Why does my NN not classify these tic tac toe pattern correctly? [closed]

Question

I'm trying to teach an AI different pattern of tic tac toe to recognize wether a given pattern represents a win or not.

Unfortunately it's not learning to recognize them correctly and I think may way of representing/encoding the game into vectors is wrong.

I choose a way that is easy for an human (me, in particular!) to make sense of:

training_data = np.array([[0,0,0,
                           0,0,0,
                           0,0,0],
                          [0,0,1,
                           0,1,0,
                           0,0,1],
                          [0,0,1,
                           0,1,0,
                           1,0,0],
                          [0,1,0,
                           0,1,0,
                           0,1,0]], "float32")
target_data = np.array([[0],[0],[1],[1]], "float32")

This basically just use an array of length 9 to represent a 3 x 3 board. The first three items represent the first row, the next three the second row and so on. The line breaks should make it obvious I guess.

The target data then maps the first two game states to "no wins" and the last two game states to "wins".

Then I wanted to create some validation data that is slightly different to see if it generalizes.

validation_data = np.array([[0,0,0,
                             0,0,0,
                             0,0,0],
                            [1,0,0,
                             0,1,0,
                             1,0,0],
                            [1,0,0,
                             0,1,0,
                             0,0,1],
                            [0,0,1,
                             0,0,1,
                             0,0,1]], "float32")

Obviously, again the last two game states should be "wins" whereas the first two should not.

I tried to play with the number of neurons and learning rate but no matter what I try, my output looks pretty of. E.g.

[[ 0.01207292]
 [ 0.98913926]
 [ 0.00925775]
 [ 0.00577191]]

I tend to think it's the way how I represent the game state that may be wrong but actually I have no idea :D

Can anyone help me out here?

This is the entire code that I use

import numpy as np
from keras.models import Sequential
from keras.layers.core import Activation, Dense
from keras.optimizers import SGD

training_data = np.array([[0,0,0,
                           0,0,0,
                           0,0,0],
                          [0,0,1,
                           0,1,0,
                           0,0,1],
                          [0,0,1,
                           0,1,0,
                           1,0,0],
                          [0,1,0,
                           0,1,0,
                           0,1,0]], "float32")

target_data = np.array([[0],[0],[1],[1]], "float32")

validation_data = np.array([[0,0,0,
                             0,0,0,
                             0,0,0],
                            [1,0,0,
                             0,1,0,
                             1,0,0],
                            [1,0,0,
                             0,1,0,
                             0,0,1],
                            [0,0,1,
                             0,0,1,
                             0,0,1]], "float32")

model = Sequential()
model.add(Dense(2, input_dim=9, activation='sigmoid'))
model.add(Dense(1, activation='sigmoid'))

sgd = SGD(lr=0.1, decay=1e-6, momentum=0.9, nesterov=True)
model.compile(loss='mean_squared_error', optimizer=sgd)

history = model.fit(training_data, target_data, nb_epoch=10000, batch_size=4, verbose=0)

print(model.predict(validation_data))