EDIT: I found the Russian wikipedia article for the second game (I was searching for the wrong name): https://ru.wikipedia.org/wiki/%D0%9A%D0%BB%D0%BE%D0%BF%D0%BE... . Looks like I forgot the rule that each base must be "activated" (have at least a single bug next to it) to produce new bugs.
One was an open map version of tic tac toe, where the goal was to get 5 of your symbol in a line. This game was called "amoeba", and if you won, you got to draw an outline around the board so far (which tended to look like an amoeba).
Another one was a kind of racing game. You'd draw the boundaries racing track on graph paper, where the race track would be several blocks wide at all points. Players would start near each other at the starting line, and get to update their velocity by one in both the x and y axes, so effectively you carried a lot of momentum. If you went out of the allowed area, you lost. So, the game revolved around being able to judge the maximum speed / momentum that would still allow you to take the corner.
Later on, I lived in other countries, and never ran into so many of these pen and graph paper games. No idea why.
It started out as "UFOs" (circles with a line through them) and mutated into X-Wings v TIE Fighters. Soon we were drawing asteroid fields, opposing planets with gun emplacements, etc, etc. Wish I could go back and look at some of those old drawings.
You could incorporate a theme, but themes tend to occur naturally.
Especially with the suffocation that comes with technology, simple pen and paper games are breath of fresh air.
An animal/mineral/vegetable is written on a card for every player but one who gets a blank card. For a couple of rounds you each draw a line before finally voting on who you think doesn't know what you're drawing. The main group is trying to demonstrate to everyone else that they know what the item is (and so drawings become very abstract) without making it obvious to the hidden traitor.
I think the introducer mentioned it was being commercialised...?
board game geek suggests there's at least one reimplementation: "Sunken Sailor"
Because I grew up with Oxford academics, my family growing up would also play the same thing but switching between English and Latin. Those who knew Latin would try to translate accurately, but us kids would write stuff that sounded more like bad Harry Potter spells, which the adults would have to make sense of.
Sometimes the missus and I will play a few matches. Though they are adults, I'll sometimes get my kids to play it with me, when they visit.
You can even play it with more than two people. When you do it with three other people, on a whole sheet of graph paper, it starts to make for some interesting commentary and labored attempts at stategy.
If you want to change it up a little, you can play with three other people and play as partners. I imagine you could do that with six or eight people, but I've never tried it.
Anyhow, just because we have newer devices and ways to entertain ourselves doesn't mean we can't enjoy the simpler things from our youth. Sometimes, I even read dead tree books. The old stuff is still fun.
* Where I retired, I don't have much in the way of strangers. We usually go out to brunch on Sundays and I'll frequently purloin someone's child, stuff them with ice cream, and play a game of this, or some rounds of Tic-Tac-Toe, or hangman. It is one of the perks of living in a very rural area.
I really do recommend people take a break and go do some of those things they did as children. Go skip rocks, play tic tac toe for hours, and climb a tree.
It helps ground me, and who doesn't like catching frogs? All those sort of things make for a great day moment without needing to be in a rush, connected, or obligated.
Beyond Tic Tac Toe ( https://boardgamegeek.com/boardgame/3937/games-art )
Beyond competition ( https://boardgamegeek.com/boardgame/3928/beyond-competition )
Beyond solitaire ( https://boardgamegeek.com/boardgame/3940/beyond-solitaire )
Sid Sackson's Games of Art collects a number of these. https://www.eaglegames.net/product-p/101319.htm
there is also MetaSquares (http://www.scottkim.com.previewc40.carrierzone.com/squares/i...)
I have made one too - Square TicTacToe(https://github.com/learnbyexample/squaretictactoe)
Here it is: http://speps.github.io/papertetris/ (Flash player required, lost source code)
Some are based on 3-4 participants https://www.conditionaldesign.org/
Some work with an arbitrary number of participants, e.g. visitors adhering stickers to art gallery walls and floor (see "red fungus"): https://web.archive.org/web/20100829051147/http://poly-luna....
No skill involved, but I spent a zillion hours playing "cricket" by writing "dot ball, 1, 2, 4, 6, out" on the edges. Then you spin the pencil in your hand without looking and slide your thumb up the edge. Whatever you landed on was the score and you marked it down on a score sheet.
As a bonus you could easily disguise the action as fidgeting - so you could play during class.
The best pencil and paper game ever
One that I don't see - or maybe I don't know what I'm looking for - is "Fish, Fruit, Flower", which we used to play as a family when I was young.
As a child, I played this game quite often with my babysitter - an older woman who for close to a decade was essentially a third grandmother.
Our paths cross every five or ten years when I'm visiting back home - she's in her 90s now - and we still fondly remember playing this game together.
I encourage everyone play these games with their children - there's something about the interaction of the players that creates warm, lasting memories for everyone involved.
The Dots and Boxes Game: Sophisticated Child's Play
by Elwyn R. Berlekamp .