Game Theory: Are you afraid to challenge the moose to a simple game?

[rickymooston]

Game Theory is a branch of mathematics that analyses optimal strategies for games like chess. One question we can ask of any game is, if everybody plays the best stretegy, whether they will win, lose or draw. A game is solved if we know the answer to this question. For example, tic tac toe is known to be a draw.

This game is deceptively simple. I game across a baby version on my iphone by acgident and got curious as to whether it is a "stupid game" like tick tack toe or a game like chess with rich strategy. The game is from Nepal but versions exist in India too. The game is asymmetric because the play is very different for both players.

The strategy is non-trivial. A paper in involving a significant search, only mansged to prove the tiger can always kill three goats.

The starting board looks like this.



The goat goes first. His job is not to get 5 of his 20 goats eaten.

Observe that the complicated looking board is draw by first making a 16 by 16 grid. Then by
Drawing in the diagonals. And lastly by making a square by joining the middle points of each of the edges on the grid.

How to play

Goat player goes first. He drops a goat on any vertex.

Tiger player can jump over any goat if there a straight line containing tiger, goat, empty vertex. For example, if the player moves on square 1, the tiger will jump over him to square 2.

Tiger player can move his tiger to any unoccupied connected empty square.

Tiger player wins if he eats 5 goats.

Goat player wins if the tiger player cannot move.

A cycle is a draw, if neither player breaks it. I guess this works by agreement.

You can play online in real time on this web site.

http://obaghchal.com/computer

I have not "figured out" all the basic strategy but for those curious, rsther thsn just wanting to try a simple new game, proceed to my next post.

[One Above All]

BM

[rickymooston]

Strategic considerations i was able to figure out.

Goat player.

You are forced to move to squares 2, 10, 14 or 22. That is, the middle of an edge. This is easy to see
After a few games!

If you do not do this, the tiger will have you for an early lunch.





One thing you can try to do in the early game is create a ”hole". The theoretical paper suggests this is imposdoble if the tiger plays right. If you get a hole, before dropping all your goats, i believe you will win.

Here is an example where i did this to the website computer. My next move was to drop a goat on vertex 17 both protecting the goat on 16 from being eaten and creating a hole on square 18!

The tiger player made a mistake in letting me do this, a bit early.



Other goat hints? Well, obviiusly, stealing a corner makes you safe. You can build chains of safety from there. Its hard to get in the middle without conne tions.

I will let you digest that while i go grab a snack. Then late, i can put in some tiger blurbs.

Note post 1 is enough for you to try the game yourself! i have been playing the game for about a week. I had to play a buman player, to get a feel for the tiger.

[rickymooston]

O,k. Now here is where you might fit in.

My start on the tiger strstegy is this.

Tigers have to be close enough together to work together but not to trip over each other. After having my ass kicked by a human tiger player, i was experimenting with his trapezoidal structure.



I show here where i, the goat am forced to move in front gannu's hungry tiger!!!



Now, i think, the goat player has to block off space whereas the tiger player has to cover player.

I am sure there are a lot of geometric patterns of interest here.

The tiger pieces in the diagram are forcing the goat player to drop on a hunger tiger!

In play, we can move the tigerd in such a way that the goat player is forced to get eaten.

The goat player can either block tigers in, using a minimum shape or block of spaces from the tigers. He does have to be csreful to have space to move as well.

I do not know how common draws are. I hsve yet to analyse the play of stronger playersvagainst each other.

[joebbowers]

'acgident' should totally be a word. It could mean when you almost have an accident but it's averted at the last second. Like dropping a glass but catching it before it hits the ground.

I had an acgident on the way to work today.
Well I'm glad you're ok!

[rickymooston]

I will grant you that Joe. It could also be used to express frustration with touch keypads on modern cellphones and tablets. A special word is required for bad corrections as well.

Do you have any thoughts on the game mentioned in the op? My first post describes the game quite well and i dont think its beyond your ability to understand. I even provided a link to a website where you can actual play against a computer.

I apologize, if my thoughts on strategy a bit long. Imagine, if i was facedcwith describing chess, lol.

[RNS]

I was never very good at games like chess. I'm far too impatient, I like to just.. go.
I've been playing this a bit last night and today and I'm finding it quite enjoyable. It's a cool concept, I like how the game is asymmetric (i.e. 4 vs 20 or vice verse). At the moment I'm finding it a lot easier to win with tigers than with goats. I will beat the computer every time with tigers, without really having to think/strategize at all.
With goats I'm still getting there. But I think I'll be able to beat the computer every time pretty soon. I don't know if that's testament to me or the predictability of the computer... probably the latter.

Thanks for sharing! I'll be sending you a challenge once I get the hang of it

[rickymooston]

I was never very good at games like chess. I'm far too impatient, I like to just.. go.
I've been playing this a bit last night and today and I'm finding it quite enjoyable. It's a cool concept, I like how the game is asymmetric (i.e. 4 vs 20 or vice verse). At the moment I'm finding it a lot easier to win with tigers than with goats. I will beat the computer every time with tigers, without really having to think/strategize at all.
With goats I'm still getting there. But I think I'll be able to beat the computer every time pretty soon. I don't know if that's testament to me or the predictability of the computer... probably the latter.

Cool! In my case, I went the other way. I sucked at tiger playing first. .

I also liked the fact one can get going rather quickly. The tactics in chess are fun but the set up, requires lot of learning.

[RNS]

haha what does this mean?


Winning pretty much every time with sheep now too. I'm just building a wall from the bottom and boxing them in. Think I'll sign up and move onto medium now.

[jaimehlers]

It's not a win unless you actually box the tigers in.  If you can't move because you run out of goats, it's a draw (I think)

[rickymooston]

haha what does this mean?

You have run out of goats to drop and thus, a goat move is to move an existing goat to an adjacent square.

It's not a win unless you actually box the tigers in.  If you can't move because you run out of goats, it's a draw (I think)

Nope, you then enter the second phase of the game. During this phase, the goat player is moving his goats around trying not to be eaten whereas the tiger player continues to move his tigers around trying to trap him.

The only way to have a draw, is to reach a state where both players are repeating the same moves in a cycle. The website does not seem to consider this, which is odd.

[RNS]

Thank you for the encouragement 

But look at the screen shot I posted another time. As you can see, it's my turn to move, but I don't have an available square to move into. So like jaime said, I would have thought it's a draw. I also would have thought the computer would know it's not possible for me to make another valid move and declare it a draw.

Btw, in case you were interested, I didn't drop them in like that. I had a few turns after dropping them all and then made a bad move.


EDIT: Is the site down for you as well?

[rickymooston]

You are right.

Their software does not have draws but this indeed looks like a bug.

Their site was down sunday morning which was sunday evenimg in nepal.

[jaimehlers]

I won (on beginner).  No goats lost.

Tigers were at 0, 3, 11, and 21.  Empty space at 15.  Last move was me putting a goat at 16 (thus blocking both tigers).

[rickymooston]

Apparently, kevin on igi tried as well.