Number of permanents
The first cards that cared about odd or even were Chaos Lord and Chaos Moon in Ice Age. The designers were trying to make cards that embodied the feeling of chaos. To do this, they designed a creature that changed control under a weird circumstance, and an enchantment that either enforced or weakened red creatures. The weird circumstance was there being an even number of permanents on the battlefield. As each player has the ability to add or subtract permanents, it was something they had some control over, but not complete control.
Converted mana cost
Some cards care about if converted mana cost is odd or even. The first card of this kind was Ashlings Prerogative from Lorwyn. Again, it was a red card that was trying to create a sense of chaos. Ashling was an Elemental Shaman, and the card was trying to communicate Ashling's quirky nature. The next card took another eight years to see print in the set Battle for Zendikar. The set was all about the Eldrazi, and R&D was trying to find designs that helped them feel alien. Unlike Ashling's Prerogative, which only cared about cards of its controller, Void Winnower only affected the opponent's cards. R&D chose to hose even converted mana costs because they liked that Eldrazi cared about "odd" things. One card showed up in Commander 2018 and Ikoria: Lair of Behemoths added four more cards of this kind; two companions with a deck restricting rule and two others.
- Ashling's Prerogative (Lorwyn)*
- Void Winnower (Battle for Zendikar)*
- Yennett, Cryptic Sovereign (Commander 2018)
- Extinction Event (Ikoria: Lair of Behemoths)*
- Gyruda, Doom of Depths (Ikoria: Lair of Behemoths)
- Lavabrink Venturer (Ikoria: Lair of Behemoths)*
- Obosh, the Preypiercer (Ikoria: Lair of Behemoths)
Unstable latched onto oddness and evenness by making four cards that cared. First was two different versions of Knight of the Kitchen Sink. Every version had a unique protection. Two of them had protection from collector numbers, one evens and one odds. Oddly Uneven was a Wrath effect that let you choose even or odd as it applied to the number of words in the cards' names. Ineffable Blessing was another card that let you choose even or odd (each version of Ineffable Blessing let you make a different modular choice), also caring about collector numbers.
- Knight of the Kitchen Sink (Unstable, #12b)
- Knight of the Kitchen Sink (Unstable, #12d)
- Oddly Uneven (Unstable)
- Ineffable Blessing (Unstable, #113e)