# #4 Great ensemble

My final submission is an ensemble of seven models:
Linear regression with polynomial features of degree 4
Ridge regression with a Nystroem kernel approximation
KernelRidge with a polynomial kernel of degree 5
KernelRidge with a kernel composed of a polynomial kernel and an RBF kernel
Ridge regression with feature engineering based on permutation probabilities
CatBoost with feature engineering based on card counting and bust probabilities
LightGBM with feature engineering based on card counting and bust probabilities
Feature engineering for the tree models was inspired by the Wikipedia article on
[card counting](https://en.wikipedia.org/wiki/Card_counting)
.
![model comparison](assets/14dbb40c7f2ea368f78dad08.png)
I thank
[@andreipaulavets](https://www.kaggle.com/andreipaulavets)
for organizing the competition,
[@ravi20076](https://www.kaggle.com/ravi20076)
for drawing my attention to it, and
[@masayakawamata](https://www.kaggle.com/masayakawamata)
for his discussion contributions.
[Source code is here](https://www.kaggle.com/code/ambrosm/blackjack-great-ensemble)
.