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Fallacies In Netrunner And How To Avoid Them by Xenasis

@Xenasis: Thanks for the article. I’m hoping this makes people think at least a few times more before having a 100 post discussion about Maxx’s mills :wink:

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These are some of the toughest decisions in the game I think and the “right” play probably depends on your economy package (and your expectation of what the Corp might do in the meantime). I’m loath to leave myself low on credits if my economy package is such that I can’t get going again without clicking back to ~5. Cards like Liberated Account and Hedge Fund really struggle with this, but if you have a Magnum Opus economy it’s not such a big deal. Sometimes it’s right to take the hit now and leave yourself in a position to bounce back quicker than if you go for broke now.

The answer, really, is to evaluate every situation on its merits and drawbacks and try to make a decision that’s as well-informed as possible given the information you have.

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Good article, and nice read! You describe a lot of pitfalls I walk into from time to time. Especially about trashing assets that are around a few turns already. I tend to forget them somehow…

With the (Noise) mills I always thought that the following applied as well (not a native English speaker, so will use more words then necesairy to explain, please bear with me): as your deck is never ‘perfectly’ randomised, mills tend to not be an even distribution of your deck. So by splitting your deck between archives and R&D, so to speak, you by default change the composition. A non-milled deck will have a different expected spread of (type of) cards then a milled one. This is a broader way to view your statement about mills given agenda’s exist. Just by milling random cards, you will have the situation that you mill more of one kind then another kind of card. Given a couple of draws from Corp, you can severely scew the deck composition. Your deck is made to function as a whole, after all.

What are your thoughts on this? Makes sense?

It’s true that in the most absolute sense, it’s not random what you mill, but since the runner has no way to predict or control what comes next, I think this is something that can basically be ignored from Noise’s perspective. From the Corp’s perspective, they can try an fix things by using cards like Jackson, Rework, Precognition to either add cards they don’t mind being milled to the deck (using Jackson Shuffle/Rework), try and pull a critical card before it could potentially get milled (overdraw with Jackson, Precog into it), or arrange the order of cards to decide what gets milled (Precognition). Overall, the ultimate answer on what gets milled is still more than random enough that most of these strategies are probably of dubious usefulness.

In terms of composition, given a deck’s % composition of ICE, Operations, Assets, Upgrades, and Agendas, if you randomly mill, say, 20% of the deck, I would expect the given composition to be about the same. In fact, until the runner knows what was milled, then you exist in a state where both all the agendas are milled and none of the agendas are milled simultaneously. It isn’t until you run archives that you know for sure. I shall name this phenomenon “Schrodinger’s Mill”. :smile:

Noise can try and alter the card distribution personally by making controlled virus plays. If you run R&D prior to playing the virus, you can then decide to either allow the card to be drawn or play a virus to mill it away. In this way you can deny specific cards to the Corp.

EDIT: The “Schrodinger’s Mill bit” is not meant to be completely serious.

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Good article, I agree with 90% of it.

“The Gambler’s Fallacy” is plain wrong though.
That’s how for exemple IRL BMWs / whatever luxury cars are made (a little more) silent. Predictive algorithms are basically made on this and are proven working for meteorology, stock markets, electronics, modern automatic gearboxes, robotics, GPS, radar… And thousand of other things like this (for more on this, check automatism & signal theory).

In this exemple, it would basically predict head btw :wink:

I don’t really understood the things on Noise’s milling. I agree information of what is milled is something good, but I can’t really take this for a good thing. Noise’s mills are bad for the corp, in a sense that it makes the corp defend on 4 servers instead on 3 only. Knowing what you can’t rely on is good, yes, but when Noise starts to mill me, I am not starting to think that is a good news for my game because I have more information. I’m starting to think “osh-t, got to defend archives rigth now”.

A little like “a runner stealing an agenda is good because you know now you won’t be drawing it, so start now to change your plans”. A runner stealing an agenda makes progress toward victory, like Noise does milling the corp. Sure, that helps to think “there’s no Astro left”, but if the Runner have all of it, I’d rather don’t know :slight_smile:

That are the two points I disagree, the rest is minor things (MaxX things on hi/lo variance).

I’m bored, so I’ll bite.

No. Take into account that both head and tails have an exact or very near 50% chance of occuring (I think properly weighted dice are a better example, but coins work as well). In this case, you can’t predict anything because you are human. Sure, if you would take 1000 coinflips by the same person, in the same location, same windspeed etc. you might get a better prediction (maybe?) for some reason, but that only works for machine-analysed data.
This is all completely meaningless for Netrunner though.

[quote]It means that despite them missing a two-in-five shot at an agenda in
your hand three times, they aren’t any more likely to hit it on the
fourth access.[/quote]

This is all that matters. As long as the context doesn’t change (i.e. the runner trashes cards from your hand), the odds of a certain result don’t change either.

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@Labbes Well, let’s all invest in umbrellas then, because without GPS all planes are gonna fall :wink:

You can use this when seing that’s the fourth time in a row the corp played something else than an agenda. Go run R&D now. You can use this in a lot of ways. Each time I used this, I had to say “sorry for my luck”…

This is actually a pretty bad expectation. I’m on my way to teach a class, so I can’t run the math on it right this second, but consider the question at a smaller sample size: if you have a 15 card deck, made up of 3 copies each of 5 different cards, your odds of drawing a 5 card hand that contains exactly one of each different card is not great. Even though it is the single outcome with the highest possibility (e.g. the odds of “a,b,c,d,e” are higher than, say, “a,a,c,c,e”), it’s not an outcome you should expect compared to the sum total of alternatives, any one of which represents uneven distribution of some variety.

If the context does not change, the chance of an event occurring do not change either.
In the example by you, context changes (or, speaking in Netrunner terms, the gamestate changes).
In the example by Xenasis in the article, it does not (runner runs on hand X times, never sees an agenda or trashes anything).
So you can’t compare them. It’s not the same thing at all.

The maths just doesn’t work on this. There’s nothing to guarantee that you’ll “screw the deck composition” by milling some random cards. For example its just as likely that you’ll mill them through all the excess Ice they were going to draw and instead have them draw the perfect mix of cards.

This is another useful way to look at milling incidentally - sure you might mill away their Hedge Fund, but you might mill them straight to their Hedge Fund.

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@Labbes well no event leads to no context change, of course.
People should drive without safebelts by this theory : “but I never had an accident before, officer…”.

The given exemple just tells you’re risking a 40% steal event four times in a row, I don’t really think it’s the safiest way to win a game.

And you know, the runner could read this on your face btw.

Soo, Dan needs a new title?

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The gambler’s falacy is that the fact the runner missed 3 times makes it more or less likely that they’ll miss again. It doesn’t, each event is independent of the last. The chance of accessing an agenda is 0.4.

Not doing anything to prevent giving up 0.4 chances to lose the game is a bad idea unless actually it’s the best you can do.

Runner accesses aren’t actually independent of each other though. If the runner has seen 3/5 non-agenda cards it’s easier for him/her to believe there are no agendas in hand. So they may be less likely to run HQ again.

Streaks either lucky or unlucky don’t mean anything, they’re just probability doing its thing.

The deck, in practice, will have a different composition pre and post mill, but there is no way to predict or know whether that composition will be better or worse, and on average, the composition will be the same.

The Gamblers fallacy presupposes that the events in question are independent. If you uncover more information about the likelihood of something, it changes the probability. The probability that it rains tomorrow is affected by whether or not it rains today, because weather is continuous, so tomorrows weather is a function of todays, and they’re not independent.

Let’s say you saw NAPD on top of R&D and couldn’t steal it, and run HQ the next turn trying to get it without any info about what was in HQ otherwise. Let’s say you see a Hedge Fund. You now know that one card in HQ is NOT an agenda, and one is an NAPD, so your probability of hitting an agenda goes down. If you know every card in HQ, accessing one doesn’t change the probability, from your perspective, of hitting an agenda on the next access as long as HQ composition didn’t change.

The gamblers fallacy doesn’t apply to the things you mentioned because we uncover new information about the probability distribution as new events occur. If we absolutely know the probabilities and the events are independent, they don’t change. (For instance, if we know half of the hands we draw with our deck are mulligans, and we ship back our first hand, the chance of drawing into another hand we would have liked to mull is still 50/50).

“Expected value” is a term in statistics that is defined as the average value. If we roll a six sided dice, the expected value is 3.5, despite the fact that you can’t ever actually roll a 3.5.

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@MasterAir @mediohxcore oh, so it applies only to the HQ multi runs then, and maybe psi accesses (if you play psi random), and nothing else ?

I was quoting this to ask where was the typo, but hey, there’s no typo there. :slight_smile:
By thinking on it for the third time, I think I knew this but was not really aware of it.

The problem is in real game, do all of you guys have poker faces to masks you’ve got x agendas ? (I’m a dancing guy, I could remove my t-shirt to make you at least say a word, or something :stuck_out_tongue: )

I would think they don’t value someone’s physical tells as highly as their in game actions. If you’re in a league with people then learning to read them could be valuable, but once you go to larger tournaments (Regionals, Worlds, etc…) that advantage is largely negated. You’d have to be able to read a completely new person in less than an hour.

I could scream and shout every time I draw an agenda but unless you know that about me I could be making a lot of sound and fury for my favorite ICE and it would look the same from your end of the table.

That’s an accurate definition, but it doesn’t particularly pertain to the use of the term in the discussion above about the qualitative impact of milling (hint: an even distribution across “1,2,3,4,5” results in an expected value of 3 for any random selection, but an even distribution across “a,b,c,d,e” does not have an expected value of “c.”)

Yes and no. Mostly yes. But…

You can’t predict how the composition will change, but it is a safe prediction that the composition will change in any given instance (in fact, for any single mill, it’s a guarantee). It’s true that those changes average out to mirror the original composition as the number of trials approaches infinity, but that’s not especially germane to any given match, where you’re dealing with a much smaller sample size of mills. Given the amount of attention players devote to striking just the right proportion of various cards in their deck, it’s worth considering the notion that any impact to that composition will have deleterious effects on their play.

Consider the following in a corp deck with a hypothetical 1:1 ratio of economy and ice (this isn’t a good deck, but it makes the example clearer):
In one match, Noise mills 4 pieces of econ and 2 pieces of ice, leaving the corp with an unusual abundance of ice.
In the next, Noise mills 2 pieces of ice and 4 pieces of econ, leaving the corp with an unusual abundance of economy.
The results across all trials conform to our expected values (1:1 ice:econ mills), but the qualitative impact on each of these individual games is much more significant. In the first match, the corp is going to struggle to rez their ice, while in the second they might be sitting on a pile of cash with not enough ice to rez.

None of this should be read to suggest that random milling is a terribly effective strategy in and of itself. It is more-or-less accurate to say that the impact on deck composition of any instance of milling x number of cards is no different than if those x cards had been on the bottom of their deck (discounting decking the corp or other game effects such as tutoring/recursion, etc.). Indeed, given the fact that much of this game is about hidden information, the net impact of random milling would be worse for the runner* until they check archives, as the corp knows what is milled and can adjust their lines of play based on how their expected draws shift as a result.

*Considering only deck composition. The biggest impact of random mills, of course, and the reason it’s much more effective here than in a game like M:TG, is that it moves some portion of the random R&D accesses into a separate server, necessitating separate protective measures.

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It does because if you don’t know what cards you milled, (or have yet to mill them), the chance of any card being drawn post mill is the same as pre mill.

Sure, decks are built with a specific composition in mind, and changing that can be bad, but there is just as much of a chance that changing it can be good. In the cases where you mill slightly more econ or slightly more ice, the corp is probably either looking for econ or ice, and you could just as easily be helping their deck composition as you could be hurting it. Unless they’re drawing literally all of their cards, it’s EXACTLY the same as the chance those cards were on the bottom of their deck. Milling doesn’t hurt them AT ALL by comparison, (of course, this is ignoring the presence of agendas, which is the real benefit of milling the corp).

The variance you get from shuffling fucks up deck composition the same as the variance from milling.

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Well the problem I have with this line of thinking (milled card could be in the bottom of the deck), is “probabilities of drawing A knowing A is allready in Archives”.

They changes, because any single corp deck use at least Jackson and can shuffle bottom cards to top.

Noise and the corp quite don’t care milling / get milled 1-3 cards, now with 10-14 cards, odds of Jackson are going up (like Maxx) and there you will shuffle.

So sure cards could come from the bottom of your deck but some of them are lost in Archives now. If a Hedge got killed, minus the one you mulligan for, odds to find the third are very low.

So ok, cards could be put under R&D instead of getting milled, but it’s a little bit more than this to me.

(+ archive protection aka the agenda problem, which sounds to me unreasonable to put aside)

And yet, a uniform distribution across a,b,c,d,e has an expected frequency of c as .2. In particular, the fact that, in a deck with 3 copies each of {a,b,c,d,e}, having a 5 card hand that has 2 copies of a single card is what you’ll draw the majority of the time doesn’t change the fact that the expected value of the frequency of any given card is still 1.

I think I get your (and @anon34370798’s) point that, if the runner gets to see the cards they milled (which usually costs a substantial resource investment in practice), then they can update their expectation of what cards are remaining in the corps deck and adjust their strategy accordingly. The problem here is that the runner doesn’t know those prior distributions with enough certainty to be able to respond accordingly in any realistic game-state.