Probability vs Chance: How likely are you to get a ship from opening X number of Super Containers?

[Grantwhy]

Chance vs Probability

A long time ago I saw a formula posted on Reddit that allowed us to work out the probability of getting a certain % drop from X number of containers.

That formula is:

1 - (1 - P)^N

P = probability of success
N = number of trials
^ = to the power of

or, to make it easier to understand,

P = % chance of a certain drop
N = Number of containers opened.

I'm seeing a posts here and on reddit where people are surprised that they didn't get a ship from the Anniversary Super Containers, even though they opened 100 or 110 of them.

So I thought I'd plug the numbers into that formula and see what the probability of getting at least one ship is. And if you have that, you have the probability of getting NO ships.

Chance of getting a Premium Ship from a Super Container is 1%

For 100 Super Containers, the chance of getting at least one ship is 63.4% which means there is a 36.6% chance of getting NO ship from opening 100 SC.

If you get the maximum 110 SC from the event, that is 66.9% chance of getting a ship and 33.1% chance of getting NO ship.

Look at the person sitting to your left. Look at the person sitting to your right. One of you three will (probably) open the maximum 110 Super Containers from the Anniversary and get no premium ships.

Super Containers are not rigged, we humans are just not good at understanding Chance vs Probability.

---

bonus post: The guaranteed drop for Super Containers is 200. Which means if you open 199 Super Containers you are guaranteed to get a ship in the 200th SC.

But, what is the chance of opening 199 SC and getting no ships?

By this formula, it is 13.53%

Which is a 1 in 7.39 chance. Basically the next time you get into a 12 v 12 random game, 3 of the players in your game will (probably) have to open 200 SC to get a ship.

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bonus bonus post: How much easier was it to get a ship from the old SC with their 1.5% chance of getting a ship?

100 SC = 77.94% chance of at least one ship = 22.06% chance of no ship

110 SC = 81.03% chance of at least one ship = 18.97% chance of no ship

The old SC guaranteed drop was 165 containers. The chance of opening 164 of the old SC and getting no ship was 8.39% (just under a 1 in 12 chance)

---

Interesting.

The guaranteed drop for the new SC is a lot kinder than the old one.

13.53% vs 8.39%

For the new SC (1% chance of a ship) , to get a 8.4% (ish) chance of getting to the guaranteed drop, the guaranteed drop would be about 246.

For all the (justified) complaints about the new Super Containers, WG have made the guaranteed drop kinder for the players.

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This post ended up a lot longer than I expected, and I rambled a bit. I really should go back and re-read it a few times, but I'm tired 😛

[Grantwhy]

disclaimer: Maths is hard.

I make NO guarantee that I've got it all correct.

Or any of it 😛

[palestreamer]

Even if you don't get a ship you can get a pretty decent pile of rewards from that many containers. But I prefer to collect ships which is why I just decided to go for the Bayard, and at least get something.

[Ensign Cthulhu]

1 hour ago, palestreamer said:

But I prefer to collect ships which is why I just decided to go for the Bayard, and at least get something.

Yep! "A bird in the hand is worth two in the bush", writ large.

[Crokodone]

Personally, as a 20th century Naval Enthusiast, you can only sail so many ships; I only got ~178 ships; but I regularly sail only five to twelve of them on a regular basis.

[Daniel_Allan_Clark]

3 hours ago, Grantwhy said:

Super Containers are not rigged, we humans are just not good at understanding Chance vs Probability.

Actually, the SC are definitely rigged...according to the math that you shared...they will drop according to the programming.

3 hours ago, Grantwhy said:

bonus post: The guaranteed drop for Super Containers is 200. Which means if you open 199 Super Containers you are guaranteed to get a ship in the 200th SC.

I have yet to see credible evidence that this is actually true.

I have yet to receive a ship from a super container since this mercy rule was implemented.

This point is probably worthy of testing.

[I_cant_Swim_]

11 minutes ago, Daniel_Allan_Clark said:

Actually, the SC are definitely rigged...according to the math that you shared

The "rigging" is an implementation of probability, using math, so all good there. The mercy rule tips this in your favor, so this is rigging we should be happy for.

And it's easy to test. Something like 20+ members all need to keep their SCs till they accumulate 200, then open them all. Everyone should have at least 1 ship - or the rigging  needs to be rigged again.

 

[LittleWhiteMouse]

I finished collecting them all from the event.  I got a submarine.

[Asym]

35 minutes ago, Daniel_Allan_Clark said:

Actually, the SC are definitely rigged...according to the math that you shared...they will drop according to the programming.

I have yet to see credible evidence that this is actually true.

I have yet to receive a ship from a super container since this mercy rule was implemented.

This point is probably worthy of testing.

Math only works if the data is "verified" and since, we can't see the "code" to validate the how they chose to crunch the numbers, this is like Las Vegas before regulation.....  We don't know.

As an aside, I opened all the containers 346 ships provide and did not get a ship.....  And, many of us are not on our host's "I love you" list so......... "let the eat cake" works for them....

I love math and hate the outcomes.....   Math is like shaving with a straight razor......it's an art to be appreciated that produces blood if you are imprecise....

Edited September 29, 2023 by Asym

[Wolfswetpaws]

2 hours ago, Crokodone said:

Personally, as a 20th century Naval Enthusiast, you can only sail so many ships; I only got ~178 ships; but I regularly sail only five to twelve of them on a regular basis.

Meanwhile, players in the Collector's Club are still knocking-off the purple festive token anniversary snowflakes from their fleets of several hundred ships.

Sure, one player can only sail one ship at a time.
But playing each of them, in turn, or even only the Tier-5 and up ships in turn, can take a while.  🙂 

[Wolfswetpaws]

51 minutes ago, Asym said:

Math only works if the data is "verified" and since, we can't see the "code" to validate the how they chose to crunch the numbers, this is like Las Vegas before regulation.....  We don't know.

As an aside, I opened all the containers 346 ships provide and did not get a ship.....  And, many of us are not on our host's "I love you" list so......... "let the eat cake" works for them....

I love math and hate the outcomes.....   Math is like shaving with a straight razor......it's an art to be appreciated that produces blood if you are imprecise....

Yes, 346 ships provide a good number of tokens and thus one could exhcange them for a number of Super Containers.
But, exactly how many Super Containers did you open?
Less than 200?

[Ensign Cthulhu]

10 minutes ago, Wolfswetpaws said:

But, exactly how many Super Containers did you open?
Less than 200?

By definition, since there were only 110 guaranteed from the event for the opening.

There were two more from a Twitch mission connected with the anniversary, two from this month's daily drop, and three from Amazon Prime. 

Anything more than that was whatever RNGesus chose to dish up from the daily container roll (and even that is now on a mercy-rule system). 

 

1 hour ago, Asym said:

And, many of us are not on our host's "I love you" list

Hmm, I wonder how you got yourself into that situation... 🧐 

I reckon I must have stolen some of your RNG, or maybe RNGesus was just making it up to me for the last few years being a touch on the lean side supercontainer-wise.

[Col_NASTY]

2 hours ago, LittleWhiteMouse said:

I finished collecting them all from the event.  I got a submarine.

I did as well. I got dubs often so I must have all the possible drops.. even subs 🥺

Good news is I got the 3K Steel from the rest of the certs. ☺️

[Daniel_Allan_Clark]

2 hours ago, I_cant_Swim_ said:

The "rigging" is an implementation of probability, using math, so all good there. The mercy rule tips this in your favor, so this is rigging we should be happy for.

And it's easy to test. Something like 20+ members all need to keep their SCs till they accumulate 200, then open them all. Everyone should have at least 1 ship - or the rigging  needs to be rigged again.

 

Yes, hit my point exactly.

Getting 200 SC for me is a long slog.

[iDuckman]

6 hours ago, Grantwhy said:

The guaranteed drop for the new SC is a lot kinder than the old one.

Yep.  And since in many cases you get two SCjr where you used to get one SC, situationally the % drop chance is 2% instead of 1.5%.  (Well, it's not linear, but close enough for these small numbers.) 

[Gnirf]

4 hours ago, Crokodone said:

Personally, as a 20th century Naval Enthusiast, you can only sail so many ships; I only got ~178 ships; but I regularly sail only five to twelve of them on a regular basis.

I am soon up on 600 mark if I count ships on regrind etc, I do have some that are preferred all the time but the rest I play varies from time to time but are limited in numbers according to new lines, regrinds etc. So the 20-30 in the most played vries from time to tim, but stays the same for a while. I have regrinded RN BCs a5 times and US DDs (fletcher only, but for the last time) several times. But now when I am on the last leg I will shift to another group whatever that might be. 

[Asym]

3 hours ago, Wolfswetpaws said:

Yes, 346 ships provide a good number of tokens and thus one could exhcange them for a number of Super Containers.
But, exactly how many Super Containers did you open?
Less than 200?

I actually, do not remember.....  I was just so happy to be done that I hit "open all" and that was that.   Sigh......it was free stuff and where I am in the game, just barely, free was good enough for that day.  I haven't played the game for three days now and no one is gathering for RO's at the moment. So........

[Asym]

3 hours ago, Ensign Cthulhu said:

By definition, since there were only 110 guaranteed from the event for the opening.

There were two more from a Twitch mission connected with the anniversary, two from this month's daily drop, and three from Amazon Prime. 

Anything more than that was whatever RNGesus chose to dish up from the daily container roll (and even that is now on a mercy-rule system). 

 

Hmm, I wonder how you got yourself into that situation... 🧐 

I reckon I must have stolen some of your RNG, or maybe RNGesus was just making it up to me for the last few years being a touch on the lean side supercontainer-wise.

Yo reap what you sow...... I followed your lead !  Oh Captain, my captain....... 

Hamlet describes how so many fee; about this game:

"I have of late, (but wherefore I know not) lost all my mirth, forgone all custom of exercises; and indeed, it goes so heavily with my disposition; that this goodly frame the earth, seems to me a sterile promontory; this most excellent canopy the air, look you, this brave o'er hanging firmament, this majestical roof, fretted with golden fire: why, it appeareth no other thing to me, than a foul and pestilent congregation of vapours...."  (wiki, 2023)

Alas, "what a piece of work is man..."      Of course, I have always subscribe to be under appreciated and to be no more than the Quintessence of Dust...

[Dareios]

the pity counter resets after you get a ship, and you dont know how far along the counter you are, so any tests will have to be 200 containers counted after the next ship drop.

[clammboy]

5 hours ago, Asym said:

And, many of us are not on our host's "I love you" list so

So How do we get on this supposed I love you list? I want on!

[Lord_Slayer]

I got enough tokens to clear out the Super Containers completely.

Mind that I have 500+ ships, most T5 and up.

Accordingly, of the ships listed as being in the containers, I was missing only 3 T8s.

 

I am now only missing 2.

 

Much of what I ended up with was Premium Time, Dubs, some steel, coal and boosters.....lots of boosters......

[Asym]

2 hours ago, clammboy said:

So How do we get on this supposed I love you list? I want on!

That's simple !  In the forum, always compliment each CM by name;  insure you fully support everything the Ensign publishes and expand all of the benefits three-fold; praise every change no matter how badly it hurts or costs you; and, remember, visit Austin if at all possible and deliver a flower arrangement to the staff there with a thank you note attached that is 14 paragraphs lone extolling their magnificent virtues and abilities.....

Do that and sacrifice a chicken over sacred charcoal, with sprigs of real sweet grass and sage; sprinkle some 10 year old single barrel Bourbon on the chicken before you dispatch it and chant:  I love this game (Я люблю эту игру)  Ya loblu eshtoo eegroo  three times in the charcoal smoke.

See how simple that is ! 

[Ensign Cthulhu]

2 hours ago, clammboy said:

So How do we get on this supposed I love you list? I want on!

Don't spit on Weegee's carpet.

[Admiral_Karasu]

8 minutes ago, Ensign Cthulhu said:

Don't spit on Weegee's carpet.

Because.....?

 

 

[Ensign Cthulhu]

1 minute ago, Admiral_Karasu said:

Because.....?

Because that will put you in their bad graces.