Skip to Content
 

Sumof2 Version 2

18 replies [Last post]
ichbin
Offline
Joined: 09/21/2010

Game : Sumof2 (Version 2)

Category : Abstract strategy
Age : 8 and up
Playing time : 40-50 minutes
Number of players : 2
Mechanic : Numbers

Components :

Board 6x6 (see picture)
36 pawns numbered from 1 to 36

Goal of the game : the winner is the one scoring less points after 2 rounds

Rules of the game

The game is played in 2 rounds.
The first round one of the 2 players play first
The second round is up to his opponents to play first.
The score is established after the 2 rounds.

Set up

The board is placed between the 2 players.
The board is filled randomly with all the 36 pawns faced up.

Gameplay

Pick the first to play
Players aternate picking 1 pawn form the board and switching 2.
Player in turn choose 3 pawns such as the value of one them is equal to the sum of the values of the 2 others.
Example :
Player choose 20, 15,5. The choice is legal because 20=15+5
Player pick 10,7,18. The choice will be illegal because no number is sum of the 2.
10+7=17 not 18.
After his choice checked the player has to remove the pawn with the value summing the 2 others and to switch the other two. (see picture)
Example : If his choice was 32,26,6 he has to remove 32 from the board and switch 26 with 6.

End of the game
The game ends when a player in turn can not find 3 pawns such as one is the sum of 2.
Then the sum of the value of remaining pawns on each camp are added.
Record the scores of the 2 players and start of the second round.

Scoring

After the second round we add the results of the 2 rounds and the player with less points win the game.

rcjames14
rcjames14's picture
Offline
Joined: 09/17/2010
I Like It

At first glance, it seems deterministic. Until you see the illustration and realize that each player has a camp... so you are actually competing to rid your area of the highest numbers. At that point, it becomes clear that there is going to be a lot more strategy to the game... because the position of objects matters.

But, I think the game really comes alive when you realize the competing interests between keeping high numbers in your camp and moving them to the other person. Ending up with high numbers is really bad. But, since they are more likely to be removed (as the total of the sum), the spot in which they exist will likely be worth 0 at the end. Very nice.

Also, I think you found a very elegant way to ensure the continual capture of pieces. Since 1 and 2 can never be removed, you'll always have the two most useful objects for summation around for all the numbers > 17.

The only thing I question is the limitless range of players. Since it is a perfect information puzzle and there is no number you cannot select, it may be clear at the beginning who will win (with a deep enough search, or the immediate elimination of key number like 3,4, etc..) That may not make the game fun.

I think players generally like the idea of having control over certain pieces... which they can deploy or hold back for just the right moment. This type of exclusive control usually adds a key element of strategy to what is usually otherwise just a puzzle. Imagine if you could move either white or black in chess! The game would never end...

Fortunately, your mechanism doesn't allow for a stale, because every move removes something. But, I do think that players will feel largely unsatisfied by the fact that there is nothing that they have exclusive control over. There's no reason not to make a move now for a later advantage. So, it will probably instead highlight player mistakes... something that can be frustrating.

innuendo
Offline
Joined: 05/25/2010
It feels like the first half

It feels like the first half of the game will be completely meaningless. Since, as pointed out, it doesn't matter where pieces are until the end it makes no difference what I "swap" until the last 5 or so rounds when the pieces become harder to match.

And James is correct in that this game is going to be very punishing to mistakes, which can ruin the enjoyment of a game.

Right now the location of the pieces is arbitrary. You could play the same game and instead of using a grid use two piles, one for each player, and get the exact same results. If this is going to be a board game make the locations of pieces matter more throughout the game, or have special pieces like "locking" or "doubling" that grant effects to pawns next to them. A locking piece makes it so you can't remove the piece or a doubling piece that makes each pawn next to it worth, well, double. Seems like this game needs that extra layer of something or after playing twice I would never pick it back up.

ichbin
Offline
Joined: 09/21/2010
Thank you for your comments

I will wait for more comments to try to debate about some points by giving examples and diagrams .
Keep in mind that the goal for each one of the players is to get rid of the pawns with biggest values.
Every move put more pressure on the opponent.
A player remove one pawn (it will not be automatically the biggest value) and switch 2 (the best switch is when a player get rid of the biggest value making it harder for his opponent and placing in his own camp pawn with the lowest value).
That is the mechanic core of the game.
So every move is important and has a meaning even if the player has in the beginning less constraints.

innuendo
Offline
Joined: 05/25/2010
It really doesn't matter

It really doesn't matter though since even if I don't as "player a" take the largest pawn, player b will. So by the middle of the game the players will still have removed on average the highest pawns, it doesn't matter who removes what in what order, the bigger pawns will still get removed first. Sure there will be some minor possition stuff early on, but it's not like I can protect a particular piece or in any real way deter my opponent from making a certain move (not to mention it largely doesn't matter what they do until the last few moves).

I love this idea but it just seems very, raw.

innuendo
Offline
Joined: 05/25/2010
It really doesn't matter

[accidental double post]

ichbin
Offline
Joined: 09/21/2010
I do not agree with you....

on it does not matter who removed the highest pawns.
It matters because the one who have less points win.
The game is going to be more and more harder.
In the beginning of the game you remove your "own" pawns (pawns on your territory) and you switch using the 2 camps (the lowest for your camp and the highest for your opponent camp).
But after some moves depending on the positions of the pawns you will have no other choice than removing pawns from your camp (or even from your opponent camp). You switch your own pawns (or the pawns in your opponent camp).
It is not hard to compute using brute force sequences of pawns where you can not find (a=b+c). There are a lot.
Example : 1,2, 10, 13, 16.
No 2 values are equal to one of the sequence 1,2,10,13.16.
If this sequence happens for example at the end of the game. the more important is to know where the pawns with highest values are (in your camp or in your opponent camp).

rcjames14
rcjames14's picture
Offline
Joined: 09/17/2010
But Is It Fun?

There is a game here. I can feel it. But, there are certain elements which may not make it fun to play.

Both innuendo and I have already pointed out that people like exclusive control over things. Perhaps certain positions are protected, others doubled. This makes the game idiosyncratic to the emerging positional landscape. But, as you have it, there is no difference between what is mine and what is yours during play. At the end, it matters what's in your camp and what is in mine. But, until that point, you can move anything that I don't move. So, there really is no chance to hold back, lock in or wait until later. Is this going to be fun?

Also, each board begins with the exact same set of numbers. Although they are divided at random between two different sets (your camp/my camp), the fundamental nature of what can be added to what will not change between games. So, as innuendo has insinuated... this game will be interesting for two plays. The first to get familiar with the dynamics, the second to confirm the optimal strategy to win. With a fixed set of numbers, there are only so many different ways to eliminate them until you end up with disconnected pieces. That number is large, but I think for most people, it will be trivial... not because they know it, but because they see it as not necessary to know. Yet, this knowledge is alone all that is necessary to win/lose the game. And, once known (say by a computer), a complete game tree can be constructed based off of the initial setup and there would be no need to play.

ichbin
Offline
Joined: 09/21/2010
I understand your concerns about the game

Thank you for your comments.
I will take for now the game aside until an idea to improve it come to my mind.
I have some ideas but adding 3 or 4 rules will not be my best wish :
- such as removing pawns under topological conditions
- replacing the pawn removed by an opponent pawns
- creating territories using polyminoes forms
- changing victory conditions
- finding some theme to the game

Anyway big thanks!

ichbin
Offline
Joined: 09/21/2010
Another minor change...

Yesterday one idea came to my mind.
I want to have some feedback if possible.
After placing randomly the pawns on the board players place rings of their color on the top of the pawns placed in their territory.
So each player will have his own pawns. that means adding new components to the game (18 blue rings and 18 yellow rings).
Added Rule 1 : player can remove only their own pawns from the board but they are allowed to switch one or 2 pawns opponent.
Added rule 2 : at the end of the game pawn of my (your) color in your (my) camp are counted for twice their value.
What do you think about the added rules?

Steve
Offline
Joined: 07/29/2008
Altered Game - 2orMore

I was thinking about this game at work again (Shhh! Don't tell the boss!) and decided to take this direction with it:

2 or more players (preferably 2 for now).

6x6 grid filled randomly with tokens with values from -18 to +18 (no zero), face down so that no one can see which token is which value.

There are 11 different-colored tokens with prime numbers that can be either positive or negative from 1 to 29 (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29), also face down but off the board or in a bag.

A player reaches into the bag or otherwise picks a random prime-number token (Ex. 11). Both players must now find a combination on the board that sums to +/- 11. Because this is the first prime # token for each player, it must be a sum of two numbers (Ex. +18-7 = +11 or -13+2 = -11).

Each player, during their individual turns, flips over two tiles to find two tiles that would total the prime number token.

The first player who finds such a combination gets to keep the prime # token. Of the two numbers used to create the combination, the opponent gets to choose which of those two numbers stays on the board and where that number goes on the board while the player who made the combination keeps the other number.

With each successful combination that a player makes, the number of tiles needed to make a combination goes up by one. If a player has made three successful combinations and are now on their fourth prime number token, they'll need to make a five-tile combination (ex. +13+7-11-3+1 = +7). The opponent, though, does not need to follow this and follows their own schedule. So, for instance, one player may have "won" 3 prime-number tokens and, as a result, now needs to make a 5-tile combination to win the next token. The opponent has won only 1 token so they only need to make a 3-tile combination. Regardless of the # of tiles needed for a combination, only one will be put back onto the board each time by the opponent.

The winner is the first to reach six tokens. In the result of a tie or if the board is no longer capable of producing a winning combination of the current token (unlikely but possible if the two players are strategic in what they choose to put back on the board), all tiles kept by the players (excluding the prime # tokens) are added up as positive numbers and the higher number wins. If that is a tie (unlikely but conceivably possible), then the players duel with pistols or flamethrowers... preferably flamethrowers (although those wouldn't be included with the game, naturally).

Anyway, that was my thought concerning the game. Enjoy.

ichbin
Offline
Joined: 09/21/2010
Thank you...

Steve wrote:
I was thinking about this game at work again (Shhh! Don't tell the boss!) and decided to take this direction with it:

2 or more players (preferably 2 for now).

6x6 grid filled randomly with tokens with values from -18 to +18 (no zero), face down so that no one can see which token is which value.

There are 11 different-colored tokens with prime numbers that can be either positive or negative from 1 to 29 (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29), also face down but off the board or in a bag.

A player reaches into the bag or otherwise picks a random prime-number token (Ex. 11). Both players must now find a combination on the board that sums to +/- 11. Because this is the first prime # token for each player, it must be a sum of two numbers (Ex. +18-7 = +11 or -13+2 = -11).

Each player, during their individual turns, flips over two tiles to find two tiles that would total the prime number token.

The first player who finds such a combination gets to keep the prime # token. Of the two numbers used to create the combination, the opponent gets to choose which of those two numbers stays on the board and where that number goes on the board while the player who made the combination keeps the other number.

With each successful combination that a player makes, the number of tiles needed to make a combination goes up by one. If a player has made three successful combinations and are now on their fourth prime number token, they'll need to make a five-tile combination (ex. +13+7-11-3+1 = +7). The opponent, though, does not need to follow this and follows their own schedule. So, for instance, one player may have "won" 3 prime-number tokens and, as a result, now needs to make a 5-tile combination to win the next token. The opponent has won only 1 token so they only need to make a 3-tile combination. Regardless of the # of tiles needed for a combination, only one will be put back onto the board each time by the opponent.

The winner is the first to reach six tokens. In the result of a tie or if the board is no longer capable of producing a winning combination of the current token (unlikely but possible if the two players are strategic in what they choose to put back on the board), all tiles kept by the players (excluding the prime # tokens) are added up as positive numbers and the higher number wins. If that is a tie (unlikely but conceivably possible), then the players duel with pistols or flamethrowers... preferably flamethrowers (although those wouldn't be included with the game, naturally).

Anyway, that was my thought concerning the game. Enjoy.

Thank you for your suggestions.
I do not recognize my game through your proposals.
A lot of people do not even know what + and - 13 or prime numbers mean.
I'm trying to have some feedback to the new added rules.
So maybe I will abandon for a while the game or rethink it.

Steve
Offline
Joined: 07/29/2008
Revision - Two Or More

Well, I decided to add another wrinkle into my revision game, Two or More (tentative title).

Originally, I thought that the added difficulty of the leader would offset the amount that the challenger was behind. In other words, if the leader had 4 tokens and was working on the 5th, the leader would need a 6 tile combination to reach the next prime number selected while the challenger would need less (Ex. Player "A" has 4 tokens already & Player "B" has 2. Player B only needs a 4-tile combination to reach the current prime token [working on a 3rd token] selected while Player A would need a 6-tile combination [working on a 5th]).

I still want to keep that but I decided that I wanted to add an extra little challenge so that someone couldn't "run away" with the game and also add an additional strategic element to the game.

All throughout the game, the number zero (0) is present. When a player takes tiles off of the board to keep after finding the combination to a prime number first, they have a chance to combine their tile total, in relation to how many prime numbers they've captured, to zero. If they can, they win automatically regardless of how many prime numbers the other player already has.

Ex. Player "A" has 5 prime number tokens already. As a result, that player has 15 tiles from the board (-18 to +18). If player "A" can match any 5 of their tiles together to equal 0, that player wins automatically. If player "B" only has 2 prime number tokens, that player would only need 2 tiles from the board to equal 0 to win automatically.

Anyway, I thought it'd be a nice wrinkle to introduce to the game so that the "opponent gets to decide what gets put back onto the board and what doesn't" has a little more strategic meaning as well as giving someone who is trailing a bit more hope of winning the game.

Any thoughts about this are welcome.

ichbin
Offline
Joined: 09/21/2010
I have suggestion...

Steve wrote:
Well, I decided to add another wrinkle into my revision game, Two or More (tentative title).

Originally, I thought that the added difficulty of the leader would offset the amount that the challenger was behind. In other words, if the leader had 4 tokens and was working on the 5th, the leader would need a 6 tile combination to reach the next prime number selected while the challenger would need less (Ex. Player "A" has 4 tokens already & Player "B" has 2. Player B only needs a 4-tile combination to reach the current prime token [working on a 3rd token] selected while Player A would need a 6-tile combination [working on a 5th]).

I still want to keep that but I decided that I wanted to add an extra little challenge so that someone couldn't "run away" with the game and also add an additional strategic element to the game.

All throughout the game, the number zero (0) is present. When a player takes tiles off of the board to keep after finding the combination to a prime number first, they have a chance to combine their tile total, in relation to how many prime numbers they've captured, to zero. If they can, they win automatically regardless of how many prime numbers the other player already has.

Ex. Player "A" has 5 prime number tokens already. As a result, that player has 15 tiles from the board (-18 to +18). If player "A" can match any 5 of their tiles together to equal 0, that player wins automatically. If player "B" only has 2 prime number tokens, that player would only need 2 tiles from the board to equal 0 to win automatically.

Anyway, I thought it'd be a nice wrinkle to introduce to the game so that the "opponent gets to decide what gets put back onto the board and what doesn't" has a little more strategic meaning as well as giving someone who is trailing a bit more hope of winning the game.

Any thoughts about this are welcome.

Mister Steve,

Why not creating a new post with your new game "Two or more"?
Do you know why?
Because your game have nothing to do with my game "Sumof2".
I tried to understand your proposals but it seems to me that you are talking about another game.
Feel free to develop your vision of your game.
I have no problem with that.

rcjames14
rcjames14's picture
Offline
Joined: 09/17/2010
Cognitive Limits

When ichbin first posted the design, I was quick to suggest an alternative way of summing up numbers along a line in a board because I thought that it would add an additional strategic element to the game. In theory, it would give the position of numbers greater importance and allow players to hide their play options.

What I had in mind was a design that combined Sumof2 with Scrabble - the board is initially seeded with numbers, players have a secret hand of numbers and then they take turns claiming numbers in a row which can be replaced by an equal number of numbers in their hand with an equal total value. So, imagine, you have a 3, 4 and 5 in your hand and you use it to replace a 1, 2 and 9 along a vertical line on the board. You collect the 1, 2 and 9 and then you place the 3, 4 and 5 back in their place arranged however you want. Then, the other player goes. The game ends when all tiles are pulled and both players pass (because they cannot make a score). At that point, the player with the most tokens wins.

Theoretically, it is very intriguing because you can compete for larger lines of numbers and use the placement of objects to set up your next turn or foil your opponent.

But, I stopped making the design when I realized that it is hard for people to add two numbers together, let alone 5 numbers. In general, people don't store numbers in their head very well as they perform operations on them. Granted, some people have no problem seeing how to add 5, 3, 8, 7, 2. But, a lot of people do. And, imagine if you had to do that with every possible combination of tokens in your hand and tokens on the board. Talk about paralysis analysis!

It is a classic case of a game which can be completely sound and strategic, but not fun because it doesn't accommodate the cognitive limits and mental pleasantries of the people playing it. A computer would love it, but an (above) average human?

ichbin
Offline
Joined: 09/21/2010
Every game has a story....

Every game has a told or untold story.
I was trying to create a mathematic puzzle.
I solved the problem.
While doing it the idea of game came to my mind.
Because of that I used numbers in Sumof2 game but I can still remove the calculation step by replacing it by symbol recognition.
That's what I'm going to do.
It is going to take me some time to do it.

ichbin
Offline
Joined: 09/21/2010
Why?

Why is this game not funny?
I just want to know why?
Is chess game or go game funny?
Meanwhile a lot of people like to play go and chess.

irdesigns510
irdesigns510's picture
Offline
Joined: 06/24/2009
i agree with "exclusivity"

rcjames14 wrote:

...so you are actually competing to rid your area of the highest numbers. At that point, it becomes clear that there is going to be a lot more strategy to the game... because the position of objects matters.

But, I think the game really comes alive when you realize the competing interests between keeping high numbers in your camp and moving them to the other person. Ending up with high numbers is really bad. But, since they are more likely to be removed (as the total of the sum), the spot in which they exist will likely be worth 0 at the end. Very nice.

...it may be clear at the beginning who will win (with a deep enough search, or the immediate elimination of key number like 3,4, etc..) That may not make the game fun.

I think players generally like the idea of having control over certain pieces... which they can deploy or hold back for just the right moment. This type of exclusive control usually adds a key element of strategy to what is usually otherwise just a puzzle. Imagine if you could move either white or black in chess! The game would never end...

...But, I do think that players will feel largely unsatisfied by the fact that there is nothing that they have exclusive control over. There's no reason not to make a move now for a later advantage. So, it will probably instead highlight player mistakes... something that can be frustrating.

i like this game alot, ive played it a couple of times with friends, its pretty easy to follow.

one thing we modified to include exclusivity of pieces was to include +1 chips (we used pennies). each player had 3 of them to use during the entire game, and they are discarded after use. They couldn't be stacked on the same piece. You play them at the beginning of your turn, before you "sum", and they stay there until the beginning of your next turn. They also do not count toward your endgame score.

ichbin
Offline
Joined: 09/21/2010
Thank you

irdesigns510 wrote:
rcjames14 wrote:

...so you are actually competing to rid your area of the highest numbers. At that point, it becomes clear that there is going to be a lot more strategy to the game... because the position of objects matters.

But, I think the game really comes alive when you realize the competing interests between keeping high numbers in your camp and moving them to the other person. Ending up with high numbers is really bad. But, since they are more likely to be removed (as the total of the sum), the spot in which they exist will likely be worth 0 at the end. Very nice.

...it may be clear at the beginning who will win (with a deep enough search, or the immediate elimination of key number like 3,4, etc..) That may not make the game fun.

I think players generally like the idea of having control over certain pieces... which they can deploy or hold back for just the right moment. This type of exclusive control usually adds a key element of strategy to what is usually otherwise just a puzzle. Imagine if you could move either white or black in chess! The game would never end...

...But, I do think that players will feel largely unsatisfied by the fact that there is nothing that they have exclusive control over. There's no reason not to make a move now for a later advantage. So, it will probably instead highlight player mistakes... something that can be frustrating.

i like this game alot, ive played it a couple of times with friends, its pretty easy to follow.

one thing we modified to include exclusivity of pieces was to include +1 chips (we used pennies). each player had 3 of them to use during the entire game, and they are discarded after use. They couldn't be stacked on the same piece. You play them at the beginning of your turn, before you "sum", and they stay there until the beginning of your next turn. They also do not count toward your endgame score.

Thank you for the feedback.

Syndicate content


forum | by Dr. Radut