How this blackjack calculator works
This tool computes the exact expected value (EV) of every possible action for your two cards against the dealer's up card, using exact probability math rather than simulation. Enter your cards and the dealer's up card, and it instantly shows which action has the highest expected value, along with the exact win, push and loss probability for each choice.
The math assumes an infinite shoe (a very close approximation of a 6-8 deck shoe), the dealer standing on all 17s including soft 17 (S17), blackjack paying 3:2, doubling after a split (DAS), and no re-splitting. This tool is for probability education, not gambling advice — see the notes below the strategy table.
What is the best move in blackjack for any hand?
The best move is whichever action has the highest expected value (EV) against the dealer's up card, found by comparing the exact win/push/loss odds of standing, hitting, doubling, splitting a pair, and surrendering. Example: a hard 11 against a dealer's 6 has a double EV of about +0.667 per unit bet, better than hitting (+0.334) or standing (-0.154).
How to find the optimal blackjack play
- Select the rank of your first card, then your second card (J, Q and K all count as 10).
- Select the dealer's face-up card.
- Read the recommended action — the one with the highest EV — highlighted at the top.
- Compare the full table of stand, hit, double, split and surrender for the exact win, push and loss odds of each option.
- Check the dealer's final-hand distribution to see how likely the dealer is to bust, make 17-21, or have blackjack.
How the expected value is calculated
EV(action) = P(win) x (+payout) + P(push) x 0 + P(lose) x (-bet) -- computed exactly with recursive probability, not simulation
- Stand = keep your current total and let the dealer play out their hand
- Hit = draw one card and decide again (every later decision also assumes optimal play)
- Double = draw exactly one more card, then stand, with your bet doubled
- Split = separate a pair into two hands of one unit bet each (an Ace pair gets exactly one extra card per hand, no further hits)
- Surrender = forfeit half your bet immediately and end the hand
Five example hands and their optimal play
| Hand | Dealer shows | Best action | EV per unit bet |
|---|
| Hard 16 (10,6) | 10 | Surrender | -0.539 |
| Hard 11 (5,6) | 6 | Double | +0.667 |
| Soft 18 (A,7) | 9 | Hit | -0.101 |
| Pair of 9s (9,9) | 7 | Stand | +0.400 |
| Pair of 8s (8,8) | 10 | Split | -0.529 |
Frequently asked questions
Why does the calculator recommend surrender for some hands?
Surrender forfeits exactly half your bet immediately, ending the hand. It becomes the best option whenever every other choice has a worse expected value than -0.5, which typically happens with weak two-card totals like 15 or 16 against a dealer's strong up card (9, 10 or Ace).
What rules does this calculator assume?
It assumes the dealer stands on all 17s including soft 17 (S17), blackjack pays 3:2, doubling after splitting is allowed (DAS), you cannot re-split a pair that pairs again, and an infinite shoe equivalent to a large multi-deck shoe. Casinos vary these rules, which shifts the exact numbers slightly.
Why is Ace-10 shown as an automatic win instead of an action table?
Two cards totaling 21 (an Ace plus a 10-value card) is a natural blackjack -- the hand ends immediately with a 3:2 payout, or a push if the dealer also has blackjack. There is no stand, hit or double decision to make.
Does this calculator account for the dealer peeking for blackjack?
Yes. When the dealer's up card is an Ace or a 10-value card, the calculator uses the probability-corrected dealer outcome distribution that accounts for the dealer checking for blackjack before you act, matching standard peek procedure.
Is basic strategy the same as counting cards?
No. Basic strategy, which this calculator computes, is a fixed set of mathematically optimal decisions based only on your hand and the dealer's up card; it never changes with previously dealt cards. Card counting tracks the remaining shoe composition, which this infinite-shoe calculator does not model.
This tool is for probability education only, not gambling advice or an inducement to gamble. Real casino results depend on the exact house rules in play (number of decks, dealer hitting soft 17, surrender availability, DAS), which can shift these exact numbers. Over the long run the mathematical expectation always favors the house -- no strategy, including perfect basic strategy, produces a positive expected value in standard blackjack.
Sources: Edward O. Thorp, Beat the Dealer (1962)