# A Fun Strategy Game.



## MichaelP. (Dec 24, 2009)

Ok, this is a great two player game to play at a restaurant, using the sugar packets they have on the table. You can use just about anything small and movable though if you have enough. So the game works like this, you set up 16 sugar packets organized in a triangle, in rows of 7, 5, 3, and 1. So it would look like this 

O = sugar packet / pieces. 

O

O O O

O O O O O

O O O O O O O

So heres how the game works. The player who goes first takes any number of pieces from any *row*. In the game you would actually take them off the table or move them to the side, but for the simplicity of this guides sake, I'll make them be dashes. So the first move could look like this...

O O -

O O - or O O O or O O O

O O O O O O O O O O O O O O O

O O O O O O O - - - - - - - O O O O O O O 


or tons of other ways. The next person then does the same thing with the packets that are left. So after two moves a position *could* be 

O

O O O

O O O - - 

- - - - O O O

And the game continues back and forth until the player who is left with the last packet loses. So an end position could be 

-

- - -

- - - - O

- - - - - - -
The person whose turn it is in this position loses because they are left with the last packet.

Things you *can't* do are 

- Take a packet from the middle of a row (And then consider the remainder of that row to be two separate rows).

- Take from more then one row at once. 

- Take multiple pieces from a *column*.

- Pass your turn.

Things you *can* do are

- Only take one packet. 

- Take an entire row.

- Take from which ever row you choose. 

- Use strategy. 

Later on I'll post some of the key strategic points to look for in a game. 
So... who wants to play? I'll go first.


O

O O O

O O O O O

- O O O O O O


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## Cyrus C. (Dec 24, 2009)

I've heard this game a lot. Some names for it are "3-5-7", "Nim", & a variation "min".

It's a fun game to play during class.


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> O
> 
> O O O
> 
> ...




*-*

O O O

O O O O O

- O O O O O O


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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> > O
> ...





*-*

O O O

* -* O O O O

- O O O O O O


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> Lucas Garron said:
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-

*-* O O

- O O O O

- O O O O O O


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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 -

*-* O O

- O O O O

*- - * O O O O O


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> Lucas Garron said:
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-

- O O

- *-* O O O

- - O O O O O


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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-

- O O

- *-* O O O

* - - - - - -* O


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> Lucas Garron said:
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-

- O O

- - *-* O O

- - - - - - O


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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-

- O O

- - - O O

- - - - - - *-*


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> Lucas Garron said:
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-

- O O

- - - - O

- - - - - - -


Alright, now the real question: Did you learn something, or were you just stumbling around?


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## nitrocan (Dec 24, 2009)

Now, the next move gets a Nobel Prize.

Actually this game is rigged.


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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O. you lose. 

Me? I've almost perfected my skills at this game. You could have beat me earlier on on YOUR 3rd move by doing this 

-

- *-* O

- O O O O

- - O O O O O

No matter what I do from this position, if you play it right, I lose. I'm going to post spoiler with all the things to look for in the game.



Spoiler



Ok, I'm going to use notation that looks like this 1352. This means their are 1 packets in the first row, 3 in the second 5 in the third and 2 in the last. When one row is gone you don't put any number in that row, so at the end of the game the final notation is "1". Remember it doesn't matter how the numbers are arranged because that doesn't affect the outcome of the game. So at the very beginning of the game the setup is 1357, but it could also be 7315. 

Their are certain situations you want to set up so that no matter what they lose. The common ones to look for are 123, which is the position I set up on the seventh move of the game to beat Lucas. Their is also 22 which can be a result of 123 (See our game) also XX, meaning if their are only two rows left and they have the same number in each. This will eventually become 22 if you mimic the other persons moves on the other row. Also 11XX. and 111. I'll post more if I think of anymore.


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> No matter what I do from this position, if you play it right, I lose. I'm going to post spoiler with all the things to look for in the game.


Or you could just look up "misére nim." 

I was just wondering if you'd have been able to win against any "mistake."


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## MichaelP. (Dec 24, 2009)

Ya, I think so, is this games name "misére nim"?

I mean, you made a mistake, and I beat you because of it.


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## Lucas Garron (Dec 24, 2009)

MichaelP. said:


> I mean, you made a mistake, and I beat you because of it.


Yes. Small sample, though.

O

O O O

O O O O

O O O O O

O O O O O O

What's the winning move? No resources.


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## MichaelP. (Dec 24, 2009)

Lucas Garron said:


> MichaelP. said:
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> > I mean, you made a mistake, and I beat you because of it.
> ...



I wouldn't even know how to get resources. lol. Ummm... I'd clear the entire 4 pile.

O

O O O



O O O O O

O O O O O O


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## Lucas Garron (Dec 25, 2009)

MichaelP. said:


> I wouldn't even know how to get resources. lol. Ummm... I'd clear the entire 4 pile.


Nope.

(Response to your move would be to clear the 1 pile.)


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## MichaelP. (Dec 25, 2009)

Lucas Garron said:


> MichaelP. said:
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> > I wouldn't even know how to get resources. lol. Ummm... I'd clear the entire 4 pile.
> ...



I'd take one of the 3 pile.

O O

O O O O O

O O O O O O


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## vrumanuk (Dec 25, 2009)

MichaelP. said:


> Lucas Garron said:
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I looked into Nim a while ago, just for fun. If I remember correctly, removing the five pile would result in a nim-sum of zero.
O

O O O

O O O O



O O O O O O


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## MichaelP. (Dec 25, 2009)

vrumanuk said:


> MichaelP. said:
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I don't understand what nim is. Is it the same game with a different setup? What does a nim of zero mean?


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## Lucas Garron (Dec 25, 2009)

vrumanuk said:


> I looked into Nim a while ago, just for fun. If I remember correctly, removing the five pile would result in a nim-sum of zero.
> O
> 
> O O O
> ...


Is your strategy for when you're trying to take the last piece, or when you are trying to make your opponent take it? 

(First post describes the latter.)


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## MichaelP. (Dec 25, 2009)

They way I learned you try and make your opponent take it.


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## vrumanuk (Dec 25, 2009)

Lucas Garron said:


> vrumanuk said:
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> > I looked into Nim a while ago, just for fun. If I remember correctly, removing the five pile would result in a nim-sum of zero.
> ...



I believe, again it has been a while, that this should work for both normal and misere games. The only adjustment needed when moving from normal to misere play is to make sure to leave an odd number of heaps of size 1 (whereas in normal play you would leave an even number).


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## Johannes91 (Dec 25, 2009)

MichaelP. said:


> Me? I've almost perfected my skills at this game.





MichaelP. said:


> I don't understand what nim is. Is it the same game with a different setup? What does a nim of zero mean?


LOL

Wikipedia has a decent explanation of nim-sum and other things: http://en.wikipedia.org/wiki/Nim#Mathematical_theory. If you're really interested in this kind of games, read Winning Ways. A++++ recommended.

Here's an interesting variation: At the beginning of the game, the heaps are arranged in increasing order of size and every move has to preserve this. For example, the valid moves from 1 1 3 5 are to 1 3 5, 1 1 2 5, 1 1 1 5, 1 1 3 4, and 1 1 3 3.

Exercise: solve this game. I didn't see how to do it and was told the solution, but it's really cool. Don't look below if you want to figure it out by yourself.



Spoiler



Pair the heaps. If there are an odd number of them, add a zero to the beginning.

1 3 5 -> (0,1) (3,5)

The nim value of each pair (a,b) is (b-a). This is because that's the number of stones you can take from b, and all moves that take from a are _reversible_: if a player moves from (a,b) to (a-k,b), he's opponent can reverse this by moving to (a-k,b-k), which restores that pair back to its previous nim value.

If you know Poker-Nim (pages 53-54 in WW), this should make sense.


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## Filipe Teixeira (Feb 15, 2019)

this is cool


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