There are a few handicap ideas I use:
- Material Advantage
- Time Advantage
- Swapping colors midway through the game
Depends on the difference in skill of the two players. For beginners playing against moderately good players, you can take off whole pieces such as Queens, or Knights (since Knights are notoriously good against beginners due to the strange L-shape pattern). Rooks and bishops are more straight forward, and could be used as deficits when the beginner has a better idea of how to play. I don't like the idea of large material deficits because it allows the beginner to think they can play more recklessly when the handicap is taken away.
For more advanced players, pawn deficits are often a good way to create balance. Peter Svidler says in this video that against a lowish 2000 rated player a f-pawn deficit proved to be one of the hardest and most fair games he has ever played. The f-pawn is the biggest pawn-weakness to make because it doesn't give any development advantages where any other pawn would. Hikaru Nakamura has had various pawn advantage handicaps against the chess engine Stockfish. With a b-pawn deficit, Stockfish won but with a h-pawn deficit, the game ended in a draw. I like these ideas because it immediately sets the player up to have a significantly weaker endgame if they choose to trade down. It also reduces their middlegame since they cannot create tension as easily, leaving the lesser skilled player with more control over the flow of the game.
The problem with material deficits, is that it does not scale very well. It is useful for absolute beginners but at higher levels, a one-pawn advantage requires the difference in player skills to be enormous. However, it does mean that opening theory is often disregarded, which is a learning-benefit since the players won't be able to rely on memorized moves and actually play the game to the best of their ability.
This requires the use of a clock, but is a fairly good way to create balance between players. The idea is to reduce the amount of time the better player has to think, which in turn leads them to have to play more intuitively rather than being able to calculate variations. This means that tactical blunders by the worse player are less likely to be noticed, and blunders by the better player become more likely. The difference in skill, will influence the recommended time controls.
I don't recommend 1 minute, because it is simply too fast to have to play for the better player (and will most likely lead to losing on time for most games). If there is a large skill gap, 2 minutes to 10 minutes can be fair, and reduce this gap as the less skilled player progresses. A good equilibrium can be figured out by playing a few games against the worse player to find where a sweet spot is. The better player will still have the advantage overall, but it is greatly reduced.
You will find that children don't use their time very effectively, if at all. When I was playing in juniors, if you gave players 10 minute time controls, they will have finished the game in under 5 minutes most of the time. It is important to emphasize that they think about their moves before playing them. This however can lead to the mindset that they should just wait 10 seconds before playing without actually thinking about any other possibilities. It can be difficult for them since their attention span is shorter than that of adults, but it is a useful skill in general to learn.
While not great for a friendly game, it is a good learning resource for lesser skilled players. The game plays normally until the better player creates an advantage (the size of this advantage can depend on the difference in skill level) and then the players can swap colors to allow the less skilled player to figure out how to win. This teaches them how to win a won position, and if they can beat the more skilled opponent in a won position, their chances in winning against an equally skilled opponent will increase. Obvious drawback is that it doesn't teach the player how to obtain the won position, but that is generally pretty hard against a better player.
Extra Idea - Letting them win:
My personal favorite when playing against weaker opponents is to deliberately give them tactical opportunities which they can take advantage of. Not a true handicap, since I'm not forced to abide by this rule but it works well. I don't like to leave pieces en prise but wherever I can give them a fork, discovered attack, skewer, mating net, etc I try to allow it. If I deem that the tactic is too difficult for them to see, I will let them know that I have made a mistake for them to learn from. Against newer players, you might want to tell them every time you make a mistake, but as they improve you can talk less and see if they can figure it out on their own. As they improve, you can start to play more towards your normal skill level, and make fewer deliberate mistakes than you did before.
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How the World Champion First Learned:
When Magnus Carlsen's dad was teaching him chess (at around age 6 before he started playing seriously), he would take away all his own pieces, so it would be 8 pawns+King vs Magnus' entire army. Even with this major disadvantage Magnus was unable to win. This is sourced from his Biography Wonderboy.