Alright, so this will be a short one. A friend of mine asked a simple question about eliminating clumps in an EDH deck. I decided to describe how I shuffle (a pile shuffle followed by iterant mash shuffling, pretty standard). But at the end of the day, theoretically speaking, clumps are a normal part of randomly distributing cards and you should expect to run into them from time to time.
I decided I wanted to explain this, and went on a completely un-asked-for rant about chance, starting with my old friend the HGDC (which I wrote about here). Of course, this resulted in me rambling on with math nerd stuff like the buffoon I am (though I did find out that if you’re running 37 lands then if every one of the 7.9 billion people on earth each shuffled a copy of your deck to “perfect randomness” every single day, a deck in a configuration where all the lands were sorted to the bottom would appear once every 7,000,000,000,000,000 years or so.) Anyway, on to the simple stuff.
A Simple Way to Vizualize Randomness in Your Deck
Let’s throw out all the numbers of your deck, and simply flip 100 coins on wolfram alpha. Pick heads or tails and simply underline all the “clumps” of 4 or more. I did this and underlined Tails:
Consider the following: Imagine those underlined clumps as clumps of lands, or clumps of non-lands. This is what random looks like. The purpose of shuffling your deck is to make it as close to randomly ordered as practically possible. You may not like it, but this is what a shuffled deck will look like.
The discrepancy is that most people will expect that if you have a 50% chance of flipping heads the results will be relatively even, but the reality is that long strings of heads or tails will often occur. This is the gap between what random is, and how the human brain tends to think about / predict random chance. But the truth is that you are not particularly unlucky if you draw five lands in a row: if you are shuffling well, there’s a good chance that clumps like that are in your deck, that’s a normal result.
701.20a To shuffle a library or a face-down pile of cards, randomize the cards within it so that no player knows their order.
Your deck won’t (usually) have 50% lands and if you want truly accurate odds you must use a hypergeometric distribution, but this simple experiment is pretty easy to help understand and visualize clumping… and why it is a naturally occurring part of a properly shuffled deck… and why methods that eliminate clumps altogether (or give you an increased chance of not having them, such as mana weaving) are cheating.
Mana Weaving
Mana weaving is a technique meant to reduce clumps. Since a sufficiently randomized deck will have clumps like above, I will advise against mana weaving because it has two possible outcomes:
You shuffle effectively afterward and your deck is “sufficiently random” so the mana weaving doesn’t affect the outcome: You wasted your time and effort mana weaving.
Mana weaving reduces clumping in some way, which means the distribution is not sufficiently shuffled / randomized since you affected the outcome: You are cheating.
Conclusion
That’s it. That’s the thought. I just thought it was a fun, simple way to communicate how random really looks and that clumping is a natural part of it. Maybe it even helps emphasize why you need to have effective sources of card draw, to help you power through those clumps, or why tutoring is so powerful.
I hope you enjoyed this simpler article for a change.
Remember: shuffle thoroughly, play at a reasonable pace, and don’t forget to have fun.