Blackjack Strategist
Select your cards and the dealer's up-card. The engine calculates optimal basic strategy and expected value for every possible action.
Explore blackjack basic strategy, expected value, and card-counting logic through a mathematical lens. This tool is educational, it illustrates decision theory and long-run expectation, not gambling advice.
Multi-deck, standard casino rules.
Select the dealer's up card and at least 2 player cards to compute optimal strategy and expected value.
This engine calculates Expected Value (EV) for every action: the average profit/loss per unit bet over many hands.
A positive EV means the action is favourable. The engine uses full basic strategy adjusted for the rules you set above.
Changing deck count, soft 17, and double after split all affect the EV calculations. Try toggling them to see the difference.
Frequently Asked Questions
What is basic strategy in blackjack? ▾
Basic strategy is the mathematically optimal way to play every possible hand combination in blackjack. It is derived by calculating the expected value of every action (hit, stand, double, split) for every player hand against every dealer upcard. Following basic strategy reduces the house edge to approximately 0.5%.
What is Hi-Lo card counting? ▾
Hi-Lo is the most widely used card counting system. Cards 2–6 are counted as +1 (good for the player when removed), cards 7–9 are 0, and cards 10–Ace are -1. A high positive count means more high cards remain in the shoe, which favours the player. This is the system the MIT Blackjack Team used.
How does deck count affect the house edge? ▾
Fewer decks give a slightly lower house edge. A single-deck game with good rules has a house edge of around 0.17%, while an 8-deck shoe game with identical rules sits around 0.65%. Card counting is also more effective with fewer decks.
Should I always follow basic strategy? ▾
Basic strategy is the optimal play assuming no knowledge of the remaining cards. Card counters deviate from basic strategy when the count suggests the composition of the remaining deck makes a different action more profitable, these are called "indices" or "illustrious 18" deviations.