Cover packs - probabilities of getting x covers

Moon Roach

Here's something I put together using Excel, then Google docs. I considered sharing the document, but couldn't figure out how to do it without compromising my secret Roach identity.

At 0.3%, which is Ant-Man in Enemy of the State (aka new 4*), the odds of drawing 0 from a 10-pack is 97%, from a 42-pack it's 88%. There's an 11% chance of getting 1 from the 42 pack.



At 1.4%, which is Elektra in Enemy of the State (aka essential 4* in PVE), the odds of drawing 0 from a 10-pack is 87%, from a 42-pack it's 55%. You're 99% likely to get 1 or fewer from the 10-pack, 98% likely to get 2 or fewer from the 42-pack, most likely to get 0.



At 1.8%, which is any of the featured characters in the Lightning Offer, the odds of drawing 0 from a 10-pack is 83%, from a 42-pack it's 46%. You're 99% likely to get 1 or fewer from the 10-pack, 96% likely to get 2 or fewer from the 42-pack, most likely to get 0.



At 5.6%, which is Human Torch in Enemy of the State (aka essential 3* in PVE), the odds of drawing 0 from a 10-pack is 56%, from a 42-pack it's 9%. You're 98% likely to get 2 or fewer from the 10-pack, 97% likely to get 5 or fewer from the 42-pack, most likely to get 2.



At 6.0%, which is Human Torch in Hot Shot (aka featured 3* in PVP), the odds of drawing 0 from a 10-pack is 54%, from a 42-pack it's 7%. You're 98% likely to get 2 or fewer from the 10-pack, 99% likely to get 6 or fewer from the 42-pack, most likely to get 2.



(I think the formatting can be improved, and the column headers changed, but that's a task for another day)

If you want to do your own spread sheet, it's easy, the formula that goes in the cell is something like this:

=BINOMDIST(0, 10, 0.06, FALSE)

which gives the chance of getting 0 out of 10 when the drop rate is 6%, not cumulative.

GrumpySmurf1002

Good stuff, never got around to doing something like this.

FWIW, I think the odds for Ant-Man are actually .00276, and Elektra is .0069 (single pack) and .0138 (10/42 pack)

I doubt they increase the overall odds on a single token, they just weight the characters differently, so a 4* is still 3.45%

My best guess is that Elektra is weighted @ 2.5 times, which means individual odds are (.345/12.5) = .00276, and thus her draw is .00276 * 2.5 = .0069. The 10/42 are then likely double that amount, so .0138. (the 10/42 are increased overall 4*, as 2* is where you see reduced draw)

I have to track down the exact 3* number these days, but similar math there, actually odds are +/- 0.05% from what are listed.

The 1 decimal place thing stinks.

Doesn't move the math much (97.274% on a 10 pack, 89.04% on a 42 for Ant-Man).

Moon Roach

GrumpySmurf1002 wrote:

Good stuff, never got around to doing something like this.

FWIW, I think the odds for Ant-Man are actually .00276, and Elektra is .0069 (single pack) and .0138 (10/42 pack)

I doubt they increase the overall odds on a single token, they just weight the characters differently, so a 4* is still 3.45%

My best guess is that Elektra is weighted @ 2.5 times, which means individual odds are (.345/12.5) = .00276, and thus her draw is .00276 * 2.5 = .0069. The 10/42 are then likely double that amount, so .0138. (the 10/42 are increased overall 4*, as 2* is where you see reduced draw)

I have to track down the exact 3* number these days, but similar math there, actually odds are +/- 0.05% from what are listed.

The 1 decimal place thing stinks.

Doesn't move the math much (97.274% on a 10 pack, 89.04% on a 42 for Ant-Man).

I knew the posted odds were rounded, but as you say it doesn't affect the result much.

But it does show that the only even halfway sensible reason for buying a pack is to get a cover of a colour you don't already have. I gave in and bought a Thing 42-pack, got 2 covers, both green, the only colour I already had, a 3* I could use, and the rest was rubbish. ~16k HP spent for what I could have bought for ~6k HP and some ISO. Oh dear. Never again, until next time.

stochasticism

Moon Roach wrote:

GrumpySmurf1002 wrote:

Good stuff, never got around to doing something like this.

FWIW, I think the odds for Ant-Man are actually .00276, and Elektra is .0069 (single pack) and .0138 (10/42 pack)

I doubt they increase the overall odds on a single token, they just weight the characters differently, so a 4* is still 3.45%

My best guess is that Elektra is weighted @ 2.5 times, which means individual odds are (.345/12.5) = .00276, and thus her draw is .00276 * 2.5 = .0069. The 10/42 are then likely double that amount, so .0138. (the 10/42 are increased overall 4*, as 2* is where you see reduced draw)

I have to track down the exact 3* number these days, but similar math there, actually odds are +/- 0.05% from what are listed.

The 1 decimal place thing stinks.

Doesn't move the math much (97.274% on a 10 pack, 89.04% on a 42 for Ant-Man).

I knew the posted odds were rounded, but as you say it doesn't affect the result much.

But it does show that the only even halfway sensible reason for buying a pack is to get a cover of a colour you don't already have. I gave in and bought a Thing 42-pack, got 2 covers, both green, the only colour I already had, a 3* I could use, and the rest was rubbish. ~16k HP spent for what I could have bought for ~6k HP and some ISO. Oh dear. Never again, until next time.

Sorry, but that doesn't follow at all. If you are buying to get a specific color that is just insane. Even if you pull the character you want, which as you have shown has absurdly low probability of happening, if you just want 1 of the 3 colors of a character then you will be disappointed 2/3 of the time even when you see the icon you want. The only time it really makes sense to buy packs tokens is if you need multiple of the characters with boosted draw probabilities and are happy with most, if not all, of the colors of those characters.

Moon Roach

stochasticism wrote:

Sorry, but that doesn't follow at all. If you are buying to get a specific color that is just insane. Even if you pull the character you want, which as you have shown has absurdly low probability of happening, if you just want 1 of the 3 colors of a character then you will be disappointed 2/3 of the time even when you see the icon you want. The only time it really makes sense to buy packs tokens is if you need multiple of the characters with boosted draw probabilities and are happy with most, if not all, of the colors of those characters.

For that situation, I kind of agree. Let's assume that you're someone who spends on the game.

For a heroic pack, you've got a ~27% chance of getting a 3* or greater. Plugging it in to my spreadsheet I see that you're 99% likely to get 6 or fewer from the 10-pack, most likely to get 2, 99% likely to get 18 or fewer from the 42-pack, most likely to get 11.



With a 10-pack costing 2800 for probably 2 or more covers that you'd spend 2500 or more on, and the 42-pack costing 11200 for probably 11 or so covers that you'd spend around 13750, you stand a pretty good chance of making a profit. The fewer covers you have already, the better the chance that you won't waste any.

What prompted my original post though, was a post I read a little while ago where a whale had one cover (I think it was of Carnage) and had to buy a whole bunch of 42-packs before he had one of each colour and could then buy covers and ISO to max the character. That's the kind of situation I was addressing with my "halfway sensible" comment, and "halfway sensible" was my tactful and diplomatic way of saying "batshit crazy", seeing as it also applied to me, at least in part.

(Interesting, bat guano is considered profanity.)

Edit: changed the image

stochasticism

That is tinykitty crazy. Multiple 42 packs. Seriously? What happened to good old hookers and blow.

jffdougan

I've run a similar post toward the beginning of the last few PvP seasons to help people assess their 10-pack for 4k points. Keeps getting buried after a few days.

Moon Roach

jffdougan wrote:

I've run a similar post toward the beginning of the last few PvP seasons to help people assess their 10-pack for 4k points. Keeps getting buried after a few days.

Maybe we should put together a definitive post with pretty graphs and get a mod to sticky it.

jffdougan

Moon Roach wrote:

jffdougan wrote:

I've run a similar post toward the beginning of the last few PvP seasons to help people assess their 10-pack for 4k points. Keeps getting buried after a few days.

Maybe we should put together a definitive post with pretty graphs and get a mod to sticky it.

PM me.