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A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051568#msg1051568
« on: March 16, 2013, 10:07:33 pm »
A Detailed Guide to PSNbows
(formatting done by Chapuz)

Spoiler for Introduction:
It's been long ago since I want to write a guide to PSNbows. So long, actually, that in the mean time the popularity of PSNbows has dwindled a lot. They got nerfed(Supernova) and players found out how to adapt to them, so they are not the king of PVP like some time ago. Still, I think for low-level farming and occasional PVP there are few more fun rushdecks to choose from.

In this guide I'll attempt to build a PSNbow from scratch, and in the mean time I'll try to give an in-depth coverage of every step and decision included. You can find a PSNbow of mine here, which has been optimized for low-level arenafarming. Here I'll try to do things a bit differently, and I'll explain every decision I made. Have fun reading!



Q: What is a PSNbow?
A: The word is an acronym that stands for "pendulum-based(P) Supernova-fueled(SN) rainbow(Bow) rush." It is a deck that uses Entropy Pendulums (upgraded) to quickly reach 2  :entropy, and then casts Supernovas (upped), and uses the quanta to cast cheap and efficient attackers (preferably upped). One thing that is apparent is that this style works exclusively best when fully upgraded. In this guide I'll cover upped PSNbows only.

So what kind of elements fit in a PSNbow? The answer is "Everyone", but they are weighted differently. I will separate them in 3 categories: Primary, secondary and tertiary elements.

Primary element: This is the element of your pendulums. This is the quanta you'll get first, by playing one or more upped pendulum, then by ending the turn. For a PSNbow, it has to be Entropy because with a PSNbow, speed is the name of the game, and you'll want to be able to cast Supernovas -and therefore creatures- as soon as possible.
It is possible to make entropy the secondary element and use some other pendulum, since quanta gained from the mark is consistent and steady, so this reduces the chance of not getting to 2 :entropy. However, this version is terribly slow compared to entropy primary element. So for this guide, the primary element will be entropy.
Also note that in the later turns (which is turn 3+ when talking about a PSNbow) you'll get a supply of entropy quanta from the pendulums. Keep this in mind, since you might as well do something with it. (for this guide, this "something" will be Discord, but other options like Chaos Power, Werewolf, Improved Antimatter etc. are all great.)

Secondary element: This is the element of your mark. You will get a steady supply of this quanta from your mark, and you'll also get this quanta from the pendulums. The mark can be entropy like your pendulums, but I think that will provide excess entropy quanta while denying you some very useful and versatile deckbuilding choices.
You can include some more expensive cards or an increased number of cheap cards from your secondary element, since you'll get a steady support of quanta. In my PSNbows I tend to use the secondary element to compensate for the PSNbow's inherent weaknesses, which is being weak vs. stalling(especialy dim shield) and being weak vs. Black Hole. With this in mind, some fine choices for secondary elements are:
  • :death The ability to add poison damage as a workaround to dim shields. I think for this guide I'll do that, since poison is very much my style, and I've never built a PSNbow with poison.
  • :gravity Elite chargers and unstoppable. Again, this is a nice way to win vs. a Dim shield deck.The chargers are also resilient to some forms of CC because they have a considerable HP. Another option is to include Black Holes (especially if you choose to add Discords into the deck).
  • :fire While it is possible to make this secondary and use lots of explosions, I won't follow this route for now.
  • :light If you want to sacrifice some of your deck's speed for some healing, and more importantly resistance to Black Holes, then add Improved Sanctuaries. I never did a deck like this, but I think the idea is fine.
  • :time This is an interesting one. One big problem of a PSNbow is that it empties its hand fast then it relies on top-decks to keep supporting damage. Making time as a secondary enables for the use of HGs to keep a steady flow of cards, but my personal opinion is that the deck becomes too slow that way.
  • :darkness The option to include Steals and Nightmares to be able to win vs Dim shield decks.
  • :aether Twin Universe to copy your best creatures.

Tertiary elements: All the elements which will be supported by your SNs. You don't want to include a total casting cost greater than 4 for these elements. This will be the meat of your deck; most of the offense comes from this department. If a PSNbow can cast 2SNs, then it can theoretically play all of the tertiary cards in the entire deck at once. Let's discuss some offensive options from the tertiary elements:
  • :aether Phase Recluse, Electrocutor if your weapon slot is free and Thunderbolt.
  • :air Improved Fog is always good, Shockwave, Thunderstorms and Wings. Maybe Flying Weapon, if you are packing 3 or more in your deck (Vamp Dagger, Discord, Arsenic)
  • :darkness Vampire Dagger if your weapon slot is free. Bloodsucker for a body and a limited amount of CC (usually this is enough vs. entropy nymph and Maxwell Demon. Will drain your death quanta though). Nightmare to deal with fractal decks and alike.
  • :death If this is not your 2nd element, then upped Recluse, Elite Mummy or 2 Arsenics.
  • :earth Upped Graboid is all-star (note that it uses some of your  :time quanta), or Steel Golem if you like some resitance to CC.
  • :fire Minor Phoenix, Fire Lance (for some limited CC) or Explosion to get rid of shields.
  • :gravity Unstoppable or Blackhole only, but I wouldn't use them unless gravy is my secondary.
  • :life Giant Frog, Upped Coctarice, Forest Spectre, Epinephrine are all good. Epi may me a bit worse since it won't provide a creature for you. The Spectre will drain your water quanta.
  • :light  Elite Pegasus or Blessing (Pegasus will use your air quanta, and Blessing is risky since it won't give you a creature)
  • :time Used for Graboids, or Precognition. Precog is a great card to thin your deck (more on this a bit later).
  • :water Abyss Crawler (resistant to CC) or Ulithraid to get rid of pesky ablilties (antimatter, paradox, devour)

Now that we know the cards we can use, we might as well start building a deck from them. The first thing is to determine the number of cards included from the primary and secondary elements.

Spoiler for A general aside related to the number of individual card copies:
general aside, not just PSNbow-related: "How much of a certain card do you want?"
The hardest choice is to determine the copy number of the individual cards in your deck. Sure, I know that I want Entropy Pendulums, but how much do I want? I don't want to draw too much instead of creatures, but I don't want to be unable to play SNs because I cannot draw a pendulum either. Lets do some math to determine the optimal number, going from 1 all the way to 6:
(let's assume 30-card decks, no deck thinning (precogs) and that you want to finish the game in 5-7 turns at most):
 
1: (7/30*100=)23% that you'll have this card in your opening hand (aka 1 in ~4 games).
Definitely not a card that you want each match. Include 1 copy of a card that might save your ass if the game draws very long. A card that might come handy but in no ways essential. A card that is very similar to other cards in your deck (in other words, redundant. Example: You want to play lots of PC. You include 6 Explosions, but you want more. You add 1 Steal.). If you are going for 100% rush, you can pack only 1 creature of your tertiary elements.

2: You have 1 copy in 15 cards. In most games you will draw 1 copy during the game, so dont count on this winning the games for you. 2 is a great number for cards that help you against your worst matchup. 2 copies is a good amount for auxiliary cards (like a few CC cards). You only need 1 copy of this card if the game draws long.

3: 3 in 30 cards, that's 1 in 10. You'll almost definitely draw 1 copy by your 3-4th turn. You'll almost always draw at least 1 copy during the game, sometimes 2. This is a good amount of weapons or shields that you need. 3 is the number to use if you definitely want to draw 1, but no more than only 1 copy during an average match.

4: 4 in 30, thats 1/7.5. You will mostly draw one by the 2-3rd turn, and you are very likely to draw multiple copies during a match. You are always happy to draw a copy of this card, since it is never a totally dead draw. You can use 4 weapons if you absolutely need to play one very early, but you must live with the fact that you will most likely draw excess copies.

5: Out of every 6 cards in your deck, 1 copy is this card. Use this number if you need one in your starting hand, but preferably not more. You'll probably draw 2 copies by the 3-5th turn. Use this number if the card is a very good adition to your strategy, but not vital. Also use it if you are afraid that excessive copies are redundant. I use 5 copies of pendulum in my PSNbows. I'm happy with 1 or 2 in my starting hand, but not with 3. Futhermore, after I reach 2  :entropy, I'm not too happy to draw a pendulum instead a creature, so I think the correct number will be 5.

6: This card is vital for your deck to work. You will always want a copy in your starting hand, but you are even happier with 2 by the 2-3rd turn. Any copy you draw is welcome. I use 6 SNs in my PSNbow since I want to draw 2 SNs ASAP(this is so vital that it is more important than not drawing excessive copies, hence the 6 instead of 5). Another good example would be a Graboid in a Shrieker rush. Every copy you draw is welcome.


For those who are interested, here is a mathematical model on the subject of starting hand probabilities, made entirely by ManofPI:
Spoiler for Hidden:
Spoiler for basic probabilities without mulligan:
Forgetting the mulligan system for a moment, unless there's something really funky that I don't know about in the way elements works, your starting hand is basically the first 7 cards drawn from your deck. It might seem intuitive that the probability of a card that you have n copies of being in your starting hand is something like (7*n)/30 -- this is actually true for n=1 -- but then having 5 copies of a card (5*7/30 = 35/30) would mean MORE than a 100% chance of having it in your starting hand. Pretty much anyone who's played elements for a while has raged at the RNG for not drawing the cards they need a few times, and knows that having 5 copies does not guarantee that you start with a certain card.

How that actually works is that the probability of it being in your starting hand is (1 - probability of the card NOT being in the starting hand), probabilities being between 0 and 1; 1 means something is certain to happen, you can multiply any numbers I give by 100 to get percentages. I'll call the probability of getting a card p(n) and the probability of not getting it p(not) = 1 - p(n), from which we get the formula I gave before: p(n) = 1 - p(not).

Let's look at a starting hand card by card. Let's say you have n copies of a card in a 30 card deck. The prob of it being the first card is indeed n/30, but once that card is drawn there are only 29 left in the deck. Therefore the prob of it being the next one is n/29 if you didn't draw it, or (n-1)/29 if you did draw it because there are only (n-1) copies left. The same holds true for the third card -- n/28 if you got none, (n-1)/28 if you got one, and (n-2)/28 if you got two -- and every card after that. Keeping in mind that for any p(n), p(not) is 1 - p(n), the probability of drawing any card BUT the one we're looking for is 1 - n/30 = (30-n)/30 for the first card, then either (29-n)/29 or (29 - (n - 1))/29 = (30-n)/29 for the second, and so on. If after x cards we still haven't drawn the card we want, the probability of the (x+1)th card being it is the initial number of copies over the remaining number of cards, or p(n)' = n/(30-x), making p(not)' = (30-x-n)/(30-x).

Now that we know that, to get the original p(not) we can just go through that formula for the first 7 cards. To save myself some typing, as an example let's say we have 3 copies of this card in our deck.
p(not) = (27/30) * (26/29) * (25/28) * (24/27) * (23 / 26) * (22/25) * (21/24)
p(not) = (27*26*25*24*23*22*21) / (30*29*28*27*26*25*24)  the parts in bold cancel out and we get:
p(not) = (21*22*23) / (30*29*28) ~= 0.4362
p(n) = 1 - p(not) = 1 - 0.4362 = 0.5638
In a 30 card deck, the probability of starting with at least one copy of a card that you have 3 copies of is 0.5638 or ~56%.

For 6 copies it works out to p(n) = 1 - 0.1700 = 0.8300, or an 83% chance of starting with it. This still means that in just slightly less than one in every five games you won't be starting with that card. You can keep going and increase the number of cards you draw with the same formula and find that with 6 copies there's still a 6.5% chance to not draw it in the first 10 cards of a 30 card deck. So if you absolutely need that card, about one in every 19 - 20 games you'll be screwed until your third or fourth turn.
Spoiler for Talking about mulligans:
Now to finish let's mention the mulligan system in a very general sense. If the card you want to start with is a 0 cost card like a pillar or pendulum, the probability of starting with it will of course always go up, very significantly if it's the only 0 cost card in the deck. In fact, if you have, say, 6 pendulums in your deck and no other 0 cost cards, the probability of starting with at least one goes from 0.83 to 0.9999999994 -- yes, all those 9s are supposed to be there.
 
However, this works in a surprising way for cards with >0 cost. EDIT:  I had a simple arithmetic mistake in some of the math in the next spoiler; as I originally thought, adding in a 0 cost card does properly lower the chances of starting with at least one copy of your >0 cost card, feel free to take a look in the next spoiler for the math behind this. This effect is most noticeable for low numbers of 0 cost cards; the more you add, the more the probability of starting with your card approaches the normal probability without mulligans.
For example, if you have a deck with 6 of your card and 24 pillars, since every starting hand has 7 cards, even if all 6 copies of your card are in there, there will be a pillar and so none of the hands will get mulligan'd. If you have 23 pillars and one other >0 cost card, there is only one hand in 30!/23! (read 30 factorial divided by 23 factorial) -- which is over 10 billion -- that will be auto-mulligan'd. In short, for >0 cost cards, the probabilities with the mulligan system are usually similar to those without it.
Spoiler for an example:
Very quick example with one 0 cost card and 6 copies of the card we want.
Probability of starting with 0 cost card before mulligan p(0) = 7/30 = 0.23
Prob of mulligan p(0not) = 1 - 0.23 = 0.77

Prob of getting our card without mulligan (after 0 cost card we have 6 more cards to draw and 29 cards left in deck):
p(nno mulligan) = 1 - (23/29)*(22/28)*(21/27)*(20/26)*(19/25)*(18/24)
p(nno mulligan) = 1 - (23*22*21*20*19*18) / (29*28*27*26*25*24)
p(nno mulligan) = 1 - 0.21 = 0.79

Prob of getting our card with mulligan:   (same as drawing all 7 cards of the hand normally)
p(nmulligan) = 0.83

So the actual prob p(n) is:
p(n) = p(nno mulligan)*p(0) + p(nmulligan)*p(0not)
p(n) = 0.79*0.23 + 0.83*0.77
p(n) ~= 0.82
Hopefully someone manages to read through that spoiler'd wall of text and learns something from it.   8)  If any of you happen to be interested in this type of math feel free to send me a PM with questions, comments, or mistakes you find. If it's specifically about this in the context of PSNBows you can also reply in this thread, of course.   ;)


Building a PSNbow

I mentioned earlier that I want 5 pendulums and 6SNs in my deck, and I also mentioned that my secondary element will be death.
Spoiler for deck base:
Hover over cards for details, click for permalink
Deck import code : [Select]
6u3 6u3 6u3 6u3 6u3 6u3 6ve 6ve 6ve 6ve 6ve 8pk

Let's add entropy cards first. I think I will use Discord as the weapon of choice, since it deals great damage and also distrupts mono and duo decks (lots of mono-aethers in the arena.) It is nice, but not vital (vs. rainbow decks a Discord is nothing but 6 damage), and I don't want to draw one when I already have one in play, so I think 3 will be enough. I maybe can get away with 4 if I wanna enforce a Discord-Blackhole combo in my deck, but for now I don't.
Spoiler for deck base 2:
Hover over cards for details, click for permalink
Deck import code : [Select]
6u3 6u3 6u3 6u3 6u3 6u3 6u5 6u5 6u5 6ve 6ve 6ve 6ve 6ve 8pk

Let's fill up the secondary element. I want to add poison damage to be able to win even if the opponent stabilized with dimshield or massive CC. Unfortunately my weapon slot is occupied -I shouldn't put Arsenics-, so I'll go with Deadly Poisons, 4 of them. (for this deck I'll give up on Flesh Recluse, an otherwise damage machine). I also add 2 Bone Walls for defense. I'll have to see if this dilutes the deck's offensive power too much.
Spoiler for Deck Skeleton:
Hover over cards for details, click for permalink
Deck import code : [Select]
6u3 6u3 6u3 6u3 6u3 6u3 6u5 6u5 6u5 6ve 6ve 6ve 6ve 6ve 718 718 718 718 71b 71b 8pk

Thats 20 out of 30 cards, let's use the remaining 10 to fill up the deck with powerful creatures:
 :earth Initially I wanted to use Steel Golems and Precognitions for time, but now the deck looks like it won't have space for precogs, so I think I'll change to Elite Graboid for earth.
 :life 2 Frogs. (Frog is great since you can have 2 copies for a total cost of 4. You can also cast a frog with only 1SN.) If the deck becomes too tight, I'll use a single Elite Coctarice instead, or a Spectre and nothing from water.)
 :fire An MP and an Explosion is my choice here.
 :water I like an Abyss Crawler here. It is resistant to most CC cards.
 :light I add a Pegasus and thus use up not only the light, but the air quanta as well.
 :time We'll have to see if some precogs can fit, but I doubt it.
 :darkness No Vampire Dagger for now, so I add a Bloodsucker. Note that it also has some amount of CC with the help of excess death quanta (which is good since  :death is my secondary element)
 :aether One Phase Recluse fits.
Spoiler for deck so far:
Hover over cards for details, click for permalink
Deck import code : [Select]
6u3 6u3 6u3 6u3 6u3 6u3 6u5 6u5 6u5 6ve 6ve 6ve 6ve 6ve 718 718 718 718 71b 71b 77g 7ae 7ae 7dm 7ds 7gm 7jr 7t7 80g 8pk

In the end I can add 1 Precognition to round out the deck.

The deck looks a bit low on creatures and it has too much death. I think I'll remove the BWs and add a Recluse and another Precog (to ensure that I draw more creatures). I also remove the Explosion in favor of another MP, and hope the DPs are enough to win vs. a dim shield deck...
This is the final version:

Hover over cards for details, click for permalink
Deck import code : [Select]
6u3 6u3 6u3 6u3 6u3 6u3 6u5 6u5 6u5 6ve 6ve 6ve 6ve 6ve 713 718 718 718 718 77g 7ae 7ae 7ds 7ds 7gm 7jr 7qb 7qb 7t7 80g 8pk

I played a few games with it, and the deck is definitely fun to play. The poison applies constant damage, the Discords work beautifully and the draws are streamlined thanks to the precognitions.

You can see how the deck evolved and changed during the building process. You can also see the thought process I empoly when building such a deck: Basically, I make some initial decisions, start to make the deck, and the rest sort of fills themselves. In the end I look at the deck as a whole, and make necessary corrections.
Initially I didn't want to use Flesh Recluse and Precognition. but in the end they all fit into the deck.

Spoiler for Some starting hand and gameplay considerations:
0 pend, 0 SN: this is the worst, yet less likely due to the auto mulligan. You'll have to discard. Discard Percogs first, then Poisons, then the most expensive creatures.
0 pend, at least 1 SN: You'll have to discard. If you have more than 2 SNs in hand, discard the excess SNs first. As soon as you draw a pendulum, you can go off.
1 or more pends, 0 SN: At least you won't have to discard immediately. Hope you draw an SN right away, you'll have the  :entropy for it. From T3, you can play your poisons without an SN.
1 pend, 1 SN: You can go off in your second turn. Just hope that you draw another SN by turn 3 so you can play your 4-cost cards. (you cannot play 2 SNs in the second turn anyways because it would generate a singularity)
2 pends, 1 SN: This is the best starting hand. You can play the 2 pends and the SN right away. Just draw another SN by turn 3; this is all you need.
2 pends, 2 SN: This is another "best" hand. You can play pend->pend->SN->some 2-cost creatures->end turn->SN->all of your creatures.
3 pend: Still good, because you can play a Discord right away in the 1st turn. pend->pend->pend->SN->discord is the correct play.
4 pend: Too much, you won't need this many. At least you won't have problem playing your secondary element-cards.
5 pend: Pretty bad. At least you won't have to discard, but you cannot really play too much offensive...

The most common starting hands are 1 pend + 1SN, 2 pend + 1 SN, 1 pend + 2 SN, 2 pends + 2 SN. Those are all petty good. ("2 pend + 2 SN" is the most favorable, with "2 pend + 1 SN in starting hand and another SN drawn in the next turn" and "1 pend + 2 SN"being very close second.)

Some tips:
Always play precog before anything else.
Always play MP before any other creature. Sometimes you can bait the CC with it.
Don't waste the PC if you have it. Keep it for some crucial permanents that really slow you down, like Dim shields, Eternity etc.
The most dangerous enemy creatures are Otyugh, Maxwell Demon, Arctic Squid and Purple Nymph. If you can fit some CC in, use it on these guys.

This is all what comes into mind now.


To wrap up:
Building a PSNbow:
1, Decide the amount of pendulums you want (this should be either 5 or 6) and the amount of SNs (I strongly recommend 6, but maybe you can try with 5 and see if it works for you).
2, Decide your secondary element. Use this element to counteract the deck's natural weaknesses (lack of damage versus (dim)shields, vulnerability to BH).
3, Decide if you want entropy cards, and how many.
4, Decide your secondary element cards.
5, Fill up the deck with tertiary cards. Make appropriate trade-offs. A total cost of more than 4 per element should be avoided. The deck should have at least 9-10 creatures (9 is only okay if you have a strong secondary theme like DBH or flying weapons. Otherwise 10-11 is recommended).
6, Fill up with precognitions if applicable.

That's it. I hope you enjoyed the reading.
Here is a list of a compendium of SN-based rainbow decks, with quite a few PSNbows included. Check them to see a good variety of this versatile deck-style.
I hope you enjoyed reading this step-by step guide and learned something in the process. Have fun with PSNbows, they are a blast to play!


Q&A Time

Q: Why now?
A: I wanted to do this for a long time, but somehow I didn't. Not because of lazyness, mind you; It is more like I didn't have a good coherent article in my head for a long time. And most recently I didn't have time because of War.

Q: Why play a PSNbow over a regular SNbow?
A: I find regular SNbows (bows with Quantum Towers, entropy mark and SNs) a bit slower on the average, since you are unlikely to be able to cast a SN before turn 3. Also, with QTs you can never be sure about your quanta output. Sure, you can expect an average output over a course of the game, but you'll never know if you can play that life-saving card on the next turn. On the other hand, QTs allow you to go beyond 4 quanta for each element. This enables you to cast great cards like Lava Destroyer.
In a PSNbow, you work with what you get. You know the amount of quanta you have, and you know what you can cast and what you cannot. In that way, I think PSNbows are more consistent. Of course, there are severe card limitations as a tradeoff.
Overall, I like PSNbows better. I think the QTs are a long-term investment over pendulums; A PSNbow is more like a "glass cannon", while a SNbow is more robust on the long term. The thing is, with a rushbow, you will not want the game to go long-term.

Q: 5 or 6 pendulums?
A: Whatever floats your boat... Personally, I think 5 is enough, but if you are afraid your quanta won't come, then try 6. The best method to determine is really to play 100 or so games with both versions and see which one clicks for you.

Q: The quanta for the primary and secondary element piles up, what to do with it?
A: I can give you two answers: One is that with a good PSNbow, the game won't last long enough for your quanta to pile up. And if it does, you are losing anyway. (With that in mind, you can include some "gamesaver" cards to eke out a win when the game is stalling and you are losing; like, make fire your secondary and add Fire Lances).
The other answer is that you can add some (some is the keyword here; don't add more than 1-2!) "sudden" gamechanging cards that cost a lot of quanta, like an Amethyst Dragon. Just be sure that this is what you want; in some games the dragon will sit in your hand uselessly all the game.
(BTW, this is why I like  :gravity as a secondary: Elite Chargers are moderatley costed so you'll fully use the gravy quanta you have, and they are very good at what they do.)
« Last Edit: March 20, 2013, 11:54:27 am by Acsabi44 »
[17:04:00] Dragon6: ‹@Acsabi44› You are Rage Potion, Phase Dragon and Momentum all in one
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Offline Absol

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051609#msg1051609
« Reply #1 on: March 17, 2013, 12:58:48 am »
Good tips, though maybe the formatting could be improved.
+rep

EDIT: are 5 pends enough? I've always run rainbow decks with 6 if possible.
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Offline Chapuz

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051614#msg1051614
« Reply #2 on: March 17, 2013, 01:10:56 am »
Yay, another game theory guide by Acsabi!!
+repping, it's awesome.
If you are too lazy or don't like formatting big stuff, just PM me and I will do it for you.
« Last Edit: March 17, 2013, 01:15:09 am by Chapuz »
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Offline Rutarete

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051639#msg1051639
« Reply #3 on: March 17, 2013, 03:59:46 am »
Great guide! Do you want to add a link to http://elementscommunity.org/forum/index.php/topic,27792.0.html for examples?
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Offline Gandora

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051679#msg1051679
« Reply #4 on: March 17, 2013, 11:38:20 am »
Very well made! :D I really like it.
You write things in a very understandable way :) +rep

Spoiler for Hidden:
Personally, I think it should look a bit more professional and some words aren't written correctly (which I think should not be the case in a guide :) ).

So, sorry if I'm not very precise but I made a very short list of a few mistakes I noticed :)
Some wrong spelling in section of tertiary elements and in the aside notes of card copies, in section 4.
Also, in description where you explain why you chose discords. Where you add creatures, there's also a little mistake.
In starting hand section: 1pend, 0SN and in 5pend.
In the paragraph below that one (petty good).

It might be that I missed some but I didn't always care, like when you wrote bc instead of because.
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Offline TribalTrouble

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051684#msg1051684
« Reply #5 on: March 17, 2013, 11:54:34 am »
Small Spelling/Grammar mistakes I saw.
Spoiler for Hidden:
"Thats 20 out of 30 cards, lets use the remaining 10 to fill up the deck with powerful creatures:
Earth: Initially I wanted to use Steel Golems and Precognitions for time, but now the deck looks it wont have space for precogs, so I think I'll change to elite Graboid for earth."

Also when you mentioned the Darkness choice you miss spelled dagger.
Great guide! :)

Offline Acsabi44Topic starter

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051687#msg1051687
« Reply #6 on: March 17, 2013, 11:58:59 am »
Thank you for the feedback and rep, people :)

Gandora/Tribal, thx for catching grammar errors. I'll fix them right now.
Chapuz, its not that I'm lazy or I dont like formatting, but I cannot really do it well. If you did it, it would be awesome.
Ruta, thanks for the link, I'll include it.
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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1051690#msg1051690
« Reply #7 on: March 17, 2013, 12:09:53 pm »
I really like the guide. It's a shame you only shook off the laziness and did it now, that the steam and the hype over speedbows have settled.

If you want, after Chapuz does the formatting, I can re-read the guide and send you a PM with most of the spelling errors I find -- kind of a correction reading.

Nice job.

Offline ManofPi

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1052008#msg1052008
« Reply #8 on: March 18, 2013, 08:05:08 am »
Great guide! Gave good general deck-building tips and made me want to build some PSNBows.  :D

Somewhat on-topic, I'd like to point out something about the math in the OP (the "general aside" spoiler section) for those interested in mathematical analysis of decks and who don't know much / want to know more / like reading about probability. I may ramble on a bit so don't read on if you don't like math.   ;)
Spoiler for Hidden:
Forgetting the mulligan system for a moment, unless there's something really funky that I don't know about in the way elements works, your starting hand is basically the first 7 cards drawn from your deck. It might seem intuitive that the probability of a card that you have n copies of being in your starting hand is something like (7*n)/30 -- this is actually true for n=1 -- but then having 5 copies of a card (5*7/30 = 35/30) would mean MORE than a 100% chance of having it in your starting hand. Pretty much anyone who's played elements for a while has raged at the RNG for not drawing the cards they need a few times, and knows that having 5 copies does not guarantee that you start with a certain card.

How that actually works is that the probability of it being in your starting hand is (1 - probability of the card NOT being in the starting hand), probabilities being between 0 and 1; 1 means something is certain to happen, you can multiply any numbers I give by 100 to get percentages. I'll call the probability of getting a card p(n) and the probability of not getting it p(not) = 1 - p(n), from which we get the formula I gave before: p(n) = 1 - p(not).

Let's look at a starting hand card by card. Let's say you have n copies of a card in a 30 card deck. The prob of it being the first card is indeed n/30, but once that card is drawn there are only 29 left in the deck. Therefore the prob of it being the next one is n/29 if you didn't draw it, or (n-1)/29 if you did draw it because there are only (n-1) copies left. The same holds true for the third card -- n/28 if you got none, (n-1)/28 if you got one, and (n-2)/28 if you got two -- and every card after that. Keeping in mind that for any p(n), p(not) is 1 - p(n), the probability of drawing any card BUT the one we're looking for is 1 - n/30 = (30-n)/30 for the first card, then either (29-n)/29 or (29 - (n - 1))/29 = (30-n)/29 for the second, and so on. If after x cards we still haven't drawn the card we want, the probability of the (x+1)th card being it is the initial number of copies over the remaining number of cards, or p(n)' = n/(30-x), making p(not)' = (30-x-n)/(30-x).

Now that we know that, to get the original p(not) we can just go through that formula for the first 7 cards. To save myself some typing, as an example let's say we have 3 copies of this card in our deck.
p(not) = (27/30) * (26/29) * (25/28) * (24/27) * (23 / 26) * (22/25) * (21/24)
p(not) = (27*26*25*24*23*22*21) / (30*29*28*27*26*25*24)  the parts in bold cancel out and we get:
p(not) = (21*22*23) / (30*29*28) ~= 0.4362
p(n) = 1 - p(not) = 1 - 0.4362 = 0.5638
In a 30 card deck, the probability of starting with at least one copy of a card that you have 3 copies of is 0.5638 or ~56%, not 70%

For 6 copies it works out to p(n) = 1 - 0.1700 = 0.8300, or an 83% chance of starting with it. This still means that in just slightly less than one in every five games you won't be starting with that card. You can keep going and increase the number of cards you draw with the same formula and find that with 6 copies there's still a 6.5% chance to not draw it in the first 10 cards of a 30 card deck. So if you absolutely need that card, about one in every 19 - 20 games you'll be screwed until your third or fourth turn.

Spoiler for Hidden:
Now to finish let's mention the mulligan system in a very general sense. If the card you want to start with is a 0 cost card like a pillar or pendulum, the probability of starting with it will of course always go up, very significantly if it's the only 0 cost card in the deck. In fact, if you have, say, 6 pendulums in your deck and no other 0 cost cards, the probability of starting with at least one goes from 0.83 to 0.9999999994 -- yes, all those 9s are supposed to be there.
 
However, this works in a surprising way for cards with >0 cost. EDIT:  I had a simple arithmetic mistake in some of the math in the next spoiler; as I originally thought, adding in a 0 cost card does properly lower the chances of starting with at least one copy of your >0 cost card, feel free to take a look in the next spoiler for the math behind this. This effect is most noticeable for low numbers of 0 cost cards; the more you add, the more the probability of starting with your card approaches the normal probability without mulligans.
For example, if you have a deck with 6 of your card and 24 pillars, since every starting hand has 7 cards, even if all 6 copies of your card are in there, there will be a pillar and so none of the hands will get mulligan'd. If you have 23 pillars and one other >0 cost card, there is only one hand in 30!/23! (read 30 factorial divided by 23 factorial) -- which is over 10 billion -- that will be auto-mulligan'd. In short, for >0 cost cards, the probabilities with the mulligan system are usually similar to those without it.

Spoiler for Hidden:
Very quick example with one 0 cost card and 6 copies of the card we want.
Probability of starting with 0 cost card before mulligan p(0) = 7/30 = 0.23
Prob of mulligan p(0not) = 1 - 0.23 = 0.77

Prob of getting our card without mulligan (after 0 cost card we have 6 more cards to draw and 29 cards left in deck):
p(nno mulligan) = 1 - (23/29)*(22/28)*(21/27)*(20/26)*(19/25)*(18/24)
p(nno mulligan) = 1 - (23*22*21*20*19*18) / (29*28*27*26*25*24)
p(nno mulligan) = 1 - 0.21 = 0.79

Prob of getting our card with mulligan:   (same as drawing all 7 cards of the hand normally)
p(nmulligan) = 0.83

So the actual prob p(n) is:
p(n) = p(nno mulligan)*p(0) + p(nmulligan)*p(0not)
p(n) = 0.79*0.23 + 0.83*0.77
p(n) ~= 0.82

Hopefully someone manages to read through that spoiler'd wall of text and learns something from it.   8)  If any of you happen to be interested in this type of math feel free to send me a PM with questions, comments, or mistakes you find. If it's specifically about this in the context of PSNBows you can also reply in this thread, of course.   ;)
« Last Edit: March 18, 2013, 07:42:52 pm by ManofPi »

Offline AnnaMall

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1052014#msg1052014
« Reply #9 on: March 18, 2013, 09:27:20 am »
+rep for another cool guide from the best contemporary elements theorist.

Would like to read about your take on why to build a PSN bow. I find them rarely used outside of restricted deckbuilding events like war. What advantages, disadvantages they have over the SNbows.

Also I usually add a Q shink for both the primary and secondary elements, cause those Q seem to pile up very easily

Offline Acsabi44Topic starter

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1052022#msg1052022
« Reply #10 on: March 18, 2013, 11:03:52 am »
+rep for another cool guide from the best contemporary elements theorist. Thank you, far too kind :)

Would like to read about your take on why to build a PSN bow. Cause I find them more fun than ordinary rushdecks. They are also highly customizable. I find them rarely used outside of restricted deckbuilding events like war. This is true, and I wonder why, since they have some apparent weaknesses, but they are pretty modifiable to complement those weaknesses.
What advantages, disadvantages they have over the SNbows. I find SNbows with QTs and entropy mark a tad slower, that's all. On the other hand, QTs allow for more expensive cards like the otherwise great Lava Destroyer. Whatever floats your boat, I guess.

Also I usually add a Q shink for both the primary and secondary elements, cause those Q seem to pile up very easily. True.
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Offline TribalTrouble

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Re: A detailed guide to PSNbows https://elementscommunity.org/forum/index.php?topic=47765.msg1052086#msg1052086
« Reply #11 on: March 18, 2013, 08:33:56 pm »
I think part of the reason they aren't used is because a large number are crushed by the recent Golem rushes due to not reliably having the CC/PC/Speed to outrush the golem.

 

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