orthogonal checks

being a way to overload x-in-6 chances.

rule

At regular intervals (night or turn) roll a check with a canny die and an uncanny die (of different colors):

• Keyed but uncertain events (a guard hearing noises, a trap being sprung, a creature being in its lair) occur if their number appears on the uncanny die.
• Adventurers have a base 1-in-6 chance to succeed in something chancey (climbing, forcing doors, swimming, etc), to which bonuses can be added from their type or because of their stats. They succeed if the canny die shows that chance or lower.
• In the underworld, a random encounter occurs if the dice show doubles. In the over-world, this occurs if the doubles shown are less than or equal to the area's encounter rate. 

why?

Suppose there's an elf blissfully unaware that they share a room with a hidden trap and a secret passage. There's a:

• 2-in-6 chance they notice the passage
• 2-in-6 chance they spring the trap
• 1-in-6 chance that they encounter a wandering monster

 One could overload this chance on a single d6 in the following way:

1. Trap sprung
2. Trap sprung
3. Passage noticed
4. Passage noticed
5. Wandering monster
6. Nothing happens

There's nothing wrong with this. But it gets strange if the elf starts actively searching. Their chance to find the passage goes up to 4-in-6, and suddenly there's no more room on your d6.

You could at this point roll twice, once for the search and once for the trap/wandering monster. But that changes the behavior. Now it's possible to find the passage and have the trap sprung where previously those were separate outcomes.

Why should the trap and the wandering monster be linked, or the trap and the searching? Why not have three independent checks? That gives us eight possible outcomes rather than the four we had with single d6 overloading.

One reason not to is that rolling more dice potentially gives away the information that there's something to find. That's probably fine in some methods of play. But it also adds complexity to the checks that need to happen.

My preference is to always make the same roll for checks: 2d6 of different colors. Conveniently, the odds of rolling doubles are 1-in-6, the odds of wandering monsters in the dungeon. Although evidently odds were greater in cities and some wilderness environs in early editions, my inclination is that wilderness encounters should be less frequent on the whole than underworld ones. (Hence the encounter rate modification.)

A last consideration should be mentioned:

• If the canny die triggers on a low roll and the uncanny one on a high roll (or vise versa), then the two can occur together but not together with random encounters.
• If the canny and uncanny dice trigger both on low or both on high, then a random encounter will usually coincide with one if it also coincides with the other.

Of these, the first seems better to my mind. A random encounter can coincide with an unexpected twist or with a bit of progress, but not all three together, unless one is more likely than not.