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Android: Netrunner» Forums » Strategy

Subject: Some Math behind Punitive Counterstrike rss

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Jonathan Jones
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Hey guys,

I've not seen this posted anywhere on this forum, so here is some math for you.



In order to flatline someone with a single punitive counterstrike, the corp needs X+L-1 credits where X is the runners money and L is the runners link. We get this by looking for how much we need, to beat the runners highest possible trace. When the runner has 11 credits and 2 link, then we need 12, playing a counterstrike for 3 and boosting its trace by 9 for a trace 14, which is exactly one higher than the runners credits + link.

If the corp has additional punitive counterstrikes in hand, each of them can be played beforehand for 3, to make the runner lose 5-L, so when the corp has 2 counterstrikes, it needs X+2*L-3 and when it has 3 counterstrikes it needs X+3*L-5.

The formula when the corp has two counterstrikes and needs two counterstrikes was already posted somewhere on this forum, but I'm going to repeat, that 2*X+2*L-2 credits are necessary in that case to boost two traces out of range of the runner.

When the corp has three counterstrikes and needs all of them, the formula is 3*X+3*L-3.

There is a very interesting last case. It can be easily seen from the above formulas, that the corp needs quite a lot more money than the runner, when it needs to hit more that one counterstrike. For example 28 credits are necessary, to kill a runner with 15 credits without link via the usage of two counterstrikes. But what happens, when the corp only needs two counterstrikes and has three in hand or at least available via the use of Atlas-Tokens.

Let the corp start by playing one counterstrike from hand, boosting its trace by Y. What Y is exactly will be determined later on. The runner now has two options, either he suffers the trace or he beats it.

1. Option: By suffering the trace the runner leaves the corp with only needing one out of two counterstrikes to hit. We have the formula available, how much money the corp needs to flatline now, so the corp pays 3+Y for the first counterstrike and then X+2*L-3, summing up to X+Y+2*L.

2. Option: Repelling the trace costs the runner some money, 5+Y-L to be exact. Now the corp needs to hit two out of two counterstrikes against a lowered creditpool of X-(5+Y-L), using the above formula the corp needs 2*(X-(5+Y-L))+2*L-2=2*X-2*Y+4*L-12, adding the 3+Y the corp payed in the first place we obtain 2*X-Y+4*L-9.

Now we can see, that increasing Y makes it more likely for the runner to choose the first option, since increasing Y increases the amount of money needed for the first option, while lowering Y increases the amount of money needed for the second option and makes this the more appealing one for the runner. There has to be a sweet spot for the corp, so we just try to find the value for Y, where both options are equally bad for the runner, where both options are equal:
X+Y+2*L=2*X-Y+4*L-9 => Y=0,5*X+L-4,5

Since we now found the best value for Y, we can easily calculate the overall money necessary to flatline, by putting our Y in one of the above formulas. We obtain 1,5*X+3*L-4,5 credits necessary, to flatline via the usage of three counterstrikes when only two are necessary.

As an example take a runner with 15 credits and no link. Our formula tells us that 1,5*15-4,5=18 credits are necessary to flatline the runner. In order to do this we play a punitive counterstrike for 3 and boost the trace by 0,5*15-4,5=3 for a trace 8 going to 18-3-3=12 credits.
When the runner suffers the trace, then we play a counterstrike for 3 going to 9. The runner needs to prevent this trace in order to survive, so he pays 5 going to 10. Then the corp plays the last counterstrike for 3, going to 6 and putting all of these into the trace for a trace 11. The runner cant prevent it and flatlines.
When the runner prevents the first trace, he needs to pay 8 going to 7. So now the corp has enough money, to play two counterstrikes in succession boosting each trace by 3 for 2*(3+3)=12 to get two traces 8, which the runner cant beat.

Remember that we thought, we needed 28 credits to flatline a runner with 15 credits and no link, using the new formula we see that in fact only 18 credits are needed, when we have three available counterstrikes. Quite a big difference!

EDIT: Added picture and examples. Corrected spelling.
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Beyer
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JonathanJones wrote:
... when we have three counterstrikes available. Quite a big difference!

I'd say. Three available counter strikes...

Also as a pet peeve*. Whenever you are presenting numbers, math, science, statistics, analysis... anything that is remotely mentally taxing don't use phrases like: easily, easy to see, etc. It's not only superfluous, it's also a personal matter whether the task is easy. From a communication point of view, you risk antagonizing those readers who find your mental exercises more than they can 'easily' handle. Thus, what could be a viable point will often be lost on people who don't agree with you on what constitutes easy arithmetic. It has nothing to do with your post, but after (too) many years in academia that particular writing style is starting to sadden me. It's a sign that the writer expects his readers to be on her/his level, rather than present a topic in an approachable manner.

I know people who can draw Feynman diagrams and explain in simple terms what they do and what they mean. I also know people who can't explain how to use the unit circle in a way anyone but themselves understand. Make it a point to present your info in an easy-to-read manner.


* You can tell this is a pet peeve from the abundance of text that has no significance to the topic at hand. I wanted to contain myself, but were I able, t'would hardly be a pet peeve, now would it


Also: Spell out how you got the numbers for the first equation. It makes the rest of the math easier to grok instantly without the need to do the computation yourself.
Say A runner has 10 creds and 2 link, your equation says the corp needs 11 creds.
11 creds - 3 to play Punitive Counterstrike +5 trace strength = 13. This is exactly enough to beat the runners highest possible trace strength of 12 (10$ +2 link).
Also also: Post a picture of Punitive Counterstrike so there is no confusion about what it costs to play or what the trace strength is exactly.


Right.. I'm done. Happy counting

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Marcel Heymuth
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Hehe, I remember you asking me that question last Wednesday
Even though the formula is absolutely correct, a (maybe) more intuitive way is the following:

If the Corp has to succeed in two traces, look at what is the maximum
amount of credits the Runner can maximally boost his second best trace to.
In case of 15, that is 7. As a Corp, you need to boost your trace 3 times just one above that. That is 8. With that, it is easy to calculate:
3x3 for playing the PC, 3x3 to boost the traces. That is 18 and therefore just what your result is.

So, in general:

1.) Divide the runners credits by 2. If it is x.5, round down to x.
2.) Add the Runner's link to x and another +1
3.) Check, whether you have at least 9 credits plus 3 times what is
x + link + 1.
4.) If yes, go for it and trace him three times with trace strength x+link+1 If not, do something else.
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Hans Otterson
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This is why I never seem to get around to building a Weyland deck.
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Beyer
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hans otterson wrote:
This is why I never seem to get around to building a Weyland deck.

Moot point. Weyland always has enough money. Getting the Counterstrikes out in time is a whole other issue...
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General Norris
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Counting is for people that don't start the game with ten credits.

Stunke wrote:
hans otterson wrote:
This is why I never seem to get around to building a Weyland deck.

Moot point. Weyland always has enough money. Getting the Counterstrikes out in time is a whole other issue...


If you play Archived Memories you'll have a Punitive kill in hand extremely often.
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Daniel Wray
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General_Norris wrote:
If you play Archived Memories you'll have a Punitive kill in hand extremely often.


You can't Archived Memories a Punitive you have never seen.
 
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Jack Keys
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cynchwyrm wrote:
General_Norris wrote:
If you play Archived Memories you'll have a Punitive kill in hand extremely often.


You can't Archived Memories a Punitive you have never seen.


I think the point is that having a single Punitive Counterstrike and Archived Memories allows you to play two Punitive Counterstrikes in a single turn. It doesn't help you find the first one, but it makes sure you can double the meat damage when an agenda is stolen without having to find a second Punitive Counterstrike. Yes, you still need to find Archived Memories, but it's almost like having six copies of Punitive Counterstrike, where the three of them require that you have another in hand.
 
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