<p>A partial answer: since Damath is a two-player game of complete information and no randomness, <a href="https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)" rel="nofollow noreferrer">Zermelo's Theorem</a> says that one of the following is true:</p>

<ul>
<li>There is a dominant strategy for 1st player. </li>
<li>There is a dominant strategy for 2nd player. </li>
<li>There are strategies for both players that guarantee they don't lose, i.e. perfect play results in a draw (like Tic-Tac-Toe).</li>
</ul>

<p>As far as I can tell, no one has yet determined which of these three is true. Checkers (aka Draughts or Dama, the game Damath is based on) was <a href="https://en.wikipedia.org/wiki/Chinook_(draughts_player)" rel="nofollow noreferrer">'solved' in 2007</a> with the aid of computers: two perfect players will always draw. Thus I would assume that modern computers are powerful enough to 'solve' Damath as well, but I don't know what the result would be. </p>

CC BY-SA 4.0
2019-11-22T21:51:32.150Z
2019-11-22T21:51:32.150Z
Benjamin Cosman
<p>I would say to try and capture high scoring pieces on addition and multiplication squares and capture negative pieces on minus and division squares. If you are to loose a piece if it had a positive score try to make the operand division or subtraction and if you are to loose a negative piece make the operand multiplication or addition.
This would maximize your score and minimize your opponents score.</p>

CC BY-SA 4.0
2019-11-22T21:39:44.620Z
2019-11-22T21:39:44.620Z
Jokus
<p><img src="https://i.sstatic.net/6DkX3.png" alt="empty board"></p>

<p><img src="https://i.sstatic.net/YROgH.png" alt="board with chips"></p>

<p>As you can see, this is an example of a DaMath board with Integers.</p>

<p>See this <a href="https://en.wikipedia.org/wiki/Damath" rel="nofollow noreferrer">Wikipedia article about DaMath with its rules</a>.</p>

<p>Is there any optimal way to win if you are the first or second player? Like a set of moves or strategies to keep in mind of when playing this game? Or an opening trap to score high and make your opponent get negative points?</p>

<damath>
Optimal way to win at Damath
X X
# Optimal way to win at Damath

(Asked by: username_0 on 2019-11-11)

![empty board](https://i.sstatic.net/6DkX3.png)

![board with chips](https://i.sstatic.net/YROgH.png)

As you can see, this is an example of a DaMath board with Integers.

See this [Wikipedia article about DaMath with its rules](https://en.wikipedia.org/wiki/Damath).

Is there any optimal way to win if you are the first or second player? Like a set of moves or strategies to keep in mind of when playing this game? Or an opening trap to score high and make your opponent get negative points?

**Tags:** damath


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## 2 answers

### Answer by username_1 on 2019-11-22. Score: 4 | Accepted answer

A partial answer: since Damath is a two-player game of complete information and no randomness, [Zermelo's Theorem](https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)) says that one of the following is true:

* There is a dominant strategy for 1st player.
* There is a dominant strategy for 2nd player.
* There are strategies for both players that guarantee they don't lose, i.e. perfect play results in a draw (like Tic-Tac-Toe).

As far as I can tell, no one has yet determined which of these three is true. Checkers (aka Draughts or Dama, the game Damath is based on) was ['solved' in 2007](https://en.wikipedia.org/wiki/Chinook_(draughts_player)) with the aid of computers: two perfect players will always draw. Thus I would assume that modern computers are powerful enough to 'solve' Damath as well, but I don't know what the result would be.


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### Answer by username_2 on 2019-11-22. Score: 1

I would say to try and capture high scoring pieces on addition and multiplication squares and capture negative pieces on minus and division squares. If you are to loose a piece if it had a positive score try to make the operand division or subtraction and if you are to loose a negative piece make the operand multiplication or addition.
This would maximize your score and minimize your opponents score.


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