1
All packs, total 4,785 cards
C: 2,569 (53.69%)
U: 1,958 (40.92%)
R: 0,209 (04.37%)
M: 0,049 (01.02%)

There's some variance from octal9's numbers but in any case that is tweakable. Octal9's numbers for reference:
Total 6,293 cards
C: 59.34%
U: 35.72%
R: 4.07%
M: 0.87%

ErikInVegas

Ohboy wrote:

Remember, you can wait till X is favourable to you, which becomes easier as your value of Y increases. Hence, as Y(the number of mythics in the big box pool you own, in case you've lost track) increases, the greater the comparative value the booster holds.



I might have made some errors above, but the idea should be roughly there.

Exactly backwards.

What actually happens is people who have excess crystals will overpay for something of little or no value the same way people with excess XP will level PWs they don't intend to use. There's simply nothing else for them to do with it.

majincob

span_argoman wrote:

Majincob, while I think the equations work out, however I would like to point out that we should compare it to your next best alternative for spending crystals. I think we commonly assume that to be the Big Box of pre-1.10.2, so I were to use your values for a Big Box (ignoring the percentage chance for the guaranteed rare to be upgraded to a mythic), you would be getting an expected value of
(With Vr being 100 * (229-198)/229 = 13.5371 )
70 * 3.9998 + 13.5371 = 293.5 for 600

In which case then converting 60 for 57.26 to 67.26 worth of your utility would be a much superior trade.

Good point, thank you. As a crystal spending outlet it does appear to be the best value. The problem I have with it is it does not compare favorably compared to other events since they set a baseline value for time/effort spent on them. It would be interesting to calculate / event earned before and after this latest patch.

span_argoman wrote:

Btw I noticed you used the numbers for 1.6 - 1.8.1 so here's the latest set of numbers I have (it's at the end of the survey in my signature):
1.6 - 1.10.1
1.6 - 1.10.1
All packs, total 4,785 cards
C: 2,569 (53.69%)
U: 1,958 (40.92%)
R: 0,209 (04.37%)
M: 0,049 (01.02%)

There's some variance from octal9's numbers but in any case that is tweakable. Octal9's numbers for reference:
Total 6,293 cards
C: 59.34%
U: 35.72%
R: 4.07%
M: 0.87%

Thank you for the update. I might have to start a spreadsheet EV calculator. Maybe Octal9 could build it into his website (since you can input your collection there).

buscemi

I think all this maths is failing to take one thing into account: It assumes that all of us want to convert our crystals into offers that already exist.

I'm sat on 2.5k crystals now, and I'm waiting for something brand new to spend them on. I own enough of KLD, and indeed SOI, BFZ and Origins (why would you buy KLD when you can buy SOI? Masterpieces? *snort*). However I choose to spend crystals on boosters, I'm never going to get the same rate of return in non-dupe rares and mythics as I will when a brand new set comes out. I'm going to drop a substantial proportion of my saved up sum on the next set Amonkey. Anything left over, I'm going to save up for random offers that might come out of the blue. The last Mythic-only offer cost 1,650, and was better value to me than any boosters in any combination. I imagine the next one will be worse value, since in the MTGPQ world the passage of time is directly proportional to an increase in value, but I'm going to save up my crystals and see. Add to that any new PWs that come along, and in a couple of months time I won't even have change left over from my 2.5k crystals.

Not only is it not worth spending real money on the game, it's not even worth spending the imaginary money that they give away to me free at the moment.

I look around facebook and it seems to me that an awful lot of of other top players seem to have figured this out too, and are sitting on at least 1000+ crystals. I think D3 noticed that and introduced the TOTP crystal sink into the game. Unfortunately for them, the new currency system isn't opaque enough, and we figured it out.

wink

Yup. Doing the same thing for the same reasons. Probably started at the same time as you too, but am only grinding the crystals half as fast, so am only at 1.2k. Lol