Blackjack Bust Probability Calculator (Your Bust Chance and the Dealer's)

How it works

Infinite-deck model: each rank has probability 1/13, ten-value cards (10, J, Q, K) 4/13 · your bust chance = sum of the probabilities of the cards that push the total over 21 (ace counts 1 when 11 would bust) · dealer: draws until 17 or more (hits soft 17 under H17), computed by recursion over every card sequence; blackjack = 21 with the first two cards

The chance of busting depends only on how many card ranks would take you past 21: on a hard 16 any 6, 7, 8, 9 or ten-value card busts you — 8 of the 13 ranks, 61.5%. A soft hand cannot bust with one card because the ace can drop from 11 to 1. The dealer has no choices, so their final total can be calculated exactly for each upcard by following every possible draw; weak upcards (4, 5, 6) bust about 40% of the time, while a 10 or an ace rarely does. The numbers use an infinite deck, which differs from a 6- or 8-deck shoe by only a few tenths of a percent, and include the dealer's blackjack before any peek.

Worked example

Hard 16 against a dealer 10, dealer stands on soft 17: the 6, 7, 8 and 9 (1/13 each) and the four ten-value ranks (4/13) bust you, 8/13 = 61.54%, while an ace to 5 gives you 17–21 (38.46%). Following every possible draw, a dealer showing 10 busts 21.21% of the time, makes 20 in 34.22% and has blackjack (a hidden ace) in 7.69% of hands, finishing on 17–21 in 71.10%.

Sources: Wizard of Odds — Blackjack dealer probabilities · Thorp, Beat the Dealer (Random House, 1966)

Frequently asked questions