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The probability of drawing an agenda at any point


#1

I have constructed a table that shows the odds of drawing an
agenda based on how many cards are left in the corporation’s deck.

Here is the table. Right click and save as. (xlsx file)

My own impetus was to see if the risk of running Government Takeover was worth it. My goal is to create a low agenda density deck, but how risky is it at any given point in the game?

THIS INFORMATION CAN BE USEFUL TO OTHERS because it takes no
prejudice on who draws the card: corp or runner. If you run 10 agendas in a 49 card deck, and have not seen one after your first mandatory draw, there is a 24% (or about 1 in 4) chance that the next card is an agenda; if there is an agenda in hand chance is 21% or almost one in five. With this knoweldge we now know the odds of a runner getting an agenda from an unprotected R&D is lower than that of a 4 card HQ, but would be the same if the corp ends with 5 cards in hand.

I offer this information to the community in the hopes that
at least a cursory knowledge will give an insightful edge to games.

Key:

The ‘Deck’ column
represents the number of CARDS LEFT in your deck.

The Purple row is
how many agenda cards are left in your deck.

The red highlight
shows popular (and not so popular) deck starting sizes.

The orange line is
your decksize after drawing a starting hand. This line is also a popular starting deck size for Harmony
Medtech (as far as I know this and Weiland are the only decks with a possible
of 6 agenda cards).

The yellow line
shows the odds of drawing an agenda after the corps first mandatory draw.

I forget what the pink area is. I think it means
it’s impossible for that starting hand size to have that many agendas in it.

(The area on the
left is grayed out as it’s of little interest to my own reasons for doing this
investigation, but it is still of use for comparison, and for those running a
reasonable amount of agenda cards)

PLEASE NOTE: This table DOES NOT take into consideration the
actual number of agenda points; only the card. On this list a Government Takeover has the same value as a
Firmware update: one card.

Do with this as you will!

Some points of note for those running low agenda density:

After the initial draw of a Medtech deck with no agendas in
hand, there is a 16% chance the next card is an agenda. If you are in this position 6 times, the
next draw, on average, will be an agenda once.

As noted earlier, if there are no agendas in the starting
hand of 6 cards in a 49 card deck with 10 agendas the odds of the next card
being an agenda is 24%. It will
take a 6 agenda deck of the same size 18 draws to get to the same odds.

If there is an agenda in the starting hand of the 49/6 deck
there is a 12% chance, or 1 in 8, that the next card is an agenda. If you end the turn with five cards in
hand you now know that the runner has a 1 in 5 chance of getting one from your
hand, and only a 1 in 8 of getting it from your deck.

Probability of drawing an agenda in a low agenda deck does
not increase at the same rate as a deck with more agendas. It increases more rapidly in high
density decks. (i.e. a high density deck’s probability increases in a
significant figure after about every 2 draws, where a low density deck’s
increases after about every 3 draws)

Discuss, ask questions, or show me where my thinking has
gone wrong.


#2

any chance of getting this into a google doc or something that doesnt require software? sounds like a great resource to study, especially for someone like me who cannot do these calculations on the fly during game


#3

Here is an HTML version in case you don’t have MS Office or compatible.

It’s harder to read, but it’s the best I could do on the fly.


#4

It’s not that hard really: at any time the probability of drawing an agenda is the number of agendas left divided by number of cards left in the deck,


#5

I forgot to mention, you can use this table for any cards that serve a similar function. Say 3 Desperado or 9 economy cards.

@v01d True, but having a table can be handy during deck construction (as I’m doing now). Also, it’s interesting to see, all at once, how the odds will change throughout the game.


#6

Sure sure, I am not advocating against having a table. I just wanted to stress that it is easy to calculate, in contrast, for example, to the probability of having some card in your starting hand which requires the hypergeometric distribution.


#7

Speaking of which!

Here’s a calculator for that very thing

Population Size = deck size
Successes in Population = Number of desired cards in starting hand
Sample Size = 5 cards
Successes in Sample = exactly 1
Hypergeometric Probability = results