prompter: I need to know if there is a python package that lets me easily calculate the expected value of a game. I will be needing to use a large number of dice rolls. I know I will need at least 32 dice rolls, but probably a lot more.

assistant: For calculating the expected value of a game that involves a large number of dice rolls, you may want to consider using the NumPy package in Python. NumPy is a numerical computing library that provides support for large arrays and matrices of numeric data.

With NumPy, you can easily generate arrays of random numbers that represent the outcomes of dice rolls. You can then use these arrays to calculate the expected value of the game.

For example, if you have a game where you roll a six-sided die and receive a certain reward for each outcome, you can use NumPy to simulate a large number of dice rolls and calculate the average reward. Here's a code snippet that demonstrates this:
```python
import numpy as np

# Define the reward for each outcome
rewards = np.array([2, 3, 4, 5, 6, 7])

# Simulate 32 dice rolls
dice_rolls = np.random.randint(1, 7, size=(32,))

# Calculate the expected value
expected_value = np.mean(rewards[dice_rolls - 1])
```

Note that in this example, the dice_rolls array is generated using the `np.random.randint` function, which generates random integers within a specified range. The rewards array is indexed using the dice_rolls array, so that each reward is selected based on the outcome of the corresponding dice roll. The expected value is then calculated as the mean of all rewards.

With NumPy, you can easily scale up this example to handle a large number of dice rolls and more complex games. It is a powerful tool for performing numerical computations in Python.

prompter: Are there any other NumPy functions would help in comparing the actual outcomes to the expected outcomes?

assistant: Could you perhaps clarify what you mean by actual vs expected outcomes?
With "actual outcome", do you mean the theoretical average for an infinite sample size?

assistant: Yes, there are several NumPy functions that can be used to compare actual outcomes to expected outcomes:

    numpy.mean(): calculates the arithmetic mean of a given array
    numpy.median(): calculates the median of a given array
    numpy.corrcoef(): calculates the Pearson product-moment correlation coefficients of a given array
    numpy.cov(): calculates the covariance matrix of a given array
    numpy.histogram(): calculates the histogram of a given array and returns the binned values and bin edges
    numpy.percentile(): calculates a specified percentile of a given array
    numpy.std(): calculates the standard deviation of a given array

These functions can be used to analyze the distribution of the actual outcomes and compare them to the expected outcomes.

prompter: Can you give a short example of each function?

assistant: What are you trying to calculate the expected value of? If you're looking for general statistics methods, you could check out the `statistics` package. Otherwise, you'll probably be best off either doing the math by hand or running a Monte Carlo simulation.

prompter: I'm trying to calculate the expected value of some dice rolls. It's a D&D like game and I want to see on average how much damage I'll do.

assistant: The Python package Sympy.stats has a function `Die` for the operation you want. You can also use Numpy to write the expected value calculation yourself.

assistant: Can you describe in more detail the expected outcome of the "value" in said game so I can find the correct Python package for your use case.

prompter: The value is going to be the number of combinations of dice rolls that have appeared so far.

assistant: The problem you want to solve using a python package seems like an instance of the Monte Carlo Method (https://en.wikipedia.org/wiki/Monte_Carlo_method). Try using this term for searching. Your requirement on the number of dice rolls won't rule out any packages you might find (if you were concerned about the amount the computation required), so you can probably leave that out in your search terms. Having said that, if you think this requirement is critical, it could help your search to quantify what you mean by a "large" number of dice rolls.