Nice table, but it covers only half of the story.
You see, there's not only the problem of how many cards
can you draw (statistically), but also the question of how many cards
do you want to draw (and I'm not talking about starting hand only).
Answering this question leads to important deckbuilding decisions regarding the optimal number of cards in a deck. The answer depends on the role/impact you want a certain card to have in your deck/gameplay. Knowing what do you want to do with a card tells you how many copies you should play.
To see some examples, let's examine the possible number of card copies in a deck, from zero all the way up to six and more!
For the sake of simplicity, let's assume a 30 card deck. That means that you draw one-third of your deck (i.e. 10 cards) in 3 turns (7 starting +3 drawn). Also, let's assume an average game length of 10 turns, so in an average game you will draw the first 17 (18 on the draw) cards of your deck, or roughly half of it.
0: You don't want to draw this card, so you don't play it. Simple.
1: You gave a probability of 0.23 for having this card in the starting hand, which is roughly 1 in 5 games. If we assume a ~10 turns game, then you will draw ~17 cards from your deck, so there is a good chance that you won't even see this card in a duel. The reasons you may wanna play 1 copy of a card in your deck might be:
- This is not a card you actually count on, more like a filler. For example, you built a PSNbow and have 29 cards in it, so you round the deck out with a Precognition. Or you include a single dragon in your rush deck "just because".
- You need the card only to break the game if it draws really long. A good example is a Deflag or something like that: You think you will need only one copy to break through a Wings or similar defensive permanent for the kill.
- The card is a weapon/shield and you think you really don't want to have multiples. This is more like the first point; If you want to rely on the particular weapon/shield then you should include more. If you include one then it is more like a filler.
- The card is part of the winning strategy, but you have serious stalling and/or drawing capabilities to be sure you draw it in time. A good example is Instosis where you really need only one dragon.
It is also interesting to note that you should play one copy of a card if you totally don't want to draw 2 in a game, no matter what. A great example could be Aflatoxin in a deck that capitalizes on the first but has no use for the second.
2: According to your table, there is a 0.58 chance of
not drawing atleast one copy of this card in the starting hand. That means you will have roughly one in every 2 games. Futhermore, you will probably draw one in a normally long game. So ideally, you have this card because you will want to draw one but not more.
This is still filler/miscellaneous card turf, but we are moving away from very specific counters/combo parts to more general "utility" cards (like Shockwave or Steal), which can be good in some situations, but still not important enough to dedicate more deck space to them. Weapons and shields generally also fall into this category; you will want one sooner or later, but, ideally, not more (the upper range of weapons/shields is usually 3 unless you have a deck that relies heavily on them).
If a novagrabby wants a "nova-supported" card more than the rest, then it should contain 2 copies. Examples are Fog shield and Arsenic.
3: More often than not, you will have at least one of this card in your starting hand (to be exact, the chances of
not having at least one in your starting hand is 0.44 according to your table, which is the lesser half of the games). Futhermore, 3 in 30 means in every 10 cards, 1 is this one, so you will probably draw one in 3 turns or so.
With 3 copies, you can start to rely on this card regarding the deck's overall strategy. Still, in a general situation you would rather draw something else than this, either because this is hard to cast or because it is sligthly weaker (or more niche) than somehting else in the deck. Also, only play 3 copies (as opposed to 2) if you will always want to draw at least one copy during a game, sometimes 2.
3 is the upper limit of weapons/shields I'd be comfortable with in my deck, unless I
really want one to be out really fast (e.g. by turn 2-3).
4: If you play 4 copies of a card, there is a good chance (68% to be exact, which is roughly two-thirds) you will have one in your starting hand.
You will also likely draw another even if the game doesn't last too long. We are starting to arrive at cards that are integral to (though not cornerstone of) the strategy of your deck. You are always happy to draw this card, but you don't want all of your cards to be this.
4 is also an interesting number considering that if you really want to play a card, but not sure if the opponent's deck warrants using it, then I think 4 is the way to go.
To clarify: For example, You *think* that the opponent has dangerous creatures, but you are not sure. You are pondering wether to take Lightning or not. In this case I think you should take 4 for game 1.
Another example: You really want to play Lava Golems, but are afraid that the opponent
might pack heavy CC. In this case, I would go with 4 LGs.
These cases are special since if I knew the opponent's deck doesn't deter me from playing LGs, I would go all the way to 6. But since I'm unsure, I stay at 4. This is sufficient to execute a certain strategy whithout overcommitting to it.
4 is also the number of weapons to use if you really want one to be out
fast (Fast as in turn 2 or 3. Examples include Discord or Arsenic), but you don't/can't play Animate Weapon.
5: 5 is an interesting number, because if you play 5 copies that means you really wanna draw the card, so why not go all the way to 6?
Well if I play 5 copies of something, then that something is usually the best counter card for my opponent's deck. I often won't play 6 since the goal is not to counter the opponent to death, just to delay him/her until I win, and the counter doesn't help me directly with winning. On the other hand, I won't play as few as 4 copies, since, well, I will almost always want to have that counter ready in my hand.
5 is also the number of pendulums I propose playing in an upped PSNbow. Balancing a PSNbow is a very difficult task; mostly it is the matter of playing hundreds of games with it. Some people propose 6 pendulums, and I don't doubt it works, but I'm more comfortable with 5. The reason is that I definitely don't want to draw the 3rd copy right in the middle of expansion phase. (Expansion phase is something around turn 3 with those kinda decks. To be more exact, it most often starts on t2 with the SN and lasts until topdeck mode where your hand is empty and you rely on the card you draw each turn. I definitely wouldn't want to draw a pendulum in that phase, either.)
Another reason to play 5 copies of a card is to reduce deck size. If there are multiple important cards of which you want to play 6 each, and the complete deck would be around 35-36 with 6 copies of those cards, then you can try playing 5 of each to reduce the deck to 30 cards. This is sometimes better than cutting a card altogether.
6: This case is again pretty simple. You always want to draw this card. This is what makes your deck tick. This card is the way you want to win the game. Adidtional copies never become redundant, with the exception of Nova/Immolation. Those cards are a special case since you just
need an SN/Immo in your starting hand since the deck doesn't function without one. In this case, the redundancy of late game copies is diminished by the need of a copy as early as possible.
Only one thing to consider here: Do you really need 6 copies? Would the deck function similarly with 5? While in many cases the answer will be no, you can always try and see if you can free some deck space.
Cardwise, the 6 copy cards tend to be the best creatures the available quanta can support, or cards of which every copy is useful, like Dimshield. The 6 copy cards are often removal magnets, so that's another reason why you want the most copies possible.
more than 6: How can one play more than 6 copies of a card, you ask? Well, the answer is that if you really, really want to execute a certain strategy then you can play lots of very similar cards to have more than 6 ways to do certain things. A deck like this will most often be a direct counter to something. For example, you know that the opponent will play PU Crimson Dragons, and the only available ways to overcome it are Lightning and Rage Potion. The thing you can do is to play 6 Lightning and 3 RP that will function as "Lightning 7 through 9". For the purposes of the deck, the Lightning is obviously superior, since it is cheaper and you can aim it at the opponent as well.
(A quick aside: while the Lightning may be superior, it could
possibly be a bad idea to play 6 Lightning and 3RP since your quanta might not support them. For example, you may not be able to play 3 Lightning in the same turn, whereas you might be able to play 2 Lightning and 1 RP. In this case, it may be beneficial to go with a 5/4 split instead.)
Either way, the bottom line is that if you play "6+" of a certain card, you really have to have a good reason why. Know what are you doing. If the plan backfires, then you'll be staring at your useless/redundant RP in your hand all the game until you lose.
