Probability, Statistics, Blackjack, Optimization, Math.
equation for the optimal α is Plot of the curves 1−(1−α)e^α and (1−α)−e^α(α−2)−e. This is a non-linear equation without a closed form, but it can be solved approximately using numerical methods, and the solution is α∗≈0.5706. This means that when the accumulated value of our stack gets bigger than