Everyone loves the Diabolic Tutor:
But how many tutors is too many? If I'm running a mono-black or black-heavy deck, is there any reason to not just put in four Tutors? What are the possible downsides?
There are two basic reasons to use a tutor:
1) You have a card that you want more than 4 of, but there is no similar substitute available.
2) To be able to have a 'toolbox' of 1-of answers to different types of threats.
So what is the card in your deck that you wish you could have more than 4 of? What are possible substitutes for it in the format you're building for? Is using a turn and extra mana to get at it preferable to the substitute card? The primary reason not to put in a tutor is if your deck can reliably deliver on its designed win condition without needing access to more than 4 of a particular card.
Toolbox decks are usually meta-game haterators, so it's tough to talk about them in the abstract. Mono-black isn't usually known for it though. Toolbox tutors are more often things like Birthing Pod searching up creatures with desirable enters-the-battlefield effects.
Diabolic Tutor specifically, your biggest challenge on that one is how it impacts your mana curve. What are the 5-drop cards in your deck you're tutoring for that you must hit on T5 in order to win? What 4-drop card are you giving up the opportunity to play on curve in order to tutor for something that comes out next turn?
Turn 4 is not a good time to be making a play that doesn't impact the board state. Turn 4 is the kill turn for aggro decks in Standard/Modern that got a half-decent starting hand. Tapping out for a tutor also communicates a lot of information to your opponent. e.g., The only reason you tapped out for 4 in mono-black standard and played a tutor instead of an Obliterator, was to go tutor for an Obliterator. They will do everything they can to be ready for it next turn!
In decks for big multiplayer games, go for it, play all the tutors you can. When games regularly go over 10 turns, getting what you need late is more important than playing on-curve early.
This question is almost too broad. It depends entirely on your deck, doesn't it? If your deck is a fast black aggro that plans to overwhelm with creatures by turn 5 then obviously taking time out to tutor up a card is an unacceptable loss of tempo. If on the other hand you're running a combo where you can't afford not to have drawn all your pieces by turn 5, then some kind of tutoring will be a necessity.
I do think Diabolic Tutor is a well-costed card: 4 mana and a card is a sizeable investment to make, to the point where it may very well not be worth it in any fast environment of finely tuned decks. It's more likely to be worth it in slow formats like Limited (where you plan to win by drawing your bombs) or possibly, as mentioned, Multiplayer - though I would caution that alerting your opponents that you just drew the best card in your deck may increase your chances of them viewing you as a threat!
I'd say it's the other way around. When is it worth wasting 4 mana worth of tempo for the gain of exchanging one card in your hand for one from your deck? I think you need a good reason even to run Demonic Tutor.
But as always in MtG it's situational. What do you want to accomplish? How have you planned to win/not lose? We can give the best suggestions if you provide a decklist.
Diabolic Tutor is simply inefficient. 2-mana tutors of limited selection like Eladamri's Call and Merchant Scroll are moderately playable, but not automatic inclusions. 3-mana tutors of limited selection like Fabricate rarely get played, but might under extreme circumstances. Diabolic Tutor gives you broader selection than these cards, but it is ultimately 4 mana to get 1 card (with nearly the greatest possible card selection), and there is very little precedent for playable 4-mana 1-for-1 card drawing / tutoring. I personally think, for Diabolic Tutor's effect to be playable in standard most of the time, it should be priced at about 3.2 mana (e.g. 3 mana with some downside like lose 2 life, or 4 mana with some upside like gain 3 life); so I would say it is overpriced by about 0.8 mana. Usually a card's efficiency, i.e. whether it is over/underpriced and by how much, is one of the first criteria you consider when determining what is good enough to play.
Correlates With Inclusion
Diabolic Tutor has seen plenty of standard and block constructed play in Mono-Black Control during the 2001 - 2003 era. This deck features a lot of the criteria that you would look for in order to play Diabolic Tutor. However, Diabolic Tutor got passed-up in later formats where some of these criteria were not as accessible.
- Mana Ramp. This deck played Cabal Coffers, which netted one mana once you had 3 Swamps in play, and netted > 1 mana after that. Diabolic Tutor is essentially adding 4 mana to the cost of whatever card you search for. Since Diabolic Tutor is already so expensive, and since it tutors-up a likely expensive card, you basically have to spend quite a lot of mana to make whatever play you had in mind. To further confirm that theory, it usually isn't worth tutoring-up a simply efficient card like Lightning Bolt, because then you'd basically be spending 5 mana to deal 3 damage. Instead, you are almost obligated to tutor-up a very devastating, sweeping play; examples of the time may include Mutilate, Mind Sludge, Haunting Echoes, Corrupt, Skeletal Scrying, or Riptide Replicator. Since these plays are so mana-intensive, you will want to pay for them using big mana rampers like Cabal Coffers or Gilded Lotus. Because Diabolic Tutor is SO expensive, mana ramp is by far the most crucial variable that will make or break Diabolic Tutor.
- Board Sweepers. In Mono-Black Control, the go-to board sweeper of the time was Mutilate. If it had access to Damnation or Toxic Sludge, it might have used those. Since Diabolic Tutor is so mana-intensive and it does not impact the board, you need the ability to dramatically catch-up on your board position after falling behind by wasting a lot of mana not affecting the board. To do this, you should use board sweepers. This is also a combo of sorts; because if board sweepers present the possibility of achieving extreme card advantage, then you will want tutors to be able to get them. Doing nothing to control the board on turn 4 also increases the possibility that a turn 5 board sweeper will have more creatures to kill.
- Life Gain. If your plan is to waste turn 4 doing nothing but tutoring, then you will probably take significant damage. Even if you then play a board sweeper to catch way up on the board, your life total will probably be low. At this point, you will probably want to play a card like Corrupt to catch way back up on life. Usually life gain doesn't do a lot of work in Magic, but Corrupt has the potential to remove another threat from the board, or to function as part of a win condition.
- Silver Bullets and Splashy Plays. Tutors give you the ability to tutor-up silver bullets like Boil that have situationally devastating impacts. If your deck offers multiple 1-of silver bullets, then you will want to combine tutoring power with it to consistently make devastating plays without drawing the situationally dead cards too often. Splashy plays, i.e. devastating or sweeping impactful cards like Damnation, Mind Sludge, Mirari, Riptide Replicator, and Haunting Echoes serve a role very similar to silver bullets; they are just as devastating, but less situational. These are the type of cards you would definitely want available in your toolbox to search for. Especially if their effects shut down varying zones of the game, causing each of them to be differently important in different situations (not color-specific situations like destroying Islands, but zone-specific situations like destroying the opponent's hand).
- Combo Pieces. Of course, the ability to search-up a combo piece to complete a combo and win the game is a powerful play. Since tutors can flexibly fetch whichever piece of the combo you are missing, they can be better than simply playing more copies of each half of the combo piece.
How Many Should You Play?
Usually 0. However, if all of the right pieces are in place to justify playing Diabolic Tutor (including if the format / cardpool is slow / weak enough), you should usually play 4. Assuming you have access to mana ramp especially, not to mention all of the other correlates with inclusion stated above, the power of tutoring can't be denied. Once you've unlocked A LOT of mana, and the post-tutor plays you make are devastating, there's minimal reason to play less than 4 Diabolic Tutors. This is not to mention that with fewer than 4 tutors, your deck will probably be inconsistent, since you are playing so many expensive splashy cards, so many silver bullets, and so many cards of niche roles like board sweepers. If your deck was a ton of cheap spot removal, then your draws would always play-out similarly. But if your deck was a few board sweepers and minimal spot removal, then you can have very swingy draws where you control the board very well or very poorly. The best argument to play exactly 3 Diabolic Tutors would be if it had stiff competition at the 4-mana slots against very strong cards like Phyrexian Obliterator.