Blackjack is the rare casino game where the math is fully solvable: for any rule set there is one optimal decision for every hand. This tool derives that decision from a real dealer-outcome model and shows the house edge the rules create, so you can see exactly why basic strategy says what it says.
How the calculator works
The engine plays out the dealer's hand from the visible upcard, dealing cards under an infinite-deck model until the dealer reaches 17 or busts. That produces the probability of every dealer final total. Your stand, hit, and double expected values are then scored against that distribution, and the action with the highest EV is recommended. Because the recommendation is computed rather than looked up, the strategy chart and the calculator can never disagree.
What the rules do to the edge
Rules move the house edge by known amounts. A dealer who hits soft 17 adds about 0.22%, removing double after split adds about 0.14%, and surrender or fewer decks give the edge back to the player. The House Edge Analysis tab breaks the total down rule by rule so you can compare a friendly single-deck game against an eight-deck shoe at a glance.
Limits and edge cases
The player input is treated as a hard total, so soft hands and pairs are shown as separate guidance rather than driving the headline play. The split estimate ignores resplits and card removal, and the house-edge figures assume perfect basic strategy with 3:2 blackjacks. Card counting, side bets, and 6:5 payouts are out of scope. Use the result as the mathematically correct baseline, not a guarantee for any single hand.