Pokemon Booster Box (36 Packs)

[Kristin Banyas]

Ialso remember opening my very first booster pack. During that time, everyone seemed to want a Charizard, and the thought of getting one seemed to be more important that everything else. I remember slowly opening the foil wrapper, careful not to damage the cards. I also remember the feeling of disappointment when I got something else.

Opening booster packs, however, was a gamble. There was no guarantee you would get the cards you wanted. Back in those days, when I was still in grade school, I only got around $6.00 every week as my allowance (nowadays, I get way much more than that, of course).

Booster packs used to cost around $3.00, and I could only get one once in a blue moon. When I got to high school, I could buy one to two booster packs every week. When I got to college, I started buying booster packs by the dozen every now and then (talk about an increase in purchasing power).

This gave me better chances of finding the cards I wanted, but it also got me spending whenever I passed by the local card store. For a period of time, I found myself buying booster packs whenever I had the money to burn. Opening booster packs became an addiction.

For the record, I have nothing against booster packs. I personally think that booster packs are a great way to find the cards you want, though it usually takes a significant amount of money and an extraordinary amount of luck to get very rare cards like Luxray GL LV.X.

Seeing that almost everyone here in 6P talks about deck strategies and the like, I decided to take a different route and talk about something else. You may not like mathematics, but I think you may find the content of the rest of this article a bit helpful (and/or entertaining, hopefully). I hope to give people some insight on booster packs.

A booster pack from the earlier expansions of the Pokmon TCG used to have eleven cards, but after a while, the number of cards were reduced to nine. Booster packs nowadays, however, have ten cards. Each booster pack has five common cards, three uncommon cards, one rare card, and one random card.

Since there are thirty-eight (38) different uncommon cards in HGSS, the odds of getting a Pokmon Collector in an HGSS booster pack should be 1/38 or 0.0263. There are, however, two other uncommon cards in the booster pack. Pokmon Collector could be any of one the three but cannot appear more than once.

At this point, I think some of you are already confused, and that is why I took the liberty of computing all the probabilities for you. As you may notice, the probabilities differ for each set because they all have a different number of cards.

My computations are based on the assumption that you are only looking for one particular card at a time. Kindly note that the probability for the random card in each set may not be accurate, but it should give you a rough idea on how difficult it is to find a card like Luxray GL LV.X in a booster pack.

Statistically speaking, booster packs from Rising Rivals and Supreme Victors give you the worst bang for your buck. That being said, it would be much more advisable for you to go and find people selling the card you want from those sets than buying and opening booster packs.

Anyway, for consistency, all booster packs came from the same set. Before I opened each one, I measured the thickness of each booster pack. There was a small discrepancy between some of the booster packs, usually around ten to twenty micrometres.

I initially attributed this to uneven foil packaging, but when I opened the booster packs, the ones that were thicker by ten to twenty micrometres had foil and/or reverse foil cards. I decided to test if there was indeed a difference between them and learned that foil and reverse foil cards were thicker than normal cards by an average of ten micrometres.

Also when you calculated the probabilities of getting a certain common card in Rising Rivals, or any other set, ignoring the reverse-holo card, the calculation would actually be 5 /number of commons in that set. (the same applies for uncommons and rares, just replace 5 with 3 and 1 respectively). So for Rising Rivals, commons have a 15.15% chance of being the one you want, and uncommons have a 9.38%, etc.

After talking to friends who play other card games, it seems people who play the naruto ccg only buy packs they are sure have their version of a secret rare in them. Most of the players have it down to almost a science without a meter, however it is likely that the naruto ones vary in size more than the pokemon tcg packs do.

I don't think that is how it works.

Lets say the probability of getting normal ninatails is A and the probability of getting foil ninetails is B. The probality of getting none of them is (1-A)(1-B) (they are independent because the reverse foil takes the place of the random card).

Thus, the probability of getting either is 1 minus the probability of getting none, that is

You need to look up the Hypergeometric distribution. And after you have cracked that then switch to using the multi-variate hypergeometric as that one can be readily applied to opening hand statistics.

_distribution#Multivariate_hypergeometric_distribution

There is also the Coupon Collector Problem to investigate. _EN/urn/urn9.html But beware that the boosters within any given box are not uncorrelated which is why if you are trying to collect a set you are best off buying whole boxes.

How would one calculate the probability of having an opening hand that had a particular makeup. For example, if a decklist had 4 Sableye and 2 special dark energy, what is the probability that the opening hand would have at least 1 Sableye AND 1 special dark energy?

the formula/math that was used is fine. It seems quite likely that Ahj911211 understands how to use the math and the assumptions that have to be made. But It is the assumptions behind its use that are the problem. And those make including any kind of formula on a website tricky. That said the multivariate hypergeometric distribution is the best way to calculate the odds precisely.

Including the top card as a candidate for a sp. dark would yield slightly higher probabilities too. Then there is the Uxie drop and other cards drawn T1. So just how many cards will you have access to T1? 10 12 14 or all 46? A deck that used 4 sableye and two special dark is going to use a lot of T1 draw if it is going for the donk.

If I understand you correctly, then I would point out that the formula

itself should not need to be aware of cards like Uxie or Collector. In terms

of the website, it would present an interface for the player to select what

they considered a desirable hand and then use the formula to calculate the

probability. It would be the players responsibility to choose the hand they

wanted. For example:

Player decides they think a good starting hand would be Sableye and special

dark so they drag those two cards to the interface and set the number of

cards to 7 to reflect an opening hand (could be 8 to represent Felicity or 4

for Judge, etc).

multiple shapes are handled with multiple lines. with each shape getting a count but also setting a flag as a good start. Once all shapes are tested you just look at the good start flag to increment a total success count.

I calculated it strictly as a 7-card hand, no mulligans or first draw considered. If a tool were to be formed for such a calculation, as you said, both factors would have to be considered. The cards you have access to the first turn and things like that would be too complex to analyze with probability, so either the model has to exclude that or it has to be run strictly through simulation.

After reading the article and some of the posts, I estimate the probability of those of us who liked this article to be nerds is 100%. Kinda reminds me of all of those Star Trek episodes when Captain Kirk would ask Spock the probability of survival. Somehow they always beat the odds. Great article, and a fun topic!

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