Understanding Chance and Clumps
A Simple Solution
(This will be a short one!)
A friend of mine asked a simple question about eliminating clumps in an EDH deck. I described how I shuffle (a pile shuffle to make sure the right number of cards are there 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 fairly frequently.
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). Naturally, 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). But let’s ignore that and move on to the simple stuff!
A Simple Way to Visualize Randomness in Your Deck
Let’s throw out all the nuances of your deck, and simply:
Arbitrarily choose either Heads or Tails
Underline all the “clumps” of 4 or more of the chosen side
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 is supposed to look like.
The discrepancy is that most people who look at the 50% chance in a coin flip will expect the results will be relatively even (Heads, Tails, Heads, Tails, and so on and so forth), but in reality long strings of Heads or Tails will occur — clumps WILL occur — and they don’t just occur sometimes, they occur FREQUENTLY. This is the gap between how the human brain tends to think about and predict random chance, verses how random chance is in reality. 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. If you want truly accurate odds you must use a hypergeometric distribution. However, this simple experiment is pretty easy to help understand and visualize clumping… and explain 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 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, it affects the outcome by reducing the clumps that SHOULD APPEAR in a properly shuffled / randomized deck… which means the distribution is not sufficiently shuffled / randomized: You are cheating.
Conclusion
That’s it. That’s the article. I just thought it was a fun, simple way to illustrate randomness and clumps. I would even go one step further and say that it helps emphasize why you need to have effective sources of card draw (to help you power through those clumps).
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.