acalculator

Should I hit or stand in blackjack?

Enter your total and the dealer’s up card to compare hitting with standing, using exact infinite-deck probabilities. The results are mathematics, not advice.

Your numbers

Hand
Dealer on soft 17
Better play
Hit

With hard 16 against a dealer 10, J, Q or K, the better play is: Hit.

Your hand
hard 16
Expected result of standing
-54.04%
Expected result of hitting
-53.98%
Chance the next card busts you
61.54%
Chance to win if you stand
22.98%
Chance to push if you stand
0%
Chance to lose if you stand
77.02%
Dealer busts
22.98%
Dealer ends on 17
12.07%
Dealer ends on 18
12.07%
Dealer ends on 19
12.07%
Dealer ends on 20
37.07%
Dealer ends on 21
3.74%

Better play: Hit. With hard 16 against a dealer 10, J, Q or K, the better play is: Hit.

The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use

How to calculate

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.

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.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Your hand total 16, Hand Hard, Dealer’s up card 10, J, Q or K, Dealer on soft 17 Stands gives Better play Hit, Expected result of standing -54.043%, Expected result of hitting -53.9826%, Chance the next card busts you 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. Your hand total 12, Hand Hard, Dealer’s up card 4, Dealer on soft 17 Stands gives Better play Stand, Expected result of standing -21.1063%, Expected result of hitting -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. Your hand total 20, Hand Hard, Dealer’s up card 6, Dealer on soft 17 Stands gives Better play Stand, Expected result of standing 70.3959%, Dealer busts 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. Your hand total 17, Hand Soft (ace as 11), Dealer’s up card 9, Dealer on soft 17 Stands gives Better play Hit, Expected result of standing -42.3154%, Expected result of hitting -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. Your hand total 16, Hand Hard, Dealer’s up card Ace, Dealer on soft 17 Stands gives Better play Hit, Expected result of standing -66.6951%, Expected result of hitting -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. Your hand total 16, Hand Hard, Dealer’s up card 6, Dealer on soft 17 Hits gives Dealer busts 43.946657%, Dealer ends on 17 11.483768%.Source: dealer recursion in content.mdx with the dealer hitting soft 17; Python 3 fractions (progress log)

How it works

The deck. An infinite deck: each card is an ace, 2, 3, 4, 5, 6, 7, 8 or 9 with chance 1/13 each, and a ten-value card (10, J, Q, K) with chance 4/13, whatever has been dealt.

Totals. An ace counts 11 unless that takes the hand over 21, then 1. A hand is soft when an ace counts 11. A soft total is 12 to 21; a soft total below 12 gives no answer.

The dealer. From the up card, the dealer draws until the total is 17 or more, and busts over 21. On a soft 17 the dealer stands or hits, as you choose. The dealer checks for blackjack first, so the odds assume the dealer does not have one: with an ace up the hole card is not a ten-value card, and with a ten-value up it is not an ace (the other hole cards keep their relative chances). The calculator works out the chance of each final total (17, 18, 19, 20, 21, bust) exactly, by adding up every way the dealer can draw.

Standing on total T:

  • Win = chance the dealer busts or ends below T
  • Push = chance the dealer ends on T
  • Lose = chance the dealer ends above T (without busting)
  • Expected result of standing = win − lose (each win pays 1 to 1)

Hitting: take one card. If it busts you, the result is −1. Otherwise take the better of standing and hitting again, and repeat. The expected result of hitting is the average of these over the next card, weighted by each card’s chance.

Better play: Hit when the expected result of hitting is higher, Stand otherwise.

Your hand: hard N or soft N, for example soft 17.

Chance the next card busts you: the chance of one card taking the total over 21.

Assumptions

  • An infinite deck. With 6 or 8 decks the numbers change only slightly.
  • The dealer has checked for blackjack and has none.
  • Only hit and stand; no doubling, splitting, surrender or insurance.
  • A total of 21 is an ordinary 21, not a two-card blackjack.

Worked examples by hand

Hard 16 against a 10. Cards 6, 7, 8, 9 (1/13 each) and ten-value cards (4/13) bust you, so the next card busts with chance 8/13 = 61.54%. Standing on 16 wins only when the dealer busts. The dealer recursion gives an expected result of −54.04% for standing and −53.98% for hitting, so the better play is Hit (Wizard of Odds: −0.540430 and −0.539826).

Hard 12 against a 4. Standing: −21.11%; hitting: −21.35%. Better play: Stand (Wizard of Odds: −0.211063 and −0.213537).

Hard 20 against a 6. Standing: +70.40% (Wizard of Odds: 0.703959). The dealer busts 42.32% of the time.

Soft 17 against a 9. Standing on 17 wins only when the dealer busts and pushes when the dealer ends on 17: −42.32%. Hitting: −14.98%. Better play: Hit (Wizard of Odds: −0.423154 and −0.149787).

Hard 16 against an ace. Standing: −66.70%; hitting: −51.71%. Better play: Hit (Wizard of Odds: −0.666951 and −0.517149).

Dealer 6, hitting soft 17. The dealer busts 43.95% of the time and ends on 17 11.48% of the time, against 42.32% and 16.54% when the dealer stands on soft 17.

A note on gambling

These results are mathematics, not advice. The house has an edge in blackjack, and every hand can lose. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).

Other questions people ask

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).