If you’re like me then I'm sure you've wondered: what is the point of this card? Let’s start with some simple stories
The Corp has 1 agenda in hand. If the Runner breaches HQ their chances of accessing that agenda is 1/5; their chances of accessing something else are 4/5
If the Runner instead plays Glut Cipher, the chances that the Corp will discard the agenda among the 10 cards is 50%. An easy way to see how this is the case is to walk through how the trashed cards would be chosen: with my friends we have the Corp shuffle the cards and then hold 5 cards in one hand and 5 cards in the other. Runner chooses a hand and the Corp discards those cards. The chances that the hand they discard contains the 1 agenda is of course, 1/2.
Curious, but not our most interesting story. Let’s try another.
The Corp has 2 agendas in hand. If the Runner breaches HQ their chances of accessing one of those agendas are 2/5; their chances of accessing something else are 3/5
If the Runner instead plays the cipher, the chances that the Corp will discard at least one of the two agendas among the 10 cards is 78%. How do we get this number? When the Corp adds cards from Archives into HQ the order the cards sit in in their hand(s) will be random - each card has a chance of being one of the 5 shuffled into the hand that will be trashed. We can then think of it sequentially: the chances that the first card they trash will be one of the two agendas is 2/10; their chances of trashing something else are 8/10. If they don’t trash one of the two agendas in that first instance, the chances that the next card they will discard is an agenda is 2/9; the chances of trashing something else are 7/9; and so on.
In other words, the Runner has 5 shots at trashing one of the 2 agendas among the 10 cards, their chances increasing with every missed shot. To determine the odds of them trashing at least one of those two agendas across those 5 shots we multiply the probabilities of the Runner missing those shots together. 8/10 * 7/9 * 6/8 * 5/7 * 4/6 = 2/9, or ~.22. Then we multiply .22 by 100 to arrive at a 22% chance that in those 5 shots we do not trash one of those two agendas, which means that the inverse, 78%, is the chance that we do trash at least one of those two agendas.
(You can do the same math with the 1 agenda example above and you’ll come to 1/2, 50%.)
Run the numbers again with 3 agendas in HQ and your chances of trashing at least 1 agenda increase to 92% (7/10 * 6/9 * 5/8 * 4/7 * 3/6 = 1/12 or ~.08 )
Interesting, no? But what does it all mean?
Glut Cipher is akin to Information Sifting. Unlike that card however, which improves with the more cards the Corp has in hand, the cipher improves when the Corp has less cards in hand. It also scrambles their plans, though of course it allows them to retrieve something useful as well.
(All of this assumes the Corp has 5 cards to pick up from Archives of course - running Glut Cipher when the Corp has no cards to pick up will obviously accomplish little.)
Now, what are the chances that in the 2 agendas in HQ scenario you will trash both of the agendas? I have no idea. My math skills are not that advanced - I don’t even know if what I wrote above is correct.
In the 2-agenda scenario there is a 22% chance that you trash 0 agendas and a 78% chance that you trash at least 1. The cases where you trash both will be a subset of the cases where you trash at least 1. Let's name the agendas A and B, and assume that we know you will trash A at some point. It doesn't actually matter whether you trash A first or last, either way you will trash 4 cards that are not A, and we want the probability that one of them will be B. You have a 8/9 * 7/8 * 6/7 * 5/6 chance of missing B 4 times. This is ~56%, which means that conditional on trashing 1 agenda, there's a 44% chance you also trash the other agenda. Multipling 78% by 44% yields a ~34% chance you get both.— OrionJA