Hi,

@Njord + all:

I found a site that actually works:

https://www.math.ucla.edu/~tom/gamesolve.htmlHere is what I get for the rock paper scissors game:

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The matrix is

0 -1 1

1 0 -1

-1 1 0

The value is 0.

An optimal strategy for Player I is:

(0.33333,0.33333,0.33333)

An optimal strategy for Player II is:

(0.33333,0.33333,0.33333)

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0 means a tie here, 1 that Player I wins and 2 that Player 2 wins. In the first row player 1 picks rock and in the first column player 2 picks rock etc. So the -1 in the first row comes from Player 1 picking rock and player 2 picking paper. As expected the optimal strategy is a 33% split.

@Glass + all:

Disclaimer: I am relatively new at this game, and clearly there are many who are better than I at it.You have to distinguish 2 phases here. The first phase is you gathering all possible moves + opponent answers and evaluating them properly. If you say that you are a poor player then your evaluation is way off the carts. However you still end up with an understanding about your winning chances when you make your move and your opponent answers accordingly. I'm not interested in your numbers here but only in the next step where you have to make a decision according to your evaluation:

With the matrix game solver I'd like to make another symmetric example called "Attack - Defend - Expand" with the following input:

- If both players make the same move, they end up both equal.

- If a player expands and the other attacks, the attacker immediately wins.

- If a player expands and the other defends, the expander increases his else equl chances of winning the game by 25%.

- If a player attacks and the other defends, the defender increases his else equal chances of winning the game by 50%.

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The matrix is

0 -0.5 1

0.5 0 -0.25

-1 0.25 0

The value is 0.

An optimal strategy for Player I is:

(0.14286,0.57143,0.28571)

An optimal strategy for Player II is:

(0.14286,0.57143,0.28571)

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So basically in this example you want to usually defend which doesn't come as a surprise. Also you want to expand double as often as attack.

@MrX:

But I don´t fully understand what you are doing or exact aim is? Neither I can understand what you mean by symmetric situation I have only posted my most abstract conclusion here. For the rest you have to read the link I posted. I have basically calculated that (at least for my simplified WarLight example), the attacker has to play differently than the defender.

Edited 11/9/2019 18:42:50