All the Agenda Math - Calculating Agenda Defensibility - Android: Netrunner

[@xiaat]

Andrej: "We're gonna release a video on agenda densities, it'll be a short one" Also Andrej: releases a 56-minute super in-depth meta defining guide which took weeks to edit I mean, count me in. That's MY kind of short.

[@jakubeichler5597]

Yeah, we all wanted this cool cyberpunk heist game and what we got in the end is hype over Quinns talking about Excel championships and Andrej’s in-depth analyses of agenda density in spreadsheets ;) But heck, this is fun, this is science! Mad respect for this to Andrej, Jeff and all involved, at least as Mad as the Dashes.

[@IxoranX]

I'M LATE, But I'm excited to see the video has arrived, I'll report back after viewing! 💜

[@tmkfnetrunner]

Living for the Netrunner community's data science arc

[@stuartterry9702]

The spreadsheet-ability of netrunner, even 'just' as a heuristic, has got to be one of its key strengths as a game. Every time I watch one of your videos about Netrunner's data I fall in love with it all over again. Some games just love to add cards or models or whatever that throw off the curve massively, but in Netrunner, the difference between 17 or 18 accesses is enormous. Thanks so much for this and all your amazing content 😊

[@leonguy1164]

yay its here, the video where metropole breaks the meta and forces nightmare archive into every corp deck, i can't wait! exciting =-)

[@MetropoleGrid]

In Standard, at most you can put twelve negative point cards in a single deck. The numbers don't lie. We all have to do it, always.

[@cephalopodwizard]

The comparison of just how many extra cards you have to add to your deck to match the power of GFI was a great comparison, I knew GFI was good, but that really puts it in perspective.

[@TheDevlain]

This is incredible. I asked myself this question so many times and tried to came up with a model that could represent this problem. This video is so underrated with only 300 likes so commenting to boost it up a little bit because this work is amazing (not only the script but to actually run all the relevant permutations and giving them in an spreadsheet file). Bravo!

[@thomasberton5657]

Fantastic work Andrej! One interesting note on the GFI vs Defensive 3-Pointer question, specifically regarding Dashability, is that Defensive 3 Pointers are inherently more "Dashable" than other agendas, because of the additional cost. If the Runner hits a Bellona on the top of R&D when they have a Mad Dash in hand, they can decline to steal and then run back with the Mad Dash. So there's an even stronger argument for GFI, since it's a bit tougher to land a Mad Dash on.

[@MetropoleGrid]

This is a huge part of why Mad Dash was so good against last year's competitive Reality+ deck that played only six defensive 5/3s. Find the Degree Mill/Bellona, bounce, and Dash back was a super common line.

[@miltonfrey7274]

I absolutely love when people do math on card games. Frank Karsten famously did a ton of analysis for Magic and I always loved reading his write-ups. This feels like the equivalent of his mana primer, very well done.

[@duff7100]

Hi Andrej, this video is huge help for me as a brand new player, it helps to get a sense of parameters that can impact deck performance. It is clear it is not a simple recipe to follow but gives trends. Thank you for all the work on this 🤩

[@IxoranX]

Been looking forward to this for a while, and it was well worth the wait! I think this is gonna be heavily referenced and end up the defacto Agenda Suites reference. Absolutely killer job, especially explaining the data and it's limitations! I sent a reddit comment your way about limited agenda suites, but I'm looking forward to getting this tool set up locally and running some numbers myself!

[@MetropoleGrid]

Cheers Ixoran! I have another script set up to automate simulations across any given deck size and format's agenda pool, outputting the data to spreadsheets. If you want me to mass run some limited data, just hit me up.

[@IxoranX]

@@MetropoleGrid @MetropoleGrid Oh! I'd love that, I did respond to your reddit post about some limited agenda suites. also excited to have access to such nice tools

[@manveruppd]

Incredible work, you must have put hundreds of hours into it! :o This will be useful to people for another ten years!

[@xdg95]

Great video! It's really eye opening how different combinations move the numbers around. I'd love to see a followup where you talk about this from a corp side play POV, since the number you calculate also relates to the number of cards the corp needs to see to find the agendas to win (except with GFI counting for 3, negatives not counting at all). Is it possible to simulate agenda flood? Etc. This also made me think about the importance of the corp staying ahead of the runner on "cards seen" (5 starting + 1/turn + corp draw vs runner access rate). Opening hand + 3x Spin or a DBS has the corp see their 17-18 much faster than the runner will.

[@MetropoleGrid]

You're totally correct about that - the calculated 'number of accesses' is the exact same value as the number of cards a Corporation needs to draw to have a ≥50% chance of seeing seven agenda points. That's also really important to keep in mind. Now, simulating agenda flood is a much simpler calculation, as it has no complicated correlation with different agenda distributions. To simulate agenda flood we only need the deck size and the number of agenda cards, and we can send that through a hypergeometric calculator. So say for instance we're playing the 49 card deck with ten 2-point agendas. If we throw that into a hypergeometric caluclator with a population size of 49, 10 successes in the population, a sample size of 5 (our opening hand), and we check for the probability of finding three or more successes in our sample (we're defining 'flood' as opening with a hand of three or more agendas), we get the P(X≥3) of 5%. The 49 card deck with 2-pointers and GFIs goes down to 3.7% That's a super useful statistic to keep in mind when deciding how aggressively to mulligan, let alone when deck building. Thanks for the kind words, eh!

[@francisfortin5663]

Wow! You did a really good job! The work itself and the explanations. I'll keep that in mind now, I need, or need to prevent, 17-18 access a game.

[@Daslikdj]

Drink every time Andre says hypergeometric distribution

[@TheDevlain]

Ethylic Coma

[@matthewcreech3854]

Now for the follow up piece on why you don't like 3 point agendas. Great work

[@dutchoh1]

You just leveled up on the nerdcore my friend! Totally down my alley, love it!

[@HaverOfFun]

This is incredible! Not only for my deckbuilding but also for convincing my maths-interested friends into maybe trying the game :D Thanks heaps!

[@whatshendrix]

This is fascinating and it's exactly the type of content I'm always looking for. Thank you so much for putting in all the hard work and your own knowledge into this!

[@hedonismbot3798]

This is a great walkthrough explaining the process and assumptions of the simulation in a really accessible way. Fantastic!

[@ashurroth6585]

Must insert GFI, nightmare archives. Towards the end when you talk about upping agenda density by lowering cards in the deck, I thought this could be good in Personal Evolution of you are going for a flatline. If they hit an urtica with mad dash they take urtica damage+1, they hit an agenda they take damage. I don't know the card pool well enough but I feel nightmare archives in this deck could really hurt and up the accesses required.

[@MetropoleGrid]

Nightmare Archives and News Team show up pretty commonly across Startup and Standard respectively. They're great!

[@anrmurse]

This is one of the most important pieces of content that the game has. Thanks!

[@RTsa2]

This is awesome stuff. Very good insights and some surprising results too! Well worth the wait. 🤩 I especially like the “dashability” metric. 👍🏻 Time to go put GFI and Mad Dash in everything. 😂 (not that I don’t already most of the time 😅)

[@willn9568]

Great detailed video which obviously took tons of work and time. Another great contribution to the community! Maybe now you could also do a very short quick conclusions video with just the bullet point takeaways and links to this video and to the other sites-that would get my click again, and it might draw more people in, possibly even driving more traffic to this great video, which took me a while to watch completely (and it was worth watching for sure).

[@asphyxiaVR]

its finally here lets goooooo!!!

[@meathir4921]

45:00 Another potent thing about running GFI is that you're not ACTUALLY adding 11 cards to your deck. You're reaping the rewards of increasing your functional deck size without the punishment of seeing your best cards less often.

[@seebasss]

This was sick, i wonder if you could get this data into the NRDB2 deck builder

[@piotrtabor959]

high quality stuff, appreciate the effort

[@tom3k_b]

Great analysis, thanks

[@randomdogdog]

I get the simple 17-18 accesses another way. There's 20 agenda points, the runner needs 7, theres 49 cares in the corp deck. 7/20*49=17-18 cards.

[@MetropoleGrid]

Could you kindly explain what the math is calculating here? I can't get my mind around it.

[@pjgoldstein6562]

I miss government takeover in builder of nations kill decks. 4 agendas. If you can hide the takeover, needed to score. Punitive if they do steal, hostile if they don't.

[@alexscriabin]

5:29 nice

[@flopus7]

Some good data analysis Would be interesting to make a netrunner dashboard

[@RuvenCH]

This is awesome, thanks so much! Question though: How does that work with Deep Dives or Kushyuks? Like there you see 6-8 cards, but generally only access one. So if there's 3 agendas in there you wouldn't get them all. However you still SEE 6-8 cards. How do you calculate that?

[@MetropoleGrid]

Cheers Robin! The data unfortunately does not have a great way to directly account for Deep Dive or Khusyuk. For simple shorthand, I'd just count them as a good 5 or 6 accesses, and not worry too much about it. :p I reckon, if you're finding the Dives and Khusyuk's to be consistently converting to agenda steals, you could model it somewhat similarly to Mad Dash - you generally win a game by stealing 6 or 5 points from servers, and then your Shaper multi-access finishes it off. However, keep in mind that you can use the 'agenda per card' statistics to get an approximation at how consistent the Dives and Khusyuks will convert. That's a good thing to keep in mind.

[@GreenMonkeySam]

34:35 - "There are 5 Cards for each (per) Agenda in the deck" Cards per Agenda should be the correct term with that column

[@alvinlee3982]

Hey Andrej! Awesome work you've done- did you ever figure out why the simulation and the hyper geometric results were different in initial development? I recall you mentioned that observation while you were developing the tool

[@MetropoleGrid]

Hey Alvin! Originally, I wasn't calculating the cumulative win-rate across all simulations, but rather the average number of accesses required to win across all simluations. To elucidate, let's say I ran a simulation one hundred times: Originally, I would look at the results and see how often the Runner won on each amount of accesses: they won on 4 accesses X times, they won on 8 accesses Y times, ..., they won on 22 accesses Z times, etc. I simply averaged those numbers out ((4*X + 8*Y + ... + 22*Z) / 100) and came up with my 'average number of accesses required to win'. This turns out to not be the best number to look at. This unfortunately goes a bit over my head, but if you check out the Giant Isopod stream, Ruben leaves a great comment explaining how this method calculates some form of negative hypergeometric distribution. Close, but not exactly it. What I eventually ended up calculating was the cumulative win-rate probability at each distinct number of cards accessed across the simulation. So let's say that across all simulations the lowest numbers of accesses the Runner won on was 4 accesses; let's say that was observed 3 times. That means their probability of winning on 4 access is (3/100), or 3% The Runner won on 5 accesses slightly more often (as the hypergeometric distribution would suggest); let's say 6 times. Therefore their probability of winning on 5 accesses is (6/10) or 6%. However, the Runner's cumulative win-rate at 5 accesses is their probability of winning on 5 accesses plus their probability of winning on 4 accesses. Therefore their cumulative probability of winning on 5 accesses is 3% + 6% = 9%. We can keep climbing up the data until we find the first number of accesses required to reach a cumulative win-rate that is ≥ 50%. This is the proper method we need to follow to get to that hypergeometric result.

[@RTsa2]

No love for Merger though? :( I put that two of those bad boys in a Harmony Medtech FA deck back in the day. I don't think it affected the number of accesses needed much at all (all the rest were 2-pointers). I think the only way it lost faster than running regular 2-pointers is if the runner saw Mergers as both of the first two agendas as Mad Dash wasn't released yet...

[@MetropoleGrid]

Heh. I kept the script/data to modern Standard or Startup, so there's no love for Merger, Vanity Project, let alone Government Takeover. It's an easy enough thing to patch into the script. For what it's worth, you can run the script in 'deck override mode' (it doesn't check for deck legality), and simply input the Mergers as three-point agendas You'll get the appropriate data. I gave it a shot, and unsurprisingly, it produces data similar to running the maximum number of required agenda points. It's not great :p

[@drewconley951]

How much MU does this program take up? :D Nice work Andrej!

[@MetropoleGrid]

I crunched the numbers, and the data sheet displays over 8.7 billion individual simulations. We're going to need a Daemon.

[@dnddmdb642]

Is 50% winrate a good threshold to use? Wouldn't you want something like 90% to suggest a solid likelihood of winning? I guess if you're comparing two different agenda suites, the comparison would still hold up at different desired win rates, though.

[@danielluna4878]

Comparing against 50% is essentially like asking "when on *average* do I lose to accesses." If you raise that percentage, you start indirectly measuring how lucky you are that it hasn't happened yet. Like, if you wait for 90% likelihood, then the number you get will only be accurate to the luckiest 10% or so of your games. Additionally, distributions of this type tend to weight towards the middle. You can also see this behavior if you look at how likely it is to roll a given value on two six-sided dice (another distribution). If you haven't seen it, there's a one in twelve of rolling a 2, a one in twelve of rolling a twelve, and a one in *six* of rolling a seven! That's because there's way more ways to roll the dice to get the average than there are to get the extremes. A similar thing happens in accesses (you only win on the first 3 accesses if they are all agendas, but you can win on the first 10 if any three of them are agendas). So because distributions weight towards the average, the average applies to far more games than you might think.

[@MetropoleGrid]

It's a great question, and Daniel's answer is perfect. However, if you use the script and output the cumulative win-rate plot, you should be able to observe the >=90% win-rate data on the plot. When I have a moment, I should be able to easily add a mode to the script so you can input your desired '>=X%'.

[@Lordpitcher_cl]

🤓 nerdgasim!, thank you! 😂

[@GarretWehrman]

Will the spreadsheet be updated with numbers to accommodate the new Startup card pool?

[@MetropoleGrid]

This is something that's unfortunately on the back log. For what it's worth, you can find all of the new Startup numbers within the Standard sheets. Currently in Startup, no Corporation can play more than six 3-point agendas, thirteen 2-point agendas, or nine 1-point agendas.

[@GameOfDroids52]

So we should ban gfi and mad dash?

[@MetropoleGrid]

In this video, I didn't really get into my gameplay/balance thoughts regarding these numbers. With Global Food Initiative two months from rotation, I reckon we don't need to do much about it. Mad Dash appears to be a necessary evil against the top-heavy defensive 5/3 suites, so I don't think you can ban that without a significant impact to top table play. Currently one of my favourite aspects of the Startup format is that the dearth of 5/3 agendas ensures Corporations have a higher 'agenda per card'. This forces Corporations to have their agendas be a proactive part of their gameplan, as it's largely unfeasible to simply play 'agenda keep away'. I like that, as nearly all Startup games do truly focus on the agendas. There's definitely more to be said here about the lack of truly defensive agendas in the format. I think I'd be interested to see what the Standard format would look like if Corporations were limited to playing no more than three 5/3 agendas in any given deck. This would hopefully limit the number of truly defensive agendas any single deck can run, while also clamping the extremes limits of the 'agendas per card' ratio. I don't think its a particularly elegant solution (I don't like seemingly arbitrarily rules overhead), but I'd be interested to see the impact it could have.

[@Kelann08]

Nice.

[@theobserver7373]

I'm curious what Government takeover would do to the number of accesses.

[@MetropoleGrid]

I ran some tests with Government Takeover and was very surprised with the results: Mendax's 'War of the World's' deck was a 44 card deck that ran a Government Takeover, three Global Food Initiatives, and three Hostile Takeovers. The Runner needs to access 20 cards to hit a cumulative 50% winrate. That's the exact same results as a conventional non-Government Takeover GFI list! I thought it would be a lot higher. The number looks to be quite volatile, as the Runner wins by stealing only two agendas 29% of the time, three agendas 14% of the time, four agendas 23% of the time, and a whopping five agendas 34% of the time. So you're more likely to have a slog of a game, but the volatility of the massive Government Takeover really does a number on the results. But on average, still not better than Food and a bunch of two pointers. Wild.

[@Tom_Blue222]

wooooooooo

[@river0099]

thank you so much for incredible content 🥹🥹