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trainer772

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PostedAug 19, 2012 2:05 pm   Last edited by trainer772 on Feb 26, 2013 8:52 pm. Edited 2 times in total

Guide to the capsule shop

To give you the upper hand in winning!
For starters, I'll begin with a few basic numbers and statistics on the 4 different types of capsules available.

Euro Jackpot
Prerelease
Euro capsule
Gcoin capsule


Euro Jackpot

Every capsule in the Euro jackpot has a random amount of euros. It also contains various 1 day items.

The 100 AP jackpot contains amounts of 1,500 - 2,000 - 2,500 - 3,000 - 5,000 - 10,000 - 20,000 - 25,000 - 50,000 - 100,000 - 150,000 - 200,000 - 500,000, to name a few.
For starters, I'll start by saying that 1USD (100 AP) should yield 3,750 euros of total net gain to make a reasonable profit.
The most common Euro Jackpot quantities that you'll come across are the 1.5k, 2k, and 2.5k capsules with the occasional 3k and 5k and the rare 10k. This means that with any one capsule, it's very likely that you'll get a negative gain.

The 200AP jackpot contains amounts similar to the 100AP jackpot except with a slightly greater chance of getting higher numbers and the 1 mil euros as the final prize. Most capsules in this jackpot will yield 1.5k, 2k, 2.5k, 3k, and 5k with the occasional 10k or 15k. That means you are almost garunteed a negative profit by buying these caps.

But what about the final prize - the half mil or the 1 mil euros? What's the chance of getting that?
The chances are pretty complicated. It depends on a lot of factors ESPECIALLY including the time the last jackpot was won. Why? Because the Euro jackpot is simply a 10000/10000 capsule without the number displayed. When you purchase one capsule, it could have been at 9847/10000 or at 492/10000. Remember, the winning jackpot is a random number between 1 and 10000, so on average 5000 capsules will be purchased between each win. However, if you buy 1 capsule at a random time, your chances to win the jackpot are around .02%.


Prerelease

For 130 AP, you could have a shot at getting a gun 2 weeks early. Is it worth it? Absolutely not.

So what are the chances on this guy? The PR caps are simply a 200/200 capsule without the current number displayed. This means that on average, 100 capsules are purchased between each win. This also means that on average, you would have to buy 100 capsules for a fair chance at getting the prerelease gun.


Euro capsule

200/200
Your chances on the 200 capsules is simply the number of caps you purchase over the number currently available. If you buy 10 at 100, your chance is 10%. However, once you start going down to 50, you're more likely buying at a much lower number by the time everyone's signals start reaching the servers. Timing is crucial with these caps, but don't be discouraged if you fail because that happens to everyone.

Indivs
Indivs are just a 200/200 capsule without the number displayed. DO NOT BUY AT ALL.

AP capsule

99/99
249/249
149/149
300/300
Your chance of winning is the number of caps you buy over the number of capsules available.
Would I rather buy from the 99s and the 149s or the 249s and the 300s? I would honestly buy 10 of the 300s rather than 5 of the 149s (although chances are technically the same, the 300 caps go slightly slower) but I'd rather buy 5 of the 99 caps over 10 of the 249 caps simply because there's a higher chance on the 99s. However, the 249s do go slightly slowly at times and it is possible to buy 5 at very low numbers on the 249s.



Refer to this post if you want to get to the nitty-gritty of all the probability math.
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trainer772

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trainer772
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PostedAug 19, 2012 2:09 pm
Now for the tips and strategies.

1. Never buy indivs. Simple rule.
2. Never buy PR caps.
3. Never buy Jackpot caps.
4. Never buy high, and never buy for the purpose of lowering caps.

So your only options are to buy euro 200s and the gcoin cap guns.

Important steps to determining when you should buy.

1. O. Observe. Camp the capsule shop for many days, look at the low capsules, and see how long it takes for them to win at certain times of the day. Observe the number of people camping the capsule and observe the time. If there are merely 40 people in cap shop, you should buy really low but when there are 80 people, you should buy slightly higher. I count the number of people in cap shop buy using my mouse scroll wheel. One scroll down the cap shop list for me goes through roughly 10 names, so if I scroll down 4 times and hit the bottom, I know I should wait longer. Basically, sit in capsule shop and look at the numbers.
In fact, your observations should go even further. It would be great practice for you to have the buy button up (like in step 2) and watch the numbers as your buy menu is up, but don't actually buy capsules!

2. R. Ready. Drop by the capsule shop every hour. Once you see a euro capsule at 130-140, a pistol cap at 60/99 or 120/249, or a primary cap at 80/149 or 130/300, camp the capsule nonstop.
Do not engage in distracting conversations while camping. Do not respond to anyone, and do not spam the chat advertising the gun. Instead, when the capsule goes down to 100 for euro, 50/99 or 100/249, or 70/149 or 120/300, you should already have the buy menu up. It helps a lot to turn shader model to 2.0 low and/or have gamma at 2.2. This way, you can see the number through the buy menu. If you have your settings right, you should see something like this. That way, you can buy quickly.

3. dunno, working on this

Flaim2

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PostedAug 20, 2012 12:19 pm

Re: Guide to the capsule shop

To give you the upper hand in winning!
trainer772 wrote:

99/99
249/249
149/149
300/300
Your chance of winning is the number of caps you buy over the number of capsules available.
Would I rather buy from the 99s and the 149s or the 249s and the 300s? I would honestly buy 10 of the 300s rather than 5 of the 149s (although chances are technically the same, the 300 caps go slightly slower) but I'd rather buy 5 of the 99 caps over 10 of the 249 caps simply because there's a higher chance on the 99s. However, the 249s do go slightly slowly at times and it is possible to buy 5 at very low numbers on the 249s.  


i'm sorry to disturb you, but at this part your math is "slightly" off.

afaik you determine the chance of a single capsule with that formula:
m := max caps count
c := current caps count
(m - c) / m

the way you suggested there is no way how the m interacts with your chance of winning making winning at numbers of 40+ nearly impossible (25% for 10 caps), but if you have watched the capshop carefully the winning c scales with m (i.e. the cap that wins is most of the time higher on a higher m, than on caps with a lower m).
i forgot how to manipulate that formula to make it applicable for 5/10 caps, but it's way back when i used combinatorics the last time.
hope somebody here does remember.

trainer772

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PostedAug 20, 2012 1:07 pm

Re: Guide to the capsule shop

To give you the upper hand in winning!
Flaim2 wrote:
trainer772 wrote:

99/99
249/249
149/149
300/300
Your chance of winning is the number of caps you buy over the number of capsules available.
Would I rather buy from the 99s and the 149s or the 249s and the 300s? I would honestly buy 10 of the 300s rather than 5 of the 149s (although chances are technically the same, the 300 caps go slightly slower) but I'd rather buy 5 of the 99 caps over 10 of the 249 caps simply because there's a higher chance on the 99s. However, the 249s do go slightly slowly at times and it is possible to buy 5 at very low numbers on the 249s.  


i'm sorry to disturb you, but at this part your math is "slightly" off.

afaik you determine the chance of a single capsule with that formula:
m := max caps count
c := current caps count
(m - c) / m

the way you suggested there is no way how the m interacts with your chance of winning making winning at numbers of 40+ nearly impossible (25% for 10 caps), but if you have watched the capshop carefully the winning c scales with m (i.e. the cap that wins is most of the time higher on a higher m, than on caps with a lower m).
i forgot how to manipulate that formula to make it applicable for 5/10 caps, but it's way back when i used combinatorics the last time.
hope somebody here does remember.  
With your math, let's assume that a theoretical machine is at 149/149. What's the chance with 1 capsule?
(149-149)/149
With the (m-c)/c formula the chance is 0 even though it is possible and rare to 1cap at 149.

What about when there's 1 capsule left?
(149-1)/149
Somehow, this formula implies that there's a small chance to lose when there's 1 capsule left. If that happens, we're down to a capsule machine that says 0/149.

=====================================================

Imagine a scenario where you have 4 cups in a row and there is a coin under one of the 4 cups. (It does not actually matter that <the 4 cups are in a row and you must pick them up in the given order> or <you can select whichever cups you want, not in a given order.> If you have 10 cards and you want a certain card, <the chance of putting them face down separately and picking whichever one you want> or <putting them in a deck and taking the first off the top> is the exact same, because true chance cannot be affected by user picks.) Back to the 4 cups.
50% of the time: You find the coin in one of the 2 cups you picked up!
50% of the time: You pick up the first 2 cups but don't find the coin. You're down to 2 cups, and it doesn't matter whether there were 4 cups originally or 8 million cups. Now the chance to find that coin is 1/2 with every random cup. The number of cups that previously existed simply cannot make the first of the two cups you pick up more likely to have the coin than the second of the two cups since the deck of cards demonstrated that the order with which you pick up the cards has no effect on chances. This is because that chance was already taken into account when you picked up 2/4 cups and had your 50% chance of winning.

Likewise, the chance of winning is irrelevant to do with the max cap count.

Let's consider the 300 capsule. Every capsule has a 1/300 chance at random when there are 300/300 capsules.

If there are 100 capsules left, each of those remaining capsules have 1/100 chance of containing it regardless of the fact that it is a 300 capsule machine. There is not a higher chance that the winning gun is at a higher number simply because the /300 is higher. Just because 200 capsules were purchased before doesn't make it likelier than the winning capsule is closer to the 51-100 range than the 1-50 range. Since every capsule between 1 and 300 has an equal chance of having the gun, for every capsule taken out, it increases the chances of the other capsules having the gun equally.

If there are 5/300 capsules left, the chance of each capsule being the winner is 1/5. Each capsule must have an equal chance of holding the gun.

If there are 2 capsules left in the 300 machine, both capsules have an equal chance of containing it, hence the chance is 1/2.

If there are two sets: 100/300 and 100/149, your chance of winning by buying 10 on either is the exact same: 10%. If they are 1/300 and 1/149 and you buy 1, your chances are the same: 100%. If there are 149/300 and 149/149 and you buy 10, the chances are the same: 6.7%. If there are 2/300 and 2/149 and you buy 1, the chances are the same: 50%.

If you buy 5 at 100, your chance is 5% regardless of the original count. Such is life and such is the quantity of losers for every winner. I'm not saying a win between 95-100 is impossible, just saying that it is very likely to lose.

End result:
The number of previously existent capsules does not matter
The order in which you pick capsules does not matter, since all capsules have the same chance
The only thing that matters is the number of capsules purchased and the current number of capsules.

Flaim2

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PostedAug 20, 2012 5:02 pm
thanks, you just have shown me the error in my logic >.<
as i said, it's way back when i used stochastics the last time.

Flaim2

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PostedAug 26, 2012 6:38 pm
well, i just remodelled my formula and the result is that it's just a more complicated looking version of your fomula ( #of caps bought / # of caps left before the buy).

i acutally meant the formula like you would take it for getting the lotto numbers:

e.g. you'd want the chance for having the 3 right numbers jackpot
winning chance = ((6 over 3)*(43 over 3))/(49 over 6)

but as we have just one winning cap in ava the formula would look like:

e.g. 40/249 caps with you buying 10 caps
winning chance = ((1 over 1)*(39 over 9))/(40 over 10)
this formula would result in a chance of 25% to win in that certain case. remarking that that's exactly the formula (caps you want to buy) divided by (caps left before the buy) -> 10/40 = 25%

after realizing this i tested it for a few more cases
(like 10 bought out of 70 = ((1 over 1)*(69 over 9))/(70 over 10) = 10/70, etc.) and they seemed to fit.

so, what i want to say is that i just provided the mathematical prove that your math was right from the beginning Razz

with that in mind and the leftovers of what i've learned in school back then you should never bet on anything that is below 66% chance for success, but that would mean to never buy any caps as long as the cap counter is above 15 (cuz 10/x = 66% -> x = 10/66% = 15), which is kinda hard...


edit:
explanation for ppl that don't understand the term (N over K):
it's a kind of abbreviation for ((N!) /((N-K)!*K!)).

explanation of X!:
it's a kind of mathematical abbreviation for (X)*(X-1)*(X-2)*...(X-(X-2))*(X-(X-1))
but because that's too mathematical for the mainstream user here's an example.
let's say X = 4.
-> X! = 4*3*2*1 = 12




TL;DR:
~mathmathmathmathmath~
chance to win = (number of caps you want to buy) / (the amount of caps left) confirmed
~more math and explanations~

bmendonc

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PostedAug 26, 2012 7:54 pm
ugh, is this what will await me in AP stats...

Aeria's solution to AVA: copy KAVA's money-making traits only, The result? A30A GG

trainer772

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PostedAug 26, 2012 8:00 pm   Last edited by trainer772 on Aug 26, 2012 8:27 pm. Edited 1 time in total
@Flaim, yea the thing is even if you buy 10 at 50 you're going to lose 4 out of 5 times. That's the reality though.


bmendonc wrote:
ugh, is this what will await me in AP stats...  
naw man. AP Stat is all about the distribution curve.




Learn to use this baby and you get a 5 on the test.

bmendonc

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PostedAug 26, 2012 8:07 pm
ah, I know all about that...

Aeria's solution to AVA: copy KAVA's money-making traits only, The result? A30A GG

Greek_Prokopis

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PostedSep 06, 2012 2:58 pm
The cool thing with me is that I have spent more than 40k to Classic x/200 capsules and have won nothing till today while having spent only less than 10k at idividual and having won Carpio and Mad Galil Very Happy...I bought all of my x/200 capsules at 80 and under...So I think it is only a matter of luck! Hope this helped Very Happy

Proud To Be Greek!
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