Blackjack strategy: the complete basic strategy chart and the maths behind it

Unlike every roulette system, blackjack strategy is not a belief. It is the output of a full calculation of every possible hand against every possible dealer card, and it has been verified by computer simulation billions of times over. This guide from the blackjack academy gives the complete chart for the most common online rule set, explains the logic behind its lines, quantifies what it saves, then covers insurance, card counting and the side bets that undo all of it.

Basic strategy chart: hard totals

A hard total has no ace counted as 11. Key: H = hit, S = stand, D = double (hit if not allowed), Rs = surrender if offered, otherwise stand, Rh = surrender if offered, otherwise hit.

Basic strategy chart: soft totals

A soft total counts an ace as 11. Because it cannot bust on one card, you double far more often. Ds = double if allowed, otherwise stand.

Basic strategy chart: pairs

P = split. Where the chart says not to split, play the hand as its hard total (5,5 = hard 10; 10,10 = hard 20). The 2,2 / 3,3 / 4,4 / 6,6 splits against small cards depend on DAS being allowed; without DAS, hit 4,4 always, hit 2,2 and 3,3 against a 2 and 3, and hit 6,6 against a 2.

Adjustments for other rule sets

• Dealer hits soft 17 (H17): double 11 against an ace; double A,8 (soft 19) against a 6; double A,7 against a 2; surrender 15 and 17 against an ace (17 only if surrender is allowed — otherwise stand). Everything else is unchanged.
• European no-hole-card (ENHC): the dealer may still have blackjack after you have doubled or split and you lose the extra bets. Do not double 11 against a 10; do not split A,A or 8,8 against an ace; do not split 8,8 against a 10. Play those as hit.
• No DAS: see the pairs note above. Double only on 10–11: hit the hands shown as D on 9 and all soft totals.
• Single and double deck: a few more doubles and splits become correct (for example double 9 against 2 and 11 against an ace in single deck). Use a deck-specific chart; the multi-deck chart costs only about 0.03% extra if you use it there.

Why basic strategy works

Every line in the chart is the answer to the same question: for this hand against this up-card, which action has the highest expected value? The logic falls into a handful of patterns that make the chart far easier to remember than 300 individual cells.

What it costs to ignore

The typical self-taught player sits somewhere around 2%, five times the cost of the same table played correctly. Ten minutes a day on the basic strategy trainer for a week closes that gap permanently. For any hand you are unsure about, the blackjack chance calculator shows the expected value of each option.

Insurance: the maths

Insurance is a side bet that the dealer's hole card is a ten-value card, offered when the up-card is an ace. It pays 2 to 1 and you may bet up to half your original stake. Whether it is a good bet depends on one number only: the share of ten-value cards left in the shoe.

Insurance would break even only if more than one card in three remaining were a ten (33.3%). A fresh shoe has 30.8%, and the cards you hold make it slightly worse. Only a card counter who knows the shoe is ten-rich (Hi-Lo true count of roughly +3 or higher) should ever take it. Even money on your own blackjack is mathematically identical: you are declining an expected 1.5 × 69.3% = 1.039 units to accept a guaranteed 1.0 unit, a 3.9% giveaway.

Card counting: how it works and why it barely works online

Basic strategy assumes a freshly shuffled shoe. Card counting tracks how the remaining shoe differs from that. A shoe rich in tens and aces favours the player — more blackjacks paid at 3:2, more successful doubles, more dealer busts from stiff hands — while a shoe rich in small cards favours the dealer. Counters bet more when the shoe is rich and the minimum when it is poor. It is legal everywhere, and casinos are free to refuse your action.

The Hi-Lo system

1. 1

   Keep the running count

   Start at 0 after the shuffle. Add or subtract the value of every card you see, including other players' and the dealer's. A full deck sums to zero (balanced count).

2. 2

   Convert to a true count

   Divide the running count by the number of decks still to be dealt. Running count +8 with four decks left is a true count of +2; the same +8 with one deck left is +8. The true count is what measures your edge.

3. 3

   Size your bet

   Each true-count point is worth about 0.5% to the player. Starting from −0.4% at a good table, you are roughly break-even at +1 and have about +0.5% at +2, +1% at +3. A typical spread bets 1 unit at true count ≤ 1, then 2, 4, 8 units at +2, +3, +4 and above (a 1–8 spread in 6 decks; 1–12 is common in 8).

4. 4

   Adjust a few plays

   The most valuable deviations (the "Illustrious 18") include taking insurance at +3, standing on 16 vs 10 at 0 or higher, standing on 15 vs 10 at +4, and doubling 10 vs 10 at +4. Everything else stays basic strategy.

Done well in a casino with 75%+ penetration and a 1–12 spread, Hi-Lo earns around 0.5–1% of the average bet over the long run — with a standard deviation per hand of more than one bet, which is why counters need bankrolls of 500–1,000 units to survive the swings.

Why counting fails online

With eight decks dealt to the halfway point, high true counts almost never arrive before the shuffle; the times you would bet big are cut away. Combined with a slow game and the same house right to close your account, live dealer counting is a hobby, not an edge. Anyone selling a course on "online card counting" is selling a course.

Side bets to avoid

Nearly every online table offers optional side bets. They are separate wagers, they do not change the main game's edge, and they are priced like slot machines. Exact figures depend on the paytable and the number of decks; the ranges below cover common versions.

A player betting €10 on the main hand at 0.4% and €5 on 21+3 at 5% has an expected loss of €0.04 on the game and €0.25 on the side bet. The side bet is six times the cost for half the stake. If you want a long-shot in the session, it is still cheaper than most, but do not confuse it with blackjack.

Bankroll for blackjack

Blackjack's edge is small and its variance is large. Standard deviation is about 1.15 bets per hand once doubles and splits are included, so over 100 hands at €10 your expected result is −€4 with a one-standard-deviation range of roughly ±€115. Losing streaks of eight or more hands happen about once every 300 hands. A session bankroll of 50 units and a stop-loss you actually obey are the minimum; the bankroll management guide covers unit sizing, session limits and how the maths changes when you add a bet spread.

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