An interesting fact about eggs: not only can they be cooked and used in many dishes, but they also come in a large number of edible varieties. Not only bird eggs, but fish eggs (caviar/roe), frog eggs, and even snail eggs can all be consumed. Furthermore, there are many types of edible bird eggs. Most folks would be familiar with chicken eggs, but maybe you’ve tried duck, quail or pheasant, and perhaps even goose or turkey eggs. For the adventurous perhaps even ostrich, pigeon or even emu eggs.
If you wanted to have eggs every day, you could go almost two weeks without duplication, simply through the types of eggs I’ve listed above. With a little research and a slightly wider view of thought on the matter, I’m sure you could go even longer without repetition, as long as the common denominator is not too restrictive.
The point is that they are all eggs.
The 7 to 9 Rule of Consistent Combo
This is a little something I learnt when I was first getting into playing Vintage Long Storm decks. This rule states that in a 60-card format, if you want to have access to something in your opening hand, you need seven to nine copies of the effect in your deck. To look at the probability of actually having something in your opening hand in EDH, you need to look at several factors:
- The number of cards in the deck.
- The number of copies of the effect in the deck.
- The number of cards you are going to see.
We can use this kind of information to calculate the probability of finding any card or copy of an effect in a deck at any given time (providing you can do the math quickly enough). For the purpose of the conversation today, let’s look at the odds of finding a given card or effect in your opening hand.
In a 60-card deck, the 7-9 rule states that we need seven to nine copies of an effect to reliably see one in your opening hand. Specifically having seven copies gives 86% probability, eight copies leads to an over 98% chance and nine copies is 110%. Therefore if I want to guarantee access to an effect in my opener, I’ll play nine copies of it. If we’re less desperate for the effect, ie able to wait a draw or two, then we can reach a degree of certainty that we could expect 100% access to an effect with fewer instances of it in our pile of 60 cards.
This is in essence the 7-9 rule. In Cifkas’ Second Breakfast list, the rule is applied heavily to allow the deck to reliably recur its namesake effect. It featured four copies of Second Sunrise and four of Faith’s Reward, totalling eight copies of the mass recursion effect. Following this rule is fairly straightforward for deck design in 60-card formats, as you are able to include up to four copies of the same card. EDH throws two mighty spanners into the works – we’re playing a singleton format and we need to fill 99 slots as opposed to 60.
Extrapolating the Math to the Big House
As with any probability equation, the 7-9 rule can be adapted to fit the different scenario that EDH presents. The first problem is recalculating what density of an effect is required in order to find it reliably. As for the 60-card format, I’ve produced some data that we can use to extrapolate this. How this is calculated: the probability of finding a copy of the desired effect, calculated as the sum of the probabilities of finding the effect on each drawn card, based upon how many cards are left in the deck (assuming that the previous draw failed to find). Here is a big table and graph of said data.
Editor’s note: The chart goes up to 30 copies, but that image wouldn’t fit. Here’s the file if you want to play with it, including both 60- and 99-card calculations.
Suffice to say, the closest probability of finding a card in a commander deck should use the 12 to 14 range as a minimum.12 copies of the effect offers as close to similar opening hand probability as seven in a 60-card format. This offers a range of high 80’s to just over 100% on an opening hand of seven. Obviously you can also increase the density of the required effect as far as needed, under the constraint of being able to find sufficient functional copies of said effect.
As a personal preference, both for explaining the extrapolation behind the maths and for meeting my preference for a slightly higher density probability, I generally recommend in the range of 13 to 15 copies, preferencing 15 copies where possible for a necessary effect. Why 15? When you look at a 60 card deck, you can roughly divide 60 cards by seven cards to get nine groups of cards (in actual fact 7 x 9 = 63, so we’re talking six-and-a-bit worth of opening hands in a 60-card deck). So if we want to make a given effect highly likely to show up in an opening hand, then we need one copy per opening hand. Nine hands of cards means nine copies of the effect. To equate this to EDH, our favourite 99 card format, a rough comparison of 99 to 60 cards is an increase of exactly 65% .This is roughly equal to an additional six opening hands in the deck, which means we would be looking to add an extra six copies of our target effect on top of the nine you need in the 60 card format.
Editor’s note: The previous section is dense, and was tough for me on the first read, but it is actually a great way to think about the math, and all the numbers and logic are there. Please give it a few reads before firing off in the comments, if you’re struggling to follow Kaka at first (unless I’m a moron and you’re all mega brains).
Combo in a non-highlander format is easy. You can find the optimal card (or two), grab a playset of four, and jam them in the pile. In singleton formats (and sometimes Vintage and Legacy), it’s not that simple. When you can only have a single copy of a card in the deck, you have to look for different cards with the same effect. As an example, say I wanted to be able to reliably exile an opponent’s graveyard. As a classical Vintage player, my mind immediately jumps to Tormod’s Crypt. In EDH however I can only have one Tormod’s Crypt, so as I want to reliably access this exile effect, I need to find 14 more functional Tormod’s Crypts. The modern players out there are probably confused as to why I didn’t immediately start with Relic of Progenitus (heh easy one, Crypt is free), which is a great example of a functional approximation of Tormod’s Crypt despite being overcosted (HAH).
We still need 13 more. Okay well how about everyone’s favourite card – Leyline of the Void? Great card, but if you weren’t in black you may well be now. Black also adds Ravenous Trap for some surprise (and often free) action. This brings us to four functional approximations off the top of my head. A quick rummage through the Gatherer database turns up a surprisingly large selection of graveyard hate, including some odd coloured gems like Bazaar of Wonders in blue. Depending on your deck design restrictions (only spells, all creatures, death by enchantments, mono blue, whatever), I’m pretty sure you could fill out 15 cards fairly easily.
What if however you were trying to find 15 copies of something much narrower, An effect that is so bizarre that it has only ever been printed once? What if you needed to find 15 functional copies of Leeches? There are plenty of ways to get poison counters, and a prolific number of ways (literally…. prolific) to proliferate more poison counters, yet only one card has ever been printed that removes poison counters. There is no Blood Drinker Worm card, nor an Anti-Coagulation Supper Slug card, and definitely no BYO Blood Drinkin’ Swamp Varmint card to clear off your toxic tokens. As such one has to consider the question:
“I need this card. There is only one copy of this card that I can put in this deck. How can I make this deck behave as if it had 15 ways to get this effect?”
I’ll bet most of you by now are taking bets on where I’m going to mention that fateful word “tutors”. You’re probably nodding along there chuckling and thinking “yep, I got fifty bucks on at the bookies that he’s about to do this.” Well, sorry gang, but look again at the last sentence – I guess I win this one.
Yes, the answer is in part tutors, and I know that a lot of people out there choose not to use them or just despise them as ruining the randomness of the 100 card deck. I can totally respect that and I do recommend using as few tutors as possible to fill the gaps, as using a tutor to fish up your target card functionally removes two copies of the effect from the deck. In the case of Leeches, this is dangerous, as there is only one copy of that effect in existence. Hence if you needed to use it again, no matter how good Demonic Tutor is, you cannot use a DT to grab the Leeches out of your graveyard. Demonic Tutor however could find a Regrowth, which could be used to bring Leeches back to your hand. In that sense you have a slightly convoluted and fairly expensive copy of Leeches relatively on tap.
My point here is that a card can best be defined by how you look at them. When I look at a Demonic Tutor, I see literally every other card that is still in my deck, from a basic land through to a Black Lotus. When I see a Regrowth, I see literally every card in my graveyard. Sometimes you have to look sideways, but looking at what things could be, what they could do for you, will often allow you to fill in those blanks.
I hope that has got you all thinking about cards in a different light. Until next time I’d like to leave you with this quote from H.P. Lovecraft as food for thought.
“Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.”
― H.P. Lovecraft
Love and Velociraptors