Obviously, these have to be done intentionally. A weaker player who nearly wins only to discover their opponent was "teaching" is probably a bit offended: their accomplishment stolen from beneath them.
What aids all of this is that Go has a handicapping system that can be very well tuned so that for people who would score within 40-60 points of one another you can probably tune the game down to even odds.
I recommend to people learning to look at the activities of someone "good" at the field but not a star for this reason, I don't know if it applies to all fields but for ex I got the same feeling learning chess by following GM's games (I was lost) and a book like "Master vs Amateur" opened my eyes to typical errors made by intermediate players that won't show up in chess books (another example is "The Amateur Mind"). I tell soccer players than besides enjoying watching the games of the big teams and star players to watch "journeymen" games from a 2nd division to learn the basics.
Also the reason why we frequently learn more from a student mate explaining something that from a veteran teacher or professor, who forgot the struggles of the beginners.
For instance, when competing to win, there's little room to be exploratory, playful, envelope pushing, maximizing learning. First tries at anything mostly fail. So I'll say "I'm going to focus on learning new things, not just on winning". And verbalize the exploration like "hmm, I wonder if...", attempt, and post mortem review ("I just tried X... and Y happened"). Or offer that as an option - "I'd like to try throwing (at target) under my leg... or would you rather I throw regular?"
Play to teach can be mixed in as a part-time objective. "Fake-oops, I dropped my card face up. What was it? What's something you might do differently knowing I have that?"
One can also optimizing for game interesting / fun. "Well I could use this card to wipe you out there, instead of discarding it, but this is so much fun, I want to fight it out".
So never "illusionary success", always transparent honesty. But being explicit that there can be more than one "game" at play. But also have to watch that this all doesn't become an "it's unpleasant to lose" avoidance strategy - if playing "for real", maybe that's to the bitter end.
He has played Uno (without the scoring and with face up hands of cards) for a while now. The other game he has been able to play and that I recommend as not being as painful for adults as some, is an Orchard Toys game called 'Where's my cupcake?', but he's only just at the snakes and ladders type stage. We played a lot of Sorry too with my six year old when he was about 4-4.5. The other thing we have done is having the three year old 'on a team' with an adult, but that obviously works better with multiple kids.
One they hit 4.5/5, there are tons of games you can play with them. That's when things start get to fun! Basically, I wouldn't worry yet - they just have to get to the right stage developmentally which they will do.
At first, early on, games should be very simple. The idea is to focus solely on the basic structure of games:
--game start
--keep attention on game
--turn taking/following in correct sequence
--problem solving around a very simple goal
--game end
--with finally very clear assessment of player ranking (i.e. You won, I/we lost or I won, You lost)
Underlying all this should be a heavy focus on the maintenance of appropriate emotional responses and behavior modeling (e.g., no gloating, no sore losers, no emotional aggression or defensiveness).Again, this is all ground-floor stuff, so kids can start learning it as early as 2-ish. Learning to take turns is a huge emotional advantage. As is learning how to both succeed and fail in games and life with grace.
A very good game that has a degree of complexity appropriate to kids that young is "Animal Upon Animal" by HABA.[0]
It's a simple stacking game: On your turn, stack this animal on that animal; if the stack of animals falls over, that's the fail state. (There is a 6-sided dice with pictures on 4 of its faces, and 1 and 2 pips on the the remaining, but it can easily be removed from the game until the child in question is ready for it.)
The 3 year old will tell you what they want to do.
At 3, my little guy's favorite toy was rated for 8+ years old, and his favorite game was chess.
He never cared if he won or lost at chess, his primary purpose was to push his pawns, castle, and then get in at least one en passant.
Maybe start with hopscotch (the regular kind with where you toss an object into a square, but with clearly numbered squares), telling them each time the number of the square they're on, the number of the square they're heading to, and the number of hops they'll do, before they do them. After a while, they'll get an understanding of how the numbers on the squares relate to what you're saying, and maybe even a vague intuition for subtraction.
Eventually, you can replace the thrown object with a rolled die (I suggest a big soccer-ball-sized die they can see from far away, with numbered faces instead of pips)—whose roll indicates how many spaces they should move rather than the space they should move to—and keep playing the same game.
Once they get that, then they're ready to play board games.
My First Carcassonne and Sushi Go! are two we like and they're playable for adults too. (A lot of kids games are terrible, ones based on licenses like Disney or Paw Patrol for example.)
Also check out Peaceable Kingdom they make cooperative games for kids (Hoot Owl Hoot, Race to The Treasure, etc.) I haven't played them personally but based on reviews some families really enjoy them a lot.
https://smile.amazon.com/Jax-8001-Sequence-for-Kids/dp/B0000...
pure instruction -> teaching through playing -> friendly match -> competitive match
Let's use a card game as an example.
Pure instruction: Both players play with their cards visible to each other, and the teacher coaches rules and strategy as they play.
Teaching through playing: The hands are now private, but the teacher will tell the student if they're making bad moves and allow do-overs. The teacher may also set up situations for the student to take advantage of.
Friendly match: The teacher is playing against the student. No coaching is given. But, nit-picky procedural rules are not always followed. (You've set that card down and your hand left it, you can't pick it up again).
Competitive match: Rules are followed to the letter.
Think of a chess game, for example. We can play by the rules to the letter, but if I decide to systematically take your pieces one-by-one or "forget" some of my own experience to perhaps make it more fun, are elements I assumed are in the original comment above.
Essentially anything where "I've consumed more calories that you have" or "I've had more years to think that you have" are an unfair advantage for purposes of fun.
This works for all ages... and for boardgames and physical games. It's their choice which mode they want to play in, and they trust and respect you more when given the choice. You treat them as a peer. You can beat them mercilessly, or you can join their side and practice the game together. And the thrill and confidence they get when they beat you playing 'for real' is just priceless.