What's a Normal Summon?
"Normal Summon" has an official meaning in Yu-Gi-Oh, but in the competitive scene we use the term to refer to a card that requires your once-per-turn Normal Summon action to fully realize its potential. Normal Summons are tricky: you can only use one of them every turn, even if you have more than one in your hand. Having too many Normal Summons can slow you down, effectively sticking you with dead cards; if you have three Normal Summons in your hand and can't use two of them, your hand performs like you have three cards that turn instead of five.
So why use Normal Summons at all? A fundamental part of game balance is to weigh the output of power a card can give you, against the frequency with which you can actually use it. There are lots of ways the design team can create balance that way: perhaps a powerful card can't be searched out of your deck so you won't have as many opportunities to play it, like Solemn Judgment; or maybe the card's just impossible to use more than once per turn, like Tour Guide From the Underworld.
Cards that consume your Normal Summon make up a big portion of the most powerful effects in the game, and using one of them is certainly better than none. Normal Summon cards are so good that if you just ignore them, you'll quickly be outpaced by most opponents. You want to play powerful Normal Summons and you want to see them in every game, but the trick is to not see too many. You want to maximize your power output each turn by using all the cards in your hand, sure, but it's important that one of those cards leverages the 'power balancing' of the Normal Summon, because the sheer potential of many of those cards is so high.
Put simply, if a Normal Summon card isn't powerful enough to justify the weaknesses inherent to the Normal Summon requirement, you shouldn't be playing it. But on the whole, Normal Summons are so good that they're worth navigating the balancing act.
With that in mind, we're going to figure out how many Normal Summons you should run in your decks so you can get the best results, as often as mathematically possible.
Obvious Normal Summons like Tour Guide From the Underworld or Aleister the Invoker are very easy to identify, but as I hinted at a few paragraphs up, other less obvious cards can count too.
If the only Warrior monster in your deck is Armageddon Knight – a monster with a useful effect that requires a Normal Summon to play – then your copy of Reinforcement of the Army can only resolve by searching you Armageddon Knight. From there you'll always want to Normal Summon it and resolve its effect – that's why Reinforcement of the Army in your deck in the first place.
Because your Reinforcement of the Army leads to an obligatory Normal Summon of Armageddon Knight, you'd want to count it as a Normal Summon as you tally up your deck's total. In the short term, a hand of Armageddon Knight and Reinforcement of the Army with three other cards is effectively still a four card hand in this hypothetical deck, even if you run three copies of Armageddon Knight; you can search that second Normal Summon, but you can't play it until next turn. That's the kind of problem you want to avoid by playing the optimal number of Normal Summons.
The most popular Normal Summon in the current format is Aleister the Invoker. It lets you search Invocation from your deck to your hand, and the end result of summoning Aleister the Invoker is usually an Invoked Mechaba on the field, with Aleister the Invoker back in your hand.
You can run three copies of Magical Meltdown to search Aleister the Invoker, plus Terraforming to search Magical Meltdown; that's effectively up to seven copies of your Normal Summon, each representing a 3500 ATK monster that can negate one card per turn for a discard.
That's the best way to think about how your Normal Summon is used: you should measure its impact by the end result. You can assess for yourself how good or bad any given Normal Summon is in the current format, and then judge it by how often you get to use it (in this case, Aleister the Invoker works as seven out of 40 cards in your deck).
In competitive Yu-Gi-Oh the most famous Normal Summon is probably Tour Guide From the Underworld or Elemental HERO Stratos. Both create massive branches of options starting with the wide variety of cards they can search, and both can deliver a vast number of different end results.
As far as end results go, the most powerful Normal Summon right now is Jet Synchron. It's only as good as whatever it makes, but with Crystron Halqifibrax still legal in the Advanced Format, a single Jet Synchron, backed up with three copies of Tuning for a total of six ways to see it, can result in incredibly powerful set-ups: boards like Borreload Savage Dragon and Herald of the Arc Light, or True King of All Calamities. And you can draw as many as five cards along the way!
Serziel, Watcher of the Evil Eye
But in my opinion, the best stand-alone Normal Summon is actually Serziel, Watcher of the Evil Eye. Serziel, Watcher of the Evil Eye searches Evil Eye of Selene and equips it to itself. With no extra commitments, demands or special requirements, Serziel, Watcher of the Evil Eye a 3600 ATK monster that destroys one card each turn.
At the same time, an equipped Serziel, Watcher of the Evil Eye is immune to targeting and can't be destroyed. That's incredibly good value for such a low investment, and with Evil Eye Domain - Pareidolia and Terraforming, you end up with an extremely reliable seven copies, much like Aleister the Invoker.
Penultimately, you have Girsu, the Orcust Mekk-Knight from Eternity Code. Affectionately called a "dumper," Girsu, the Orcust Mekk-Knight dumps a card from your deck to the graveyard. It's similar to Tour Guide From the Underworld and Elemental HERO Stratos in scope, creating massive trees of options both in what you get from the graveyard and what kind of board you can make afterwards. Girsu, the Orcust Mekk-Knight doesn't come with other cards that search it, but it doubles up with stuff like Armageddon Knight and Scrap Recycler that are also dumping the same card, so your Normal Summon options can go from there.
The last kind of Normal Summon we should talk about is the 'effective' Normal Summon. Throughout the game there have been tons of cards that more or less require your Normal Summon without explicitly saying so. The current poster child for that is Numeron Network. It requires you to control no monsters to use its effect, and once you do you can only summon one time. Because you're always Special Summoning something after you use Numeron Network, the resolution is effectively occupying the same role as your Normal Summon would for that turn.
Now that you're armed with that information you can assess how many Normal Summons to play.
Typically you want to see one Normal Summon in a turn, never two. But that isn't always the case: there are decks where the Normal Summon makes or breaks the entire flow of the strategy. Orcusts come to mind. With those decks you'd want to run as many Normal Summons as you can, but there's still a correct maximum; a point where adding more Normal Summons actually starts to reduce the odds that you'll see only one Normal Summon, because of how much you're increasing the odds of seeing two. We'll come back to that in a moment, but don't worry, we've got a system.
The last thing to factor in is Side Decking. When you go second you start with a sixth card, and that can throw off all of the math quite a bit. Sometimes it's correct to have five Normal Summons in the deck going first, but four if you're going second. You can actually mitigate that problem by simply siding out your extra Normal Summon.
With all that in mind, I've created a spreadsheet that will help you see how many Normal Summons you should play. You can find it here. It might look like a lot of information, but once you get comfortable it's pretty easy! Here's how it works.
The correct number of Normal Summons for a given deck can often draw a lot of debate, but by looking for the mathematically optimal scenarios and avoiding costly cases where diminishing returns work against you, finding real answers is easier than it seems. Check out the decks you've got built right now, compare them to the recommendations in the spreadsheet, and see how they stack up!
Let me know how it goes over on facebook, or drop me a line if anything seems tricky; I'm happy to help.