Blackjack Hand Calculator

Basic strategy is the mathematically optimal play for every possible hand combination against every dealer upcard. It is derived by computing the expected value of every action (hit, stand, double, split, surrender) using combinatorial analysis or Monte Carlo simulation. Following it perfectly reduces the house edge to approximately 0.5%, making blackjack one of the best games in the casino for the player.

Some hands have nearly identical EVs between two actions. For example, 16 vs 10 is famously close between hitting and standing. These "close calls" are where card counting deviations become valuable. The Illustrious 18 deviations identified by Don Schlesinger capture the most profitable spots where the true count changes the optimal play. A +1 true count can flip 16 vs 10 from hit to stand.

The infinite deck approximation used here assumes each card is drawn independently. In reality, removed cards change the remaining deck composition. A deck rich in 10s and Aces favors the player (more blackjacks, better doubles), while a deck rich in small cards favors the dealer (less likely to bust). This is the fundamental principle behind card counting and why single-deck games have different basic strategy than 8-deck shoes.

The biggest mistake players make is playing "hunches" instead of math. Never take insurance (it is a side bet with a 7.69% house edge; the dealer makes blackjack only 4 times in 13). Never stand on 16 vs 7 just because you are "scared to bust." The dealer is not "due" for a bust after winning several hands. Streaks have no memory. Each hand is mathematically independent, and the EV calculation does not care about your previous results or feelings.