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In game of FIFA there are packs by opening which a user receives soccer player cards. The higher the rating of a player card the rarer it drops depending on some kind of random number generator. Since there is a marketplace for users to buy and sell cards it is logical to suppose that this RNG is somehow shared. Some user get absolute gem from a dozen packs and for some it can take a hundred or more. Based on my experience on average it may take opening dozens of packs to find a decent card.

Also there are some special types of cards - in form - which are even more rare since they only drop during a period of a single week. The next week new different in form cards are released. Any given pack may contain both regular and in form cards.

In form cards are released every week the same day at the same time. Suppose that this event creates an increase in amount of opened packs for a short period of lets say few hours. Does the chance of getting a rarer card (not necessarily special) change during said period?

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From your description I don't see how it could increase the probability of a single player getting a rare card. There does not seem to be any interaction between the probability of getting a rare card and the number of packs opened.

I suppose you mean that if, let's say, on average each 12th pack contains a rare card, then it is easier to be the 12th person when there are more packs being opened, but bear in mind that pack openings are (hopefully) independent trials. That means, if you have opened a pack and did not get a special card, it gives you no information whatsoever about the probability of getting a card upon opening the next pack.

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    $\begingroup$ If I understood you it gives me no information as an insider. But what about as an observer to the system. Assuming that during the week N packs are opened it means that there are N/189 packs per hour. During some period that per hour ratio is somehow changed, meaning that there are k*N/189 packs/hour. If probability of RNG giving rare card in a single pack is the same in any moment of time it means that average rare card per hour ratio increases comparing to average weekly. Just like the more people play lottery the more winners there are. Does it make sense? $\endgroup$ – Serge Rykovski Feb 2 '18 at 12:55
  • $\begingroup$ Yes, the number of rare cards gained by all the players will be above average. However, that is not because the chance of getting a card in a pack would be higher, simply there were more packs opened. Imagine you are flipping a coin, having 50% of getting a head. If you flip the coin 10 times, you might get 5 heads and if you flip it 10000 times, you might get 5000 heads. But that does not mean that getting a head became more probable. $\endgroup$ – Jan Kukacka Feb 2 '18 at 13:00
  • $\begingroup$ So if I am among those players at that period I am more likely to get a rare card? Its just common sense. However there may be some kind of paradox or rule I'm not aware of because of my limited proficiency in probability theory and statistics. $\endgroup$ – Serge Rykovski Feb 2 '18 at 13:07
  • $\begingroup$ No. It is true that the "average rare cards per hour" is higher at this time period, but so is the number of players who are dividing those cards among themselves. Each player's chance of getting a rare card upon opening a pack remains the same. $\endgroup$ – Jan Kukacka Feb 2 '18 at 13:11
  • $\begingroup$ That makes sense. However there's one more detail. Only a small subset of players participate in this increase, so their chances should be higher than of those who doesn't? $\endgroup$ – Serge Rykovski Feb 2 '18 at 13:36

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