# Should I hit or stand in blackjack?

Computes exact infinite-deck blackjack odds for one hand against the dealer’s up card: the expected result of hitting and of standing, the chance to bust, and the dealer’s final totals.

- Page: https://www.acalculator.org/game/blackjack-calculator
- JSON spec: https://www.acalculator.org/game/blackjack-calculator.json
- Version: 33061ba75463

## Default answer

Example with the default inputs (Your hand total 16, Hand Hard, Dealer’s up card 10, J, Q or K, Dealer on soft 17 Stands): With hard 16 against a dealer 10, J, Q or K, the better play is: Hit.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| total | Your hand total | The total of your cards, counting an ace as 11 when the hand is soft. |
| hand | Hand | Soft if an ace in your hand counts as 11 (such as ace and 6, soft 17); hard otherwise. |
| up | Dealer’s up card | The dealer’s face-up card. 10, jack, queen and king all count as 10. |
| rule | Dealer on soft 17 | Whether the dealer stands or hits on a soft 17 (the table rules say which). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| hand | Your hand | Your total with hard or soft, such as hard 16 or soft 17. |
| play | Better play | Hit or stand: the choice with the higher expected result (hit or stand only). |
| stand | Expected result of standing | The average win or loss per bet if you stand, as a percent of the bet. |
| hit | Expected result of hitting | The average win or loss per bet if you take a card and then keep hitting or standing, whichever is better. |
| bust | Chance the next card busts you | The chance that one more card takes your total over 21. |
| win | Chance to win if you stand | The chance the dealer busts or ends below your total. |
| push | Chance to push if you stand | The chance the dealer ends on your total. |
| lose | Chance to lose if you stand | The chance the dealer ends above your total without busting. |
| dealerBust | Dealer busts | The chance the dealer’s hand goes over 21. |
| dealer17 | Dealer ends on 17 | The chance the dealer stops on 17. |
| dealer18 | Dealer ends on 18 | The chance the dealer stops on 18. |
| dealer19 | Dealer ends on 19 | The chance the dealer stops on 19. |
| dealer20 | Dealer ends on 20 | The chance the dealer stops on 20. |
| dealer21 | Dealer ends on 21 | The chance the dealer stops on 21. |

## Method

Infinite deck (each card value 1/13, ten-values 4/13). Dealer final totals by recursion from the up card, given no dealer blackjack. Stand = P(win) − P(lose); hit = average over the next card of the better of standing and hitting again.

## Assumptions

- An infinite deck: every card has the same chance whatever has been dealt. With 6 or 8 decks the numbers differ only slightly.
- The dealer checks for blackjack first, and these odds assume the dealer does not have one.
- Only hit and stand are compared; doubling, splitting and surrender are not.
- A total of 21 is an ordinary 21, not a two-card blackjack. A win pays 1 to 1.
- Results are mathematics, not betting advice.

## Worked examples

1. total = 16, hand = hard, up = 10, rule = s17 gives play = Hit, stand = -54.043%, hit = -53.9826%, bust = 61.538462%. Source: Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (stand −0.540430, hit −0.539826, rounded to 6 decimals): https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/.
2. total = 12, hand = hard, up = 4, rule = s17 gives play = Stand, stand = -21.1063%, hit = -21.3537%. Source: Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (stand −0.211063, hit −0.213537): https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/.
3. total = 20, hand = hard, up = 6, rule = s17 gives play = Stand, stand = 70.3959%, dealerBust = 42.315049%. Source: Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (stand 0.703959); dealer bust from the dealer recursion in content.mdx, Python 3 fractions.
4. total = 17, hand = soft, up = 9, rule = s17 gives play = Hit, stand = -42.3154%, hit = -14.9787%. Source: Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (17 standing vs 9 −0.423154; soft 17 hitting vs 9 −0.149787): https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/.
5. total = 16, hand = hard, up = A, rule = s17 gives play = Hit, stand = -66.6951%, hit = -51.7149%. Source: Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (stand vs ace −0.666951, hit −0.517149): https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/.
6. total = 16, hand = hard, up = 6, rule = h17 gives dealerBust = 43.946657%, dealer17 = 11.483768%. Source: dealer recursion in content.mdx with the dealer hitting soft 17; Python 3 fractions (progress log).

## FAQ

### Should I hit or stand on 16 against a 10?

Hitting is very slightly better with hit or stand only. With an infinite deck, standing returns −54.04% of the bet on average and hitting −53.98%. Both lose most of the time; the difference is small. (With a pair of 8s, splitting is better than either.)

### What is the chance of busting on the next card?

It is the chance the next card is too big. On hard 16, any card from 6 to 10 busts. The 6, 7, 8 and 9 have chance 1/13 each and a ten-value card 4/13, so the chance is 4/13 + 4/13 = 8/13 = 61.54%. A soft hand cannot bust on one card.

### How often does the dealer bust?

It depends on the up card. With an infinite deck and the dealer standing on soft 17, a 6 busts 42.32% of the time and an ace 16.65% of the time (given no dealer blackjack). The calculator shows every final total.

### What does "expected result" mean?

The average win or loss per hand as a percent of the bet, if you played this spot many times. −54% means you would lose about 54 of every 100 staked over many hands. It says nothing certain about the next hand.

### Why does the calculator ignore doubling and splitting?

It compares only hit and stand, the choice every hand has. Doubling, splitting and surrender depend on your two cards and the table rules, and can change the best play (for example doubling 11 against a 6).

## Sources

- Wizard of Odds, Expected Returns in Infinite-Deck Blackjack (stand and hit tables, dealer stands on soft 17): https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/
- Wizard of Odds, Dealer Odds in Blackjack under U.S. Rules (dealer final totals, given no dealer blackjack): https://wizardofodds.com/games/blackjack/dealer-odds-blackjack-us-rules/
- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, chapter 4, conditional probability: https://math.dartmouth.edu/~prob/prob/prob.pdf
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/