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Cumulative Hypergeometric Distribution


#1

So using statistical analysis via CHD, I’ve been able to find out quite a bit about specific Netrunner cards, strategies, and even the game itself. I’m in the midst of writing up an article that utilizes it in optimizing deckbuilding, and I was wondering if anyone else has any ideas of what I can analyze to break the game down even further.

A sample of what I was able to derive via CHD: (you may have seen me post this on BGG)

When accessing 1 card from R&D on the first runner turn: (49 card corp, 10 agendas)
20.41% chance of finding at least one agenda

With 1 R&D Interface: (Two card access)
36.99% chance of finding at least one agenda
3.83% chance of finding at least two agendas

With 2 R&D Interfaces: (Three card access)
50.40% chance of finding at least one agenda
10.18% chance of finding at least two agendas
0.65% % chance of finding at least three agendas

With 3 R&D Interfaces: (Four card access)
61.18% chance of finding at least one agenda
18.05% chance of finding at least two agendas
2.31% chance of finding at least three agendas
0.10% chance of finding at least four agendas

With 3 R&D Interfaces and a Maker's Eye (Six card access)
76.67% chance of finding at least one agenda
35.50% chance of finding at least two agendas
9.03% chance of finding at least three agendas
1.18% chance of finding at least four agendas
0.07% chance of finding at least five agendas
<.01% chance of finding at least six agendas

NBN: The World is Yours


The legend on the right identifies deck size and number of ice, respectively. NBN is blue, red is the average corp deck.


#2

Your baseline is wrong. The deck is 10/49 = 20.4% agendas, so (ignoring mulligans) the chance of drawing an agenda from R&D unaided is 20.4%, not 22.73%.


#3

Keep in mind though on the first runner turn, the corp will have drawn 6 cards. That means it would be 10/43, however it doesn’t account for the possibility of the odds of one of the ten agendas being in HQ. The math gets muddled in guesstimating, but CHD accounts for this distribution.

Though my baseline was still wrong. I counted for 44 cards rather than 43. Damn first turn draw.


#4

Assuming no mulligan, the cards the corp has drawn are random and therefore do not affect the agenda distribution.

Think about it this way – if I draw 5 cards off the top of a standard 52-card deck of playing cards, what are the chances that you will then pull a spade from the top of the deck? 1 in 4, the same 1 in 4 that they were before I drew the five cards. The fact that I pulled random cards off the top does not change the underlying distribution. There’s no guesstimating needed.


#5

Sorry, this is only correct if you reshuffle the card you drew into the deck before you draw another one. This is why we use CHD when we play card games. We are playinh the cards we draw, the population is constantly decreasing, so drawing a spade means there is one less spade in the deck and the odds of drawing another spade are lower. Runnining CHD statistics can also tell you how likely you are to draw 2 spades in a row or how many cards you will have to draw if you don’t have test run or opus after a mull in your ct deck


#6

The odds of drawing one spade are only lowered if a disproportionate number of spades compared to other cards have been drawn.


#7

The odds change if you have knowledge of which cards have been removed, but as long as it’s random to you, you proceed with the original percentages. CHD statistics are not the issue at all; as far as I can see the tables would be accurate if you started with odds of 10/49 rather than 10/44.

One more thought experiment: I cut a standard deck of playing cards in half. I keep one half, and give you half, and you now draw a card off the top. Have your chances of drawing a spade changed since I cut the deck?


#8

In the above scenario he odds have changed because the cards are. Randomly distributed, not evenly distributed. I’m on a phone so I can’t plot it out for you but you would calculate the odids by taking the population of sll suits (16) and check the CHD for having 8 of each suit drawn in the top 25 cards (half the deck) you will observe that the odds are lower than 100%. So the distribution is most likely to be uneven and the odds of drawing a spade are either higher or lower than 25%. In a tcg game we know exactly what cards are in our own decks so why guess at the probabilities of certain events when we can just calculate them to an exact number? This is a big deal when building decks … even if adding or removing a card changes the distribution only slightly


#9

If you remove cards from a deck but have no information about the cards that have been removed, the odds of drawing a specific card from that deck do not change.


#10

If you read the above post I explained there are odds on top of odds. You don’t kneed to know what the removed cards are for your chances to change. The chance of drawing another spade is based on the chance of your removed cards being non spades


#11

If you don’t know anything about the cards that have been removed, then the removed cards have the same probability distribution as the whole deck and removing them doesn’t change a thing.

I feel like I’m talking to people from some sort of alternate universe.

OP is wrong and should correct his charts.

If one of you disagrees then we can make a wager on it and get a neutral party to arbitrate.


#12

I had realized after the fact I should have calculated RDI using 49 cards rather than 43, so the numbers are skewed a bit, though not enough to warrant a different conclusion.


#13

Actually, I think it pretty much invalidates them. You should rerun them with 49 and then post the new numbers. :slight_smile:


#14

Original post updated with the correct math. The original numbers were skewed by no more than 4%, so no, I don’t think the minor miscalculation “invalidated” the results.


#15

Nah, don’t bother running the numbers. As long as we don’t know what those extra cards are the statistics are all the same right Creed?