Fallacies In Netrunner And How To Avoid Them by Xenasis

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[quote=“hotfuss, post:58, topic:3717”]
the whole argument that “those 3 Jacksons might as well had been at the bottom of the deck” while true is not the same as playing a game where you know Jackson is gone. [/quote]

Yes, that’s why everyone is saying that milling is actually good for the corp because it gives them that knowledge.

If x3 Jackson are the bottom of your deck for the entirety of the game, you’re not going to draw him (aside from the unlikely scenario that you draw all the way through your deck). There’s no functional difference aside from knowledge between the game where x3 Jackson is milled and x3 Jackson is at the bottom. Milling is no more likely to cause the x3 Jackson to be inaccessible and so doesn’t have an impact.

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Lets say that when you play netrunner there is a 1 in 100 chance that the single Jackson card you use will be on top of your deck, and 1 in a 100 it will be at the bottom ( these odds are just to use round numbers). In a universe with no milling. You would play 1 in a 100 games where you wouldnt see that Jackson because he was at the bottom of the deck.

In a land far far away were milling exists, again in 1 in 100 games you will never see Jackson, but in the scenario were that Jackson was at the top he is now gone due to milling, which means you would play a total of 2 in 100 games with no Jackson, (but this time at least you know it). Yes, you will dig deeper in your deck now but there are no more Jacksons to be found. You might say that in the case were Jackson was at the bottom your milling might make it easier to reach him, but how often do we see a corp reach the bottom of the deck even in Noise games? (Still there is a chance that that 1 mill could get you that bottom Jackson and this is where things get very complicated which I guess is the point some people want to make: the impact of milling is so subtle we tend to dismiss it as non existant).

I apologise for using such extreme examples but I simply do not understand why people insist so much on saying that two mechanics that have very similar effects on the game are practically the same thing (agendas aside as we keep saying of course).

On many, many cases yes, milling is just the same as removing the bottom card from R&D and its very easy to understand why but just because this holds true for the majority of the cases we shouldn’t be under the illusion that milling didnt have an impact in some of our games.

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Here is what you are missing:

Lets say the corp draws 50/100 cards during a game, for sake of argument. Let’s say during this game, Noise mills only one card. There is a 49/100 chance your jackson is in the bottom 49, and you wont see it. There is a 1/100 chance noise mills the Jackson. There is ALSO a 1/100 chance noise mills a nonjackson card and Jackson is the 51st card in your deck. So, in total, there is a 50/100 chance you see Jackson, and a 50/100 chance you don’t.

Compare this to the obvious, where noise mills no cards, where there is also a 50/50 you will see the Jackson after drawing 50/100 cards.

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Err, that exemple is typically rigth but with number of Jacksons = 2, this is no more working the same : Jackson can recur a milled Jackson… (and Agendas, blablabla).

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Yes but here is the tricky part, in “real” netrunner, the chance of reaching the last card of your deck (or the 51st of your example) is extremely low. The odds are not “symmetrical” for lack of a better word and that is the very fine detail I am trying to point out and why you cannot say milling is the exact same thing as removing the bottom card from your card.

One concept interacts with the bottom of the deck and one with the top. And the chances of seeing top cards are not the same as seeing the bottom cards. Yes Noise’s mill does give you the same “chances” to draw the card you wanted but if that card was at the bottom and we know that in netrunner in 99% of the games you never see the bottom card, his dig effect doesnt “shift” the odds one card down as you are saying (as far as the bottom card is concerned for example).

TL/DR: As you say there is a 1/100 chance Noise will mill a nonjackson card, and in a game where all cards are drawn yes that would even out the odds because at some instance the 51st card would be Jackson. But in a game where you DONT see the whole deck you cannot use that analogy. You have to also apply the chance that this will be a game where you will actually reach card #51.

edit: messed up the quote

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You misunderstand. For any game against Noise, let’s say, you will have X draws to find a Jackson Howard before you’re overwhelmed with mills or whatever and will lose. If you find Jackson in X draws, you win. For any X, it doesn’t have to be 50, it could be 15, the chance that Noise mills away a Jackson you would have drawn to save you is EXACTLY the same that he mills a nonJackson card and allows you to get to a Jackson that was X+4 or whatever cards from the top of you deck where you otherwise would not have.

The odds ARE symmetrical. If 3/49 cards in your deck are Jackson, you have a 3/49 chance of finding Jackson on any draw. Noise can either mill Jacksons or nonJacksons to affect that chance over the course of the game, but the 3/49 chance he mills a jackson and hurts your odds are exactly balanced out by the 46/49 chance that he mills something else and helps your odds. On average, 3/49 cards you draw will still be Jackson.

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I think the critical detail here is that what you’re saying is only true in hindsight. If Noise mills a Jackson off the top of your deck, then yes, that does have an impact on the game. If you’d drawn that card instead, it’d be available to you; now it’s not. Nobody is arguing against that. However, this is true only after the mill has happened. Before that card was milled, neither of you knew what it was. If Noise made you choose to mill the first or second card from the top of R&D, would that make a difference (assuming neither player knows which card in R&D is what)? Would you ever prefer one over the other? No, because you’ll never know if the card you want is the first or the second, so it doesn’t matter if you flip a coin or always choose the first.

I like to think of undrawn cards as in a quantum state: before you draw that card from the top of your deck and see it’s a Jackson, that card is not a Jackson. Until you observe what card it is, it’s 3/40 Jackson, 3/40 PAD Campaign and so on. That Jackson only becomes a Jackson when you look at it. Before that, all cards in your deck are exactly the same.

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A similar example is this: You play Special Order to fetch your Corroder, and it turns out it was on the very top of the deck. You have every right to be bummed because you might as well have clicked to draw it instead, but the fact that you know this now does not make the Special Order a bad play. It was probably the best play before you knew this, because the top card wasn’t a Corroder before you played the Special Order.

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I 'll guess we 'll have to agree to disagree, I was about to go into detail again describing why the chances dont even out but the truth is all I had to say has already been said, and the last example we used was as good as it gets to putting a picture to the whole thing.

So nice talk, I believe its best not to keep dragging this on!

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Schrodinger’s Mill in action, folks! That’ll be $50 for royalties. :stuck_out_tongue_closed_eyes:

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Totally correct.

Bottom line, you don’t want to be milled because it A) leaves an agenda vulnerable in archives or B) Ups the concentration of agendas still in R&D.

If you knew in advance you’re going to get milled 10 times in a game, it still doesn’t make a given card less or more likely to be seen. These odds only change during the game when the milling happens, and the corp knows which cards now all have slightly better odds to be seen (all still left in R&D) at the expense of the milled card.

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@Minotower B) is untrue until you Jackson agendas back to R&D. Plus Jackson could actually lessen that density if you Jackson 3 non agendas :wink:
That’s not because you draw or the runner mill cards that agenda density changes in R&D.

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Ok I found this topic so interesting I discussed it with my playgroup, the result was a really nice visualization of whats going on. With the risk of busting people’s balls I wanted to share it, I believe it will at the very least make it easier to find our point of disagreement (believe me, I have no problem being proven wrong but I really want to understand why I am wrong cause this bad boy has been bugging me)

Check this illustration

The green color shows the cards a corp will see in a game.
X is the potential position of a single Jackson card.

We know that the probabilities of a corp drawing a card in a netrunner game are fixed (for example 1 in 49 for a single copy) and thus we have a closed system where these odds are preserved. If milling also followed a specific behaviour or “law” (for example in the illustration Noise mills 1 card every game) you would get the exact same result, because milling gives you 1 additional chance to look at a card.

The problem is milling doesnt follow a pattern. Milling doesnt have a fixed probability of happening. You might draw a virus, you might play it or you may not, you might lose it to net damage, or you might simply never draw it. In a set of 5 games probabilities say you will see your single Jackson Howard 1 time in each position. But for milling there is simply no rule, what happens in the first 5 games may not happen in the next 5, and even if you keep stretching it to infinity you wont see a pattern.

The whole mill factor is an independent system of probabilities, totally chaotic and following no pattern. When you throw that at a closed system (a deck with 1 Jackson) you will mess up that deck’s odds.

I believe that it all comes down to that, If there is something in this last detail I am missing, at least I am confident that it is now easy for someone to point any error out. Or help them see the point im supporting which is the probabilities of milling and card positions in a deck are two independent things, and since one of them follows no pattern it will never show a fixed probability.

EDITS:

Things i should have already included: the order of the games is compltetely irrelevant, they are for visual convenience, whats important is that probability says in 5 games you will see Jackson at 5 different positions, you can read the table anyway you want.

Also, do not assume that the fact that I used 0 and 1 scenario means the chance of them happening is 50-50. It is NOT. You have a lot of random variables (draw, not draw, damage) but you also have human choice. And there is no pattern in that, so we cant say that stretched to infinity we would end up with 50-50 (which would mean you would have an equal number of games were the corp saw more Jackson and ones where it didnt see him, because yes, I could have created the tables in way that they would have caused more Jackson Howards to be seen than the average 9).

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Why does the order of the corp’s deck follow a pattern, but the order of the mills does not?

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In your examples for milling being something that happens or doesn’t happen, it’s curious that you never applied the mill during the 4th game; the one game where it would make a beneficial difference to the corp, but two times you chose to mill in game 1 where it has a detrimental effect. Over the long run, if the milling is TRULY chaotic and not targeted, you should see the mills in game 4 as often as game 1, no? So over the long run, the chances should even out again.

Targeted milling is a completely different beast and requires that Noise has some idea of what the card on top of RnD is, either via having seen it before from Medium or using a card like Woman in the Red Dress.

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In your picture you picked 3 patterns of milling and summed them to get a number that agrees with you. But the full distribution of how 0 or 1 cards could be milled across 5 games has 2^5 = 32 possibilities (00001, 00010, 00011, …). You need to enumerate them all to accurately compute the expected values. In particular you never put the mill during game 4.

There is no “chaos” about it. Probability theory is about counting possibilities. If two things are independent you just multiply them (which is, indeed, what you’ve done by making 2-dimensional tables). So count them all!

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To go a bit more into this, you’ll have noticed that the only games in your chart that get affected by milling at all are games 1 and 4. If you have a .5 chance of milling in game one, you’ve got a 50% chance of turning game 1 from being a jackson game into a no jackson game. However, you’ve also got a 50% chance of turning game 4 from being a no jackson game into a jackson game. This evens out just fine, and the rest of the games are unaffected.

If you’re not convinced it evens out fine, think of it as a chart that has 4 possibilities, all equally likely. You could have no mills, in which case you get 1 jackson in game 1 and 0 jacksons in game 4. You could have 2 mills in which you’d get 0 jackson in game 1 and 1 jackson in game 4. You could have a mill in 1 and no mill in 4 in which case you’d get 0 jacksons, or you could have no mill in game 1 and a mill in game 4 and you’d get 2 jacksons. This is 4 possibilities and 4 jacksons over all, which exactly matches what we’d expect with no mills (since with no mills you’d always get 1 jackson in game 1 and no jacksons in game 4, meaning each ‘set’ gives you 1 jackson, meaning 4 ‘sets’ would get you 4 jacksons).

EDIT: I also want to add that I hope you don’t feel like you’re being piled up on. This stuff is notoriously hard to understand intuitively which is why it was a big part of the article we’re discussing. I’m sure going over it more carefully like we have been to explain it is valuable to the community at large, since the concept is both important and tricky.

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Yeah, have to agree with everyone else here.

Drawing up a few scenarios where the mills can negatively affect the corp’s draws doesn’t prove that it actually does, it just proves that it CAN, which none of us take issue with. If you draw up every single possibility of when the corp gets milled and where jackson is, it turns out that the corp still has a 3/5 chance of drawing Jackson.

Unless you can “target” the mills by knowing where the cards the corp wants to draw are, milling doesn’t help you deny the corp a specific card in the long run. As you can see, given that you mill a random card, (and I have accounted for all possibilities of both mill and Jackson location), there is a 15/25 chance the corp draws jackson, the same as if they were drawing 3/5 of their cards with no mill.

If it helps conceptually, the reason for this is that if you don’t mill the corp at all, he can’t find Jackson in time if it’s in the bottom two cards. However, if you do mill a random card and Jackson is 4 cards deep, there is suddenly a 3/5 chance the corp finds him that he would not have had if you didn’t mill him.

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You are all correct that you can fix these tables anyway you want. I edited my original post to explain why that doesnt change the argument. The 0 - 1 mills does not mean we have a 50-50 scenario, I hope the simplicity of the example didnt confuse you with that, it just gets way more complicated with lets say 7 to 15 viruses per game.

The argument is that when you bring an independent system of probabilities that does not follow a pattern, it will screw up a system that acts with one. Pattern+Chaos=Chaos. Its supposedly some concept in mathematics but I 'd be lying If i remembered its exact name. Any mathematician friends?

Because that is the entire argument here, the corp draw mechanic has a pattern and milling does not! :stuck_out_tongue:

If anyone can find a pattern in milling, you 've solved the problem.

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There is no reason to consider specific cases only when you draw up this example/simplification. It is simple enough that you can draw up every possibility, (which is what you need to do to if you want to use the example calculate the actual probability). In my post I outlined literally every example of 1 mill in a 5 card deck with one Jackson and found that the probability of drawing Jackson with one random mill inserted is 3/5. Every example you drew up is included in my table, (ignoring the no-mill scenario which is trivial).

You drew up only cases where Noise milled the top card of the deck, (as opposed to milling some time after the corp has drawn some number of cards), which ignores key cases. You also failed to mill a card in any example where Jackson was the 4th card down, which accounts for literally every case where Noises milling actually hurts you. You can’t assume that Noise doesn’t mill a card when Jackson is 4 cards down because Noise has no idea where the Jackson is.

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