Super Micro FIDE Chess
The ZX81 famously hosted a 1K chess game written by David Horne (released in 1982). But as impressive an achievement as it was to squeeze the game of chess into just 1K of memory, it didn't actually contain the full rules of chess. Enter Super Micro Fide Chess, Written by Stefano Marago and based on the Micro-Max chess engine developed by H.G.Muller. This more recent chess game includes all the rules of chess that ZX Chess didn't (en passant, castling and under-promotion). It's not the strongest chess engine ever. I can beat it without much difficulty and I'm a very weak chess player (you can see I've checkmated the computer in the picture to the left), but I think it would put up a decent fight against a total beginner. That said, I've only played the "fast" version of the game (which wasn't fast by modern standards). It took a long time to "think", especially in the endgame, so the stronger version of the program may be a tougher opponent. In any case, I find it mind boggling this program can even exist. I'd like to see how it fairs against level 1 of the Stockfish engine one of these days... One thing to note: After you make a move, the screen will go blank. Your computer is not broken, it's just thinking about the next move. The ZX81 can be programmed to turn the screen off to speed up calculations.
K-Bird (1K Hi-res mode)
This is the first of many games to feature in this list from the prolific Dr BEEP (Johan Koelman), who at the time of writing has written nearly 70 Hi-res 1K ZX81 games. He doesn't seem to show any signs of slowing down, either. Astonishing.
K-Bird is basically Flappy bird for the ZX81. The flapping mechanics are a little different so I'd say it's not quite as maddening as the original, but it's still a challenging game. The more pipes you pass through, the faster the game gets until it's all but impossible. Because of the iffy membrane keyboard, the best games for the ZX81 employ a simple control scheme (and this one needs just one key to play).
Shapestack (1K Tetris)
Of course there's a version of Tetris for ZX81. There's a version of Tetris for everything. This one is my favourite Tetris clone for the system but to be honest, it can be frustrating to play on a genuine unmodified ZX81. It's too easy for your fingers to wander away from the keys without realising. Also, the only score that it keeps is the number of lines you clear (probably due to memory constraints) and for some unknown reason, hitting the shift key crashes the game. But still, it's a very solid Tetris clone and I love Tetris so it gets a thumbs up from me. You can actually buy this game on a physical cassette tape from Cronosoft along with "LazyFrog"...
Zxlider
Zxlider is another Dr BEEP creation and it's my favourite of the bunch so far. It's essentially an endless runner in the vein of Canabalt. You play as a clothes iron. Your goal is to jump between an endless procession of platforms and iron out any small bumps. But if you hit a large bump or fall off a platform, you lose one of your 5 lives. Ocassionally, "turbulence" will shake the screen and make things a little bit more difficult. The game increases in speed as you play. It's a simple idea but a really fun one and it has the kind of quirky surrealism that's missing from much of modern day game development. I love it.
LazyFrog
Lazyfrog is, you guessed it, a Frogger style game. Not much to say about this one. It's Frogger, surely you know how Frogger is played...
It uses the ZX81's built-in character set for graphics, so as you can see it's a little more abstract than most other clones. Nevertheless, it's a solid conversion and still fun to play. It has the same control issues as Tetris but that can't really be helped (damn that membrane keyboard).
Painter
Yep, it's another Dr. BEEP game again. This time he's made a simple maze game not dissimilar to the old Konami arcade game "Amidar". If you've played that game you know what to expect here: paint the pathways of the maze in black whilst avoiding the enemies. As the game progresses, you must go over each line more than once to paint them in and of course, there are more enemies on screen to avoid (The movements of enemy characters don't seem to have any programmed A.I. and appear to move randomly, but that would probably be impossible to include in such a small program). It's a simple, familiar concept that's very well-done.
Stupid Cupid
Our next game here is, you guessed it, from Dr. BEEP (I did say he was prolific!). This time he tackles the Shoot 'Em Up genre. The goal, as you've probably figured, is to shoot the hearts with cupid's bow as they make their way down the screen while at the same time avoiding being hit yourself. In the second "bonus" round, a group of hearts circle in place and you must shoot them all before the round ends. The game then repeats with greater speed. At the risk of sounding like a broken record at this point, it's simple but it's fun and like all the games here, it has that "just one more go" quality to it.
Nohzdyve
Written by the fictional star programmer Colin Ritman (for the equally fictional early 80's game publisher Tuckersoft), you may recognise Nohzdyve from its background appearance in Bandersnatch, the choose you own adventure episode of Charlie Brooker's Netflix series Black Mirror. But what some viewers may not know is that Nohzdyve is actually a genuinely playable game. Matt Westcott (the real author of Nohzdyve) has done an excellent job capturing the casual psychedelic weirdness present in so many of these early Spectrum games. If you want to play it, you can download the game from this website (link) and run it in an emulator or even on a real ZX Spectrum (and a very fun game it is, too). Nobody appears to have made a ZX81 version however, but thankfully Dr. BEEP recently programmed his own 1K conversion of the game. The premise is very simple: collect balloons (these were eyeballs in the original version) to increase your score as you hurtle towards the ground, with each balloon scoring you 10 points, while avoiding hitting the walls and the oncoming barrage of gnashing teeth hoping to chomp you up on the way down. Sadly, due to memory constraints, some aspects of the game didn't make the cut (like graphics for the washing line, air-con units and any animations). Nevertheless, it's very faithful to the Spectrum version and fast too. There's a hypnotic quality to the dodging and collecting game play that draws the player in.
Cylon Attack
Another Shoot 'Em Up from Dr BEEP, Cylon Attack is essentially a Space Invaders clone flipped on its side. As such, I won't go to the trouble of explaining the basic premise, but I will explain a few of the differences. Firstly, there are no protective bases for your Viper to hide behind from which you can safely snipe at the enemies. Secondly, while your Viper can only fire one shot at a time, it is possible to fire a volley of shots if you move your Viper up and down the screen. If you hope to survive, this is vital to remember because... Thirdly, it's FAST! Like, really fast. The Cylons advance at blistering pace, making it a real challenge to take out every single one before they reach your starfighter and end the game. If there is one criticisim I can make, it's that it might actually be a little too fast. I've yet to clear even a single screen of advancing raiders. PROTIP: Pick off the Cylons to the edge of the formation to buy yourself some time and you might have a chance. Like all of Dr BEEP's 1K games, this is a very polished and skillfully programmed effort, so if you like a challenge I can recommend it.
Pong
A well-programmed conversion of Pong from Dr BEEP (again). First to 10 wins. Angle your bat just so to speed the ball past your opponent. It's Pong. Surely even plankton at the bottom of the Mariana Trench know about Pong. What else is there to say? For two players only. On a side note, I think playing a game of Pong by myself might be the second saddest thing I've done in recent times. The first thing? Telling a handful of people on the Internet about it. Needless to say, I won (and also lost).
Dr Who
Proving that no genre is beyond his 1K coding abilities is this neat little Doctor Who themed platformer from Dr BEEP. The objective here is rather simple: Guide the "Doctor" (well, the Doctor's namesake at least) to retrieve the key to the TARDIS while avoiding Daleks guarding the platforms. I guess the Doctor must have misplaced their sonic screwdriver, because the only means of avoiding a quick death available to you is the ability to jump over enemies. There are eight levels to finish in total (and 8 lives with which to beat them all). Owing to having a definite end, it is perhaps less replayable than some of the other games I've covered here, but no less impressive a feat of programming. An enjoyable experience while the challenge lasts (though you'll probably still beat it in a single sitting).