linearly varying_binomial distribution calculations

pip install linearly-varying-binomial-distribution

This is a wrapper module for the previous repo: C PROGRAM

Description of the math

Imagine the cardpool of a ptw game looks like:

One can flip a card. there is a probability (here say 0.02) to have a prize at the beginning.

• If one does not have the prize for 50 attempts in a row, the constant (here say 0.02) will be added to the existing probability (so that the chance of having the prize is increasing) until one finally has the prize, at which point the chance will reset to the original one.

For example, one tried 52 times and there have been no successes. At this point their chance for success for the 53rd time will be 0.08. If the 53-rd try is a success, then the chance for the 54-th try will be reset to 0.02, otherwise the chance becomes 0.10. Also the maximum number of tries allowed here is calculated 99, where the chance is 1.

If he tries 60 times, we can calculate the chance of getting the prize with the following code:

from lvbdist import LVBdistribution
x = LVBdistribution(
    0.02, # the starting probability 
    0.02, # the constant to add
    50    # numbr of failures before triggering the addition
)
x.have_success_within_n_attempts(60) # 0.911490

How about the probability they just get the prize at the 60th turn

x.have_first_success_at_n(60) # 0.024964

We can calculate the average number of attempts they need to make to have the prize:

x.have_first_success_at_n_E() # 34.59455

We can also calculate the average successes in 60 attempts:

x.have_m_successes_within_n_attempts_E(60) # 1.443428

Function names are self-descriptive. Note that functions ending with _E are expectated values. There always exist a function without the _E suffix.

Refer to the lazily generated doc for all functions.

Building

Requirements: setuptools, and any modern C compiler shall work

Clone the repository:

git clone --recurse-submodules https://github.com/cleoold/linearly_varying_binomial_distribution_calcs_Python

You can install the package by running

make install

Developing

(Optional) set up a virtual env

python3 -m venv . # pyvenv .
source bin/activate

build the package in-place in the lvbdist folder by running

make debugging

And then build the distributable:

bin/pip3 install wheel
make release