An Analytic Derivation of Blackjack Win Rates

We study the win rate for the game of blackjack and derive a stochastic model for the advantage (i.e., expected win) process. Assuming proportional betting, we derive an explicit formula that estimates the win rate as a function of the number of decks used and the proportion of cards dealt before reshuffling. We derive a relationship between the “aggressiveness” of betting and risk. Risk is measured as the probability of wealth dropping below a specified level before it exceeds a higher, specified level.