Double-Chording (a useful ability everyone can do regardless of mastery) as well as Chord-Gleaning (perhaps the most powerful but also difficult to understand tier-2 power of the Spy mastery) are explained using screenshots.
I Cry: Hi. Why So Sly, Spy Guy? Also, What's a Double-Chord?
If you look at the leaderboards for Endless Multiverse you'll notice that most of the top scores come from the Spy mastery (as of this writing, anyway). The reason for this is because the Spy's second-level Chord-Glean ability turns more monsters on the board (which the game thinks makes it harder) into something that actually makes the board easier since you have more opportunities to see through the monsters that already exist. It also, when there are enough monsters nearby and is done properly, allows you to solve most situations that would require you to make a guess.
In addition almost every player and mastery has access to Chord, Right-Chord, and the powerful Double-Chord (the only exception is Commander when above 5 gold) which will double or triple the speed of your gameplay.
I will teach you through example.
What is Chording? How do I Double-Chord?
Before we get into how to chord-glean we'll need to explain something that is shockingly not brought up in the tutorial for DemonCrawl, yet was also a core feature of the original MineSweeper: chording.
In the image above we have a cell with a 2 in it, which has two flagged cells nearby. This means that all other adjacent cells do not have monsters. Rather than clicking on each undiscovered cell individually, we can left-click on the "2" to reveal all adjacent un-flagged cells. This is called a "Chord" as seen below.
You can also "Right-Chord."
In the image above we have a cell with a 2 in it, which has a single flagged cell and only one undiscovered cell adjacent. This means that the undiscovered cell must be a monster. Rather than right-clicking on each undiscovered cell individually, we can right-click on the "2" to mark all adjacent un-discovered cells as flagged since there is only one possible solution. This is called a "Right-Chord" as seen below.
You can also "Double-Chord," or blindly mash both left and right click simultaneously on discovered cells, to force the game to check both cases. If those adjacent to the cell can only have monsters, the monsters are marked. If those adjacent to the cell can't possibly have monsters, the cells are discovered. This will speed your gameplay up immensely. You don't have to read the numbers inside the cells you double-chord! You can just mash it down a line of cells and if there's any no-brainers then the game will solve those situations for you.
If you had mistakenly flagged a cell as a monster where there isn't one then the game will work off of your assumption, and cause further mistakes. But as long as you haven't mis-flagged a cell as a monster when there isn't one chording will not make mistakes unless you started with a mistake.
The Example: How do I Pull off the Spy's Chord-Glean?
The spy's chord-glean ability requires you to chord, not right-chord, on top of a cell labeled 4 or more. You can not chord a cell that has all of its adjacent cells solved, so when you see a 4+ you'll want to plan out how to avoiding solving all of the nearby cells in order to use the spy's power. This is the Spy's insane arcane dance, as it requires you to carefully plan how you step around your knowns and unknowns in order to glean more information in the future. Let's explain through example:
In the image above you will see a cell labelled "4" under the mouse cursor. We need to chord this cell in order to use the spy's second level power.
For any other class you'd want to chord the "1" to the top right of this cell (and if you're mashing double-chords, you would have already done so), because a monster already exists adjacent to the "1" so these cells cannot have a monster.
However, if we discover this cell through chording the "1" then we can't discover it by chording the "4" and our chance to use the Spy's chord-glean is lost. So when playing the Spy we instead need to use the fact that this cell is not a monster...
To flag both of these cells as monsters, since that must be the case for the "4" to be satisfied. So now...
When the Spy chords the "4"...
We can see through (glean) all the adjacent monsters! These numbers tell us how many monsters are adjacent to the cell they are in, just like the numbers in our discovered empty cells. They don't include the monster in their own cell, though, just like a typically gleaned cell.
You'll find that this power is usable constantly...
As long as your Spy can do the dance and avoid needlessly discovering cells around a 4+ you may find yourself gleaning nearly every monster.
You must change how you play in order to pull off this dance, though, and learning to incorporate a new strategy will be slow at first. Until you can re-wire your brain to use the Spy's chord-glean any situation where you are timed will be a nightmare for you.