# Obtain fixation probabilitiesΒΆ

Using the implemented Moran process <how-to-use-moran_process> the fixation
probabilities can be approximated using a method on the `Game`

class:

```
>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[3, 1], [1, 2]])
>>> game = nash.Game(A)
```

The `fixation`

method returns a dictionary mapping the final states to the probabilities:

```
>>> np.random.seed(0)
>>> probabilities = game.fixation_probabilities(initial_population=(0, 1, 1, 1), repetitions=200)
>>> probabilities
{(1, 1, 1, 1): 0.765, (0, 0, 0, 0): 0.235}
```

This above shows that approximately (estimated over 200 iterations) 23.5 % of the time the first strategy will take over a population with a total of 4 individuals (when the initial population begins with 3 individuals of the other type).