[It's December Days time! There's no overarching theme this year, so if you have ideas of things to write about, I'm more than happy to hear them.]
Board and card games have been a part of my life since the very beginning of memory. Computer games followed shortly after, but the requisite manual dexterity to move and push buttons at the same time would come later on in life, as would the necessary keyboard and mouse skills. We'll get back to that in a bit.
I don't remember much of games like Candy Land or other toddler games. Presumably, they got played all the same, but memory for me tends to start around five or six years of age, and I already know that at those times, I was intellectually ahead of my social development. Early games in memory, then, are games like Sorry!, which have relatively complicated rules about movement of pieces, and a little dose of strategic thinking, once more than one of your pieces is on the board at any given time. That game could also be a good one for a card counter to start learning on, if they were so inclined.
The random element of Sorry! may have been a little too much for me, even though it got played a lot. Perhaps because the large numbers encourage counting in multiple, but also that there's a card that requires you to count backward and one that lets you split the number among as many pieces as you can move, so there's a little bit of addition and subtraction practice there, too.
Cribbage is also a favored card game in the family. Not just because of the low numbers it takes to play, but also because there's maths practice there, counting, adding, keeping a running total in your head, finding lots of creative ways to add up to 15.
Pinochle and Wizard help with bidding and tricks and trumps games, as well as figuring out how to keep a handful of cards all together. Hearts is there for when you want to get gently annoyed with each other for a bit and really practice your card counting.
I mention the math practice a lot because in games that involved a bank, like Payday or Life (not Conway's Game of Life), it always fell to a child to take on the role of the banker. The older children were wise to this, and happily deferred to the younger children on the matter. A child doesn't necessarily realize it, but playing games of this sort provides plenty of maths opportunities that won't occur in schools. (Payday, for example, uses simple interest as a core mechanic for building score.)
Surprisingly, we're not a Scrabble family, not really. Our linguistic pursuits tended to Boggle, so that we could show off the variety of language we had, rather than being constrained by point values and grid placements. Or spot-the-object games, where being able to describe objects by alternate names could often net useful points.
We don't play Cluedo with Dad any more, not since he was able to successfully win on one room, with one or two cards shown him.
I'm not entirely sure where the divide between "games are fun to play with children" and "look at all the lovely practice kids get" was for my parents, but considering how much they discouraged the use of computer and video gaming in favor of other activities, I suspect the weight falls a little bit more on the practice side. At least for the early years.
Right now, the library does occasional programs meant to help young people with their reading and math skills, and the specifically math-focused games always seem dry to me. We get to play a fractions game by building pizza pies. This game has a mechanic where you roll two number dice and an addition of subtraction symbol, along with an endless loop that you have to get out of by reaching the exit exactly. They're serviceable, certainly, but I've always felt that things that are supposed to be games should be enjoyable first and educational later.
Which brings us to Math Blaster. Which I enjoyed playing its early days incarnation, with an alien running back and forth between rockets, where you had to stop them at the one that would launch into the correct solution. And the incarnations of the Carmen Sandiego series (of which World was the only one I could finish - after a while, the time constraints on USA and Time started to get ridiculous to me, expecting me to chart a path where I only needed one clue to get to the next destination, but also to consistently pick the interview that would provide details about the suspect so that I could eventually collect the warrant necessary.) And an okay game called Headline Harry, where the player was a cross-time newspaper reporter collecting the facts and key words on an important historical event - but on a deadline against a tabloid that would distort the events if they made it to print first. (You had to figure out what time period you were in amongst a couple of possible stories and then input the correct people, places, and so forth.) At the time, all of these games came with a reference work that was supposed to be instrumental to your success in helping you decrypt the clues and go forward.
My absolute favorite of the bunch of those sorts of games are the Dr. Brain series. Puzzle-solving at its finest, with adjustable difficulty, no less, across a wide range of disciplines from art and music to logic, programming, and cryptography. Sadly, with the general demise of the Sierra brand, Dr. Brain hasn't been around for a couple decades.
So there was plenty of "edutainment" in my early computer gaming as well. I'm not surprised that I went into school pretty confident that I could handle whatever it threw at me, at least in terms of the schoolwork.