One point of difference, several changed answers
Three busts 37.4% of the time, two points more than a 2. That sounds like nothing and it moves real decisions: hands that must hit against a 2 can stand against a 3, and the margins involved are among the thinnest on the chart.
Everything below is computed for multi-deck, dealer stands on soft 17, double after split allowed, one split only, no surrender. Change those rules and some answers move; the rules are worth more than the strategy.
Every Hard Total Against a 3
Your total down the left. The gap column is what playing the runner-up instead costs you per unit staked — the number a strategy chart leaves out.
| Hard totals | Play | Runner-up | Gap |
|---|---|---|---|
| 5 | hit | stand | 0.1569 |
| 6 | hit | stand | 0.1450 |
| 7 | hit | stand | 0.1757 |
| 8 | hit | double | 0.1442 |
| 9 | double | hit | 0.0196 |
| 10 | double | hit | 0.2032 |
| 11 | double | hit | 0.2575 |
| 12 | hit | stand | 0.0186 |
| 13 | stand | hit | 0.0390 |
| 14 | stand | hit | 0.0965 |
| 15 | stand | hit | 0.1540 |
| 16 | stand | hit | 0.2115 |
| 17 | stand | hit | 0.4145 |
| 18 | stand | hit | 0.7683 |
| 19 | stand | hit | 1.1324 |
| 20 | stand | hit | 1.5052 |
Every Soft Total Against a 3
A soft hand holds an ace counted as eleven. It cannot bust on the next card, which is why the answers here look reckless next to the hard totals and are not.
| Soft totals | Play | Runner-up | Gap |
|---|---|---|---|
| A,2 | hit | double | 0.0814 |
| A,3 | hit | double | 0.0580 |
| A,4 | hit | double | 0.0364 |
| A,5 | hit | double | 0.0163 |
| A,6 | double | hit | 0.0261 |
| A,7 | double | stand | 0.0293 |
| A,8 | stand | double | 0.1085 |
| A,9 | stand | double | 0.2409 |
Every Pair Against a 3
Splitting doubles your money on the table. The full splitting reference covers all hundred pair decisions; these are the ten you face against this card.
| Pairs | Play | Runner-up | Gap |
|---|---|---|---|
| A,A | SPLIT | hit | 0.4143 |
| 10,10 | stand | SPLIT | 0.2381 |
| 9,9 | SPLIT | stand | 0.0938 |
| 8,8 | SPLIT | stand | 0.3391 |
| 7,7 | SPLIT | stand | 0.1775 |
| 6,6 | SPLIT | hit | 0.0970 |
| 5,5 | double | hit | 0.2032 |
| 4,4 | hit | SPLIT | 0.0993 |
| 3,3 | SPLIT | hit | 0.0434 |
| 2,2 | SPLIT | hit | 0.0570 |
What Changes From a
What Changes From a 2
Moving from a 2 to a 3 changes 3 of the 34 decisions. Each one is a hand where a card’s difference in the dealer’s hand flips your correct play.
| Hand | Against a 2 | Against a 3 | Gap here |
|---|---|---|---|
| A,6 | hit | double | 0.0261 |
| A,7 | stand | double | 0.0293 |
| Hard 9 | hit | double | 0.0196 |
What This Upcard Is Worth to You
Averaged across all 34 hands, your expected value against a 3 is +0.1083 per unit. The full ranking of upcards, best to worst for the player:
| Dealer upcard | Your average EV | Dealer busts |
|---|---|---|
| 6 | +0.2498 | 42.3% |
| 5 | +0.1984 | 41.6% |
| 4 | +0.1511 | 39.4% |
| 7 | +0.1436 | 26.2% |
| 3 | +0.1083 | 37.4% |
| 2 | +0.0683 | 35.4% |
| 8 | +0.0352 | 24.5% |
| 9 | -0.0852 | 22.8% |
| Ace | -0.1100 | 16.7% |
| 10 | -0.1602 | 23.0% |
One caveat that matters, and most charts hide it. These figures are computed with the dealer peeking for blackjack, so hands where the dealer already has 21 are removed before the averaging. Against an ace that removes a great deal — roughly 31% of the time there is a ten underneath. It is why an ace looks less punishing than a 10 in the table above and is in fact the worst card you can face. The average is honest about the hands you actually get to play, and silent about the ones that end before you act.
The Ten Closest Calls Against a 3
These are the hands where the right answer is barely right. Getting any of them wrong costs less than 0.058 per unit — worth knowing, not worth agonising over at the table.
| Your hand | Correct play | Runner-up | Gap per unit |
|---|---|---|---|
| A,5 (soft 16) | hit | double | 0.0163 |
| Hard 12 | hit | stand | 0.0186 |
| Hard 9 | double | hit | 0.0196 |
| A,6 (soft 17) | double | hit | 0.0261 |
| A,7 (soft 18) | double | stand | 0.0293 |
| A,4 (soft 15) | hit | double | 0.0364 |
| Hard 13 | stand | hit | 0.0390 |
| 3,3 | SPLIT | hit | 0.0434 |
| 2,2 | SPLIT | hit | 0.0570 |
| A,3 (soft 14) | hit | double | 0.0580 |
Reality check: playing every one of these 34 hands correctly does not make blackjack a winning game. Basic strategy brings the house edge to roughly 0.5%, which is the cheapest game on most floors and still a negative-expectation one. The value of this page is that it tells you how much each decision is worth, so you can spend your memory where it pays.
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Open the Black Box →Reality check: no strategy on this page turns a negative-expectation game into a positive one. Strategy reduces how much the house takes and how fast your bankroll disappears — it does not guarantee profit. Only ever bet money you can afford to lose entirely.