Why would you ever buy a 40 pack?

20three

Unless I'm deliriously tired and can't seem to math right now, it doesn't add up.

The daily sale prices heroic tokens at 100 hp, times that by 40 and you get 4000. That is a third the cost of a 40 pack. So unless you are an impatient fool and can't wait 40 days, why would you ever buy a 40 pack? It's not even like the odds are significantly better as it claims on the bottom, an extra .1% for 3 stars vs 2? WOW! The legendary token it comes with is not worth about 7000 hp to be honest, I just don't get it.

fmftint

do you get a buying 40 singles?

didn't think so

Unknown

if all players used logic before deciding to purchase something, d3 wouldn't earn a penny anymore.

XandorXerxes

I could have sworn the odds used to be better if you bought 10 or 40 packs, but looking at them now... doesn't seem to be. 3*s go from .6% each to .7%, that's about it.

It really comes down to the guaranteed LT, and the instant rewards mentality. How many HP would you pay for that chance at a 5* cover and/or a 4* guarantee?

If you're just looking at the math, the odds of not pulling a 4* cover in a 40-pack are very small - 14% (this includes you pulling IW and Star-Lord though, and I've still managed to do not pull any 4*s in four 10-packs). However, if you're specifically looking for a top-10 4* you have a 45% chance of not pulling one. Top 5? 67% chance. Assuming 112 pulls though (the price of a discounted 40-pack in terms of HP expenditures at 100 for a single token), and your odds of a top-10 are now 89.5% and a top-5 are 67.6%.

Given that 5*s are a 10% shot, and each 4* is a 3.8% shot... that's a 29% shot of a top-5 4* and a 48% shot of a top-10 or 5* in one LT. When you combine that with the other 40 tokens from the heroic you get:

5*: 10%
top-5 4*: 45.73%
top-10 4*: 65.9%

If you want a specific 4* (ex: Ice Man, not Ice Man Blue):

40-pack: 7.7% of pulling it not counting the LT. 11.21% including the LT.
112 tokens: 20.1% of pulling it.

Ergo, if you are spending 11,200HP on heroic tokens, unless you want that 10% shot at a 5* you are going to want to buy individual tokens, assuming you can tolerate waiting 112 days.

These are all pretty low odds in general, so take that for what it's worth. Also, because I got curious:

Number of heroic tokens required to pull a specific 4* with >90% accuracy: 1151
Number of Legendary tokens required to pull a specific 4* with >90% accuracy: 60
Number of Legendary tokens required to pull a specific 5* with >90% accuracy: 69
Number of Legendary tokens required to pull a specific cover of a specific 5* with a >90% accuracy (assumes even distribution of covers): 209

wymtime

Another way to look at it is if you want Nova your odds are better to pull the 40 pack then the daily deal plus 39 more. It is the same odds but an increase in odds. If you have most characters maxed and the HP to do so you will be able to use the extra covers you pull as well. It becomes a really bad deal if you don't have a lot of characters championed and you have to sell the covers for ISO. You get the same covers and a LT in one go.

puppychow

Last off season, I bought a 40 cover pk for 10k hp. It helped me build my 2* champs, and the dups were sold for iso to champ a few more 3*, which in turn gave me more LT tokens (including a Phoenix green that I was missing). My 40 pk purchase was a good decision, as it gave a jolt to my roster. So it really depends on your personal situation, to some degree.

Eddiemon

20three wrote:

Unless I'm deliriously tired and can't seem to math right now, it doesn't add up.

The daily sale prices heroic tokens at 100 hp, times that by 40 and you get 4000. That is a third the cost of a 40 pack. So unless you are an impatient fool and can't wait 40 days, why would you ever buy a 40 pack? It's not even like the odds are significantly better as it claims on the bottom, an extra .1% for 3 stars vs 2? WOW! The legendary token it comes with is not worth about 7000 hp to be honest, I just don't get it.

It's rounding issues. If you look at the 2*s you'll realise there is a 4-5% reduced chance of pulling a 2* when you add them all up. This isn't reflected in the changes to the 3 and 4 star categories due to rounding.

IIRC your chance of pulling a 4% goes from 3.8 to 4.8% and your chances of pulling a 3* also increase. And you get a legendary which guarantees a 4* or better.

If you draw 120 tokens at 4% chance of a 4* you can expect around 4.8. If you draw the 40 at 5% and add in the legendary you can expect 3.0. The thing is you have the 3 now as opposed to over the course of the next 3 months for the same HP. (and I know I did some rounding there, but I'm lazy)

GurlBYE

Because you've got a lot of money and a different value proposition.

IFORANI

Only buy one is with 80 vaults.

GurlBYE

Also why heroic when the others have bonus percentages?

XandorXerxes

Eddiemon wrote:

20three wrote:

Unless I'm deliriously tired and can't seem to math right now, it doesn't add up.

The daily sale prices heroic tokens at 100 hp, times that by 40 and you get 4000. That is a third the cost of a 40 pack. So unless you are an impatient fool and can't wait 40 days, why would you ever buy a 40 pack? It's not even like the odds are significantly better as it claims on the bottom, an extra .1% for 3 stars vs 2? WOW! The legendary token it comes with is not worth about 7000 hp to be honest, I just don't get it.

It's rounding issues. If you look at the 2*s you'll realise there is a 4-5% reduced chance of pulling a 2* when you add them all up. This isn't reflected in the changes to the 3 and 4 star categories due to rounding.

IIRC your chance of pulling a 4% goes from 3.8 to 4.8% and your chances of pulling a 3* also increase. And you get a legendary which guarantees a 4* or better.

If you draw 120 tokens at 4% chance of a 4* you can expect around 4.8. If you draw the 40 at 5% and add in the legendary you can expect 3.0. The thing is you have the 3 now as opposed to over the course of the next 3 months for the same HP. (and I know I did some rounding there, but I'm lazy)

If you assume a 0.25% rate for 4*s when buying a 10/40 pack (the maximum that should still round to 0.2%), you have a 7.8% chance of getting 3+ 4*s in those tokens. If you assume the minimum rate for singles - 0.15% - you have a 23% chance of pulling 3+ 4*s in 112 tokens. At the maximum rate, there is a 36% chance of pulling zero (0) 4*s in a 40-pack (sans LT, getting there). At the minimum rate, there is an 18.4% chance of getting 0 4*s in 112 singles. There's a 74% chance that you're pulling 1 or 0 4*s in heroic tokens, 50% in 112 singles assuming max/min rates. Singles, by far, have the edge over the 40-pack. If you assume only a 1% discrepancy as you do, instead of the 2% I'm using in these figures, obviously those odds even further favor singles.

The 40-pack has two advantages - the guaranteed 4* and the chance for a 5*. At 112 singles, even at the minimum 4* chance that would round to .2% you're more likely to get 3 or more 4*s than 0. It's all in the amount of risk you're willing to take. If you don't need any 4*s, obviously you shouldn't buy singles. However, if you need ISO, the 112 is much more likely to get you more ISO. If your 40-pack is 1/2 3*s, and 1/2 4*s, you will make only 2K more ISO than if your 112 singles were all 2*s. Good luck getting an all-gold-half-4* 40-pack.

GurlBYE wrote:

Also why heroic when the others have bonus percentages?

Heroics are 100/token 1/day. Others are 200/token. Their 40-packs cost more as well.

Eddiemon

GurlBYE wrote:

Also why heroic when the others have bonus percentages?

Heroic generally has the best percentages.

Take Jet, Set, Go where Nova's percentage goes from 3.6% to 4.8% You may notice there are no other 4 stars available.

Heroics have 24 4 stars available, so that 3.6%/24 is 0.15% which they show as 0.2% because of rounding. That increases to 4.8%/24 in the 10 and 40 packs which is exactly 0.2%. You've actually gained 0.05% chance per character, but the table isn't granular enough to show it. It is exactly the same bonus to 4 stars as in Jet Set.

3 stars (all 40 of them) all get a visible increase in heroics, but don't seem to get any upgrade in Jet, Set, Go. Which makes sense because the 2*s in jet set go only drop by 0.2% each where they drop by 0.4% in heroics.

So you pay more for a 40 pack in an event for no actual improvement over Heroics, but it often gives you access to characters who are not in the heroic pack yet and at better odds (at expense of the other 4 stars).

It's easier to see this by looking at how the 2 star percentages change. Because there are less 2 stars an increase in 3 and 4 star chances is more visible by how their percentages drop.

TLCstormz

What about the DDQ Vault 40 packs?

And the A/B Testing PvE 80 Item Vaults?

By the who, it is sooooo much appreciated when you mathematicians participate in these kinds of discussions!!!

Malcrof

Off season 40 packs are only 10k HP, and have boosted rates as well, i never buy 40 packs except the occasional off season, they still come with the LT.. yes i know the 40 x 100 would be cheaper.. but waiting over a month to get what i can get in 30 seconds.. i don't have that kind of patience.

puppychow

XandorXerxes wrote:

Heroics are 100/token 1/day. Others are 200/token. Their 40-packs cost more as well.

Yes and no. The offseason pvp 40 packs cost 10k (current BOP for example). Heroic is 11k

puppychow

TLCstormz wrote:

What about the DDQ Vault 40 packs?

And the A/B Testing PvE 80 Item Vaults?

By the who, it is sooooo much appreciated when you mathematicians participate in these kinds of discussions!!!

If the 80 item vault has stuff I need, yes I do clear it out on occasion. It would have to be over half useful (not sold for iso) though. DDQ? Currently hoarding 230 and 220 tacos. Will clean out when I reach 300 (or later). Nuff said.

puppychow

Malcrof wrote:

Off season 40 packs are only 10k HP, and have boosted rates as well, i never buy 40 packs except the occasional off season, they still come with the LT.. yes i know the 40 x 100 would be cheaper.. but waiting over a month to get what i can get in 30 seconds.. i don't have that kind of patience.

I used similar logic when I was looking to max champ my 2s. Now that most of them ARE champed now, I have no reason to play with RNG anymore.

Monged4life

I agreed with the logic of buying 100hp heroics being much cheaper than a 10/40 pack, so thought I'd give it a go. I have 2000 hp so will get 20 tokens over the next 20 days (for 2/3rds) of a 10 pack. Going by my last few pulls all I need to beat is 10 2*s...

First token I opened today contained a 4* (Starlord, but still...). I approve of this thread!

Calnexin

The 40-pack doesn't have any better odds than a 10-pack, either, and if I'm remembering right the cost of a 40-pack is 4x the 10 pack (at least it was around Christmas). So, given the daily deal (generally 200 hp discount per item), you save yourself 800 hp by buying 4 x 10 packs, and have the exact same draw odds.

So yeah - absolutely no reason to buy a 40-pack, even if you absolutely positively have to have it right now. You can go 4 x 10 and spend the same amount of hp with the exact same draw odds.

Monged4life

Calnexin wrote:

The 40-pack doesn't have any better odds than a 10-pack, either, and if I'm remembering right the cost of a 40-pack is 4x the 10 pack (at least it was around Christmas). So, given the daily deal (generally 200 hp discount per item), you save yourself 800 hp by buying 4 x 10 packs, and have the exact same draw odds.

So yeah - absolutely no reason to buy a 40-pack, even if you absolutely positively have to have it right now. You can go 4 x 10 and spend the same amount of hp with the exact same draw odds.

You're forgetting the 'free' legendary token. So in essence they're paying 600hp to get that, as well as the whole lot on the same day.

PeterGibbons316

10-packs and 40-packs are the quickest way to whale a new 4* character during their release event. In Jet Set Go for example Nova has a much higher draw rate than any other time, so if you want him maxed (I've seen several already) the fastest way to do it is to buy the single, 10-pack, and 40-pack every day to try and get as many covers as you can afford.

I got 2 covers on release, another during the event, and two from the singles that I bought every day / earned during the event, and now have a L111, 1/2/2 Nova. Not super impressive, but still damn good for a character that was just released because I was able to take advantaged of the increased draw rates during the release.