Appealing thinking games, that are easy to make; easy to learn, and easy to play

Question

$\color{Green}{\text{My Question in short}}$:

Unprovable claim: Someone who is familiar with 100 thinking-games, and plays 30 of them reasonably well, is more prepared to go to math than the average community.

The most important available facilities, are volunteers. There are some people who travel to villages and deprived areas. I know one of them, They can teach simple games and hobbies to local educators so that children can enjoy a wider variety of games and hobbies, and the children can be taught and raised better. Note that almost all attempts are individual or team, that's why there is no significant money for this work.

Goal: My goal is not to make games for kids. My goal is to create a booklet/ notebook/ ... of suitable thinking-games for different age groups. If such a booklet is available to these volunteers, they can introduce local educators and children to better hobbies and thinking-games. I am looking for suitable thinking-games.

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Properties of a suitable game:

0. Easy to make [The most important factor is the zero factor]
1. Does not require mobile
2. Easy to learn, and easy to play
3. As attractive as possible
4. Preferably durable
5. Involving as many players as possible
6. Can be played/done in a short time, playable/doable as short as possible

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EDITED:

About the age-range: No specific age range can be specified. The age-range of children is between 4 to 15 years. The age distribution is almost uniform. I realize that this wide range includes a large number of age-ranges. I am not an expert, but I believe that the target society may need to be divided into 5-7 different age-groups.

$\color{Green}{\text{End}}$.

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$\color{Red}{\text{Details start here}}$:

I am looking for a significant number of thinking-games and board games that have these properties [however, even a single offer would be welcome]:

Properties of a suitable game in detail:

0. Easy to make. Due to financial difficulties, it is not possible to buy games. But we can think of "building the games". The shape and form of the beads and pieces should not matter, and their shape and form can be reduced to the simplest accessible state. Beads and pieces should be designed in a very simple shape and form. [For instance, bottle caps can be used as beads, smooth cut pieces of wood (cuboid woods) can be used as pieces. The design of the game screen, should be possible in a short time, for example 1 or 2 hours. If the beads and pieces have different sizes and forms, they should be distinguished by coloring, or marking, or some other simple ideas.]

1. Does not require mobile. Children in the target community do not necessarily have access to a mobile or computer, so mobile and computer games may not necessarily be suitable suggestions.

2. Easy to learn, and easy to play. The game should be "simple" and "light" [or at most "light-medium"]. [The game should not have too many details; rules and restrictions should be simple. There is no sensitivity to the number of rules and restrictions, but it is better not to have too many]

3. Attractiveness[As attractive as possible]: Completely abstract games may not be very fun for kids. Definitely, Snakes and Ladders/ Mensch ärgere Dich nicht does not have the beauty of chess, but during Snakes and Ladders/ Mensch/ ... more friendly interactions are formed. And these very mild social interactions are very effective in "appealing" the game and "motivating" players and kids to get back to it. A game that does not create social interactions between players will largely lose its appeal. In my opinion, games that are played on paper do not have much chance to attract a general audience. I think it is a lot of fun for kids to move the beads or pick up and touch the pieces. Another reason to avoid abstract games is that, most likely, there will be no teacher to do this with the children (Probably, after the first few days, children have to play on their own, so games should be as attractive as possible for children); and the game itself should be engaging for children. [*: I guess this section may not be agreed upon by everyone, ignore it if necessary]

4. Preferably durable. In addition to being easy to build, we need to be able to build them at a reasonable cost and expect them to last at least a year. For example, card-based games will not be very suitable. In card-based games where the cards need to be unknown, if the cards are damaged, they become marked and known. Preferably games are not cards, as they are easily damaged.

5. Involving as many players as possible. The more players can play at the a time, the better. Creating a team, for each turn or piece, is not an interesting idea, this idea has many problems in practice. (See my comment to this answer.)

6. Can be played in a short time, playable as short as possible. It is better that the game-play is not too long.

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The most important factor is the zero factor. After this factor, attractiveness will definitely be the next priority. I am looking for games that satisfy the zero factor along with a significant number of these factors. Years ago, I asked a question on this site and I received a convincing and satisfying answer. During that question, I became acquainted with the Ricochet Robot and Can't Stop; in which Ricochet Robot clearly satisfies almost all of the above conditions, and Can't Stop is also very satisfying. Also, Ortho-Projections has almost all the conditions and the only problem is that it is not attractive for children (Also, one can find other games in Hamkins's page; see here and here). For instance, the Simon Tatham's Puzzles (Link to the game for mobile) are eligible for almost every factor, except that their biggest drawback is that it is either impossible or very difficult to play without a mobile phone or computer.

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EDITED:

I forgot to mention popular games like 9 men's morris and 12 Men and their simpler variations. Of course, these are not the only popular two-player games that are easy to make and play, which belong to this brilliant category (brilliant category of simple light classic board games). Each game in this brilliant category satisfies most of the above features, and their main drawback is that they are two-player, and may not be appealing to children.

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EDITED:

I came across this MO post, but I have not read it yet, I think I should read it patiently. Probably, this page may contain related content, or perhaps even this page.

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I know some other games, but I am not an expert in the field of mathematical-pedagogy. I would welcome stronger connections [E-mail/ chat conservation/ video conversation/ ...] with educators to receive more advice from them. My main purpose in raising this issue here, is to find lots of games; preferably with the properties listed above.

Consider that my goal is to get acquainted with a significant number of engaging and fun thinking-games, that reinforce aspects of mental, mathematical, and logical skills in the form of games; however, even a single offer would be welcome.

Answer 1

Set ( https://en.wikipedia.org/wiki/Set_(card_game) ) Set is my go to for primary school: You could make your own version without too much trouble. It's about pattern matching, it's real time, as many students as you want can play it at once, and its very simple. 8 year olds can beat 16 years but it's completely skill/observation based. It seems to hit most of your criteria anyway. There's an online version here if you want to try it out: https://smart-games.org/en/set/start

Answer 2

I am writing about 2 number sense games. Some of these are pencil and paper, but all have been received enthusiastically by my students. In addition the students would play these games when I was not around.

a) Guess the number. The enthusiasm for this game among my students always surprises me, but it has been a favorite for over 25 years.

1. One person, is the "teacher". S/he picks a number - it can be any number. S/he writes it down on a piece of paper and folds the paper up and puts it somewhere that everyone playing can see.
2. The "teacher" needs a large paper to write on. (or blackboard, or whiteboard, or anything). The important things is that when s/he holds it up, everyone will see it.
3. The "teacher" calls on people in order to guess the number. After each number is guessed, the teacher writes it down at the top of the paper/board if it is larger than the number picked and says lower OR at the bottom of the board if it is smaller than the number picked and says higher.
4. Subsequent high guesses are written at the top of the board under previous high guesses and subsequent low guesses are written at the bottom of the board on top of previous low guesses.
5. After several guesses the board might look like this: 37,000,222 60,000 49,000 10,001 19 This space is empty and room for future guesses.
   10
   5
6. When someone finally guesses the number, the teacher unfolds the paper with the number to show that the guesser is right. Then the guesser becomes the "teacher".
7. If a real teacher shows the class, the teacher, might pick a regular number, then a very large number, than a negative number, then a fraction. This will give the students an idea of the range of possibilities.

b) Create the numbers from 1 - 100

1. You will be making numbers using 5 dice. Depending on the abilities of the students, you can use addition, subtraction, division, multiplication, exponents, parentheses, square roots, parentheses. Students can all put two numbers "together" so that if one dice has 6 and one dice has 1, you can make 16 or 61.
2. This can be played solitaire, or as a team, or competitively. My students loved to play this as solitaire once they finished their classwork.
3. Students start with papers where they make a list of numbers from 1 to 100 with room for their work next to each number. (IF they are playing as team you only need one list per team) They also needs lot of scrap paper.
4. The dice is spun (students take turns spinning). Students must use all 5 numbers to make any number from 1 - 100. They put their expression next to the number.
5. First one to make all the numbers wins. This can take time to do - so teams may be preferable or you can end after 10 or 20 spins. Then whoever made the most numbers wins or whoever made the smallest or largest number wins etc.