Hello all.

I’ve always wondered about how many times one should run a hand until he/she gives up before not finding an agenda. I did some quick Bayesian analysis using R to find some probabilities. My assumptions that there is a fresh game state, with 49 unknown cards (corp deck size), and 11 agendas left in the deck. These numbers can be easily changed in the code.

I will post the full output (and the code) below, so that you can draw whatever conclusions you’d like from it. I think one of the more interesting things is, given that the corp has 5 cards in hand,

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.42753

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.5723637

so running two additional times without seeing an agenda only increases the likelihood that the corp has no agendas by ~15%.

I am very confident in my math (I am a PhD student in statistics and probability, and I’ve coded this type of thing several times before), but feel free to argue if you think there is a mistake. Also I used R which is a free easy to use and download programming language. Like I said the numbers are easily modifiable to figure out other probablities that you’d like. It is possible that 11 agendas is a high number. It may be interesting to set the deck size to 40 to see what happens in a TWIY FA deck.

Here is the full output: (code is at the end, and forgive the ugliness. You can’t do much with R to make it pretty)

------1 cards in hand------

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 1

probability of 1 agendas in hand given that none were seen

[1] 0

—2 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 1

probability of 1 agendas in hand given that none were seen

[1] 0

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 1

probability of 1 agendas in hand given that none were seen

[1] 0

------2 cards in hand------

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.8135593

probability of 1 agendas in hand given that none were seen

[1] 0.1864407

probability of 2 agendas in hand given that none were seen

[1] 0

—2 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.8971963

probability of 1 agendas in hand given that none were seen

[1] 0.1028037

probability of 2 agendas in hand given that none were seen

[1] 0

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.9458128

probability of 1 agendas in hand given that none were seen

[1] 0.05418719

probability of 2 agendas in hand given that none were seen

[1] 0

------3 cards in hand------

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.6592636

probability of 1 agendas in hand given that none were seen

[1] 0.3085915

probability of 2 agendas in hand given that none were seen

[1] 0.03214494

probability of 3 agendas in hand given that none were seen

[1] 0

—2 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.7528365

probability of 1 agendas in hand given that none were seen

[1] 0.2349277

probability of 2 agendas in hand given that none were seen

[1] 0.01223582

probability of 3 agendas in hand given that none were seen

[1] 0

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.8240929

probability of 1 agendas in hand given that none were seen

[1] 0.1714425

probability of 2 agendas in hand given that none were seen

[1] 0.004464648

probability of 3 agendas in hand given that none were seen

[1] 0

------4 cards in hand------

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.5320373

probability of 1 agendas in hand given that none were seen

[1] 0.3816789

probability of 2 agendas in hand given that none were seen

[1] 0.08120828

probability of 3 agendas in hand given that none were seen

[1] 0.005075518

probability of 4 agendas in hand given that none were seen

[1] 0

—2 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.6185261

probability of 1 agendas in hand given that none were seen

[1] 0.3327939

probability of 2 agendas in hand given that none were seen

[1] 0.04720481

probability of 3 agendas in hand given that none were seen

[1] 0.00147515

probability of 4 agendas in hand given that none were seen

[1] 0

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.6933428

probability of 1 agendas in hand given that none were seen

[1] 0.2797864

probability of 2 agendas in hand given that none were seen

[1] 0.02645735

probability of 3 agendas in hand given that none were seen

[1] 0.000413396

probability of 4 agendas in hand given that none were seen

[1] 0

------5 cards in hand------

—1 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.42753

probability of 1 agendas in hand given that none were seen

[1] 0.4180293

probability of 2 agendas in hand given that none were seen

[1] 0.1363139

probability of 3 agendas in hand given that none were seen

[1] 0.01740177

probability of 4 agendas in hand given that none were seen

[1] 0.0007250739

probability of 5 agendas in hand given that none were seen

[1] 0

—2 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.5024754

probability of 1 agendas in hand given that none were seen

[1] 0.3930475

probability of 2 agendas in hand given that none were seen

[1] 0.09612574

probability of 3 agendas in hand given that none were seen

[1] 0.008180914

probability of 4 agendas in hand given that none were seen

[1] 0.0001704357

probability of 5 agendas in hand given that none were seen

[1] 0

—3 runs without seeing an agenda

probability of 0 agendas in hand given that none were seen

[1] 0.5723637

probability of 1 agendas in hand given that none were seen

[1] 0.3581725

probability of 2 agendas in hand given that none were seen

[1] 0.0656974

probability of 3 agendas in hand given that none were seen

[1] 0.003727512

probability of 4 agendas in hand given that none were seen

[1] 3.882825e-05

probability of 5 agendas in hand given that none were seen

[1] 0

And here is the code:

```
a <- 11 # #agendas in corp deck
N <- 49 # #corp deck size
for(n in 1:5){
message("")
message("------",n," cards in hand------")
for(t in 1:3){ #t is the number of runs without seeing an agenda
message("")
message("---",t, " runs without seeing an agenda")
d <- 0
for(i in 0:n){
d <- d+((n-i)/n)^t*dhyper(i,a,N,n) #denominator for bayes theorem
}
for(j in 0:n){
message("probability of ", j, " agendas in hand given that none were seen")
print( ((n-j)/n)^t*dhyper(j,a,N,n)/d) #numerator / denominator
}
}
}
```