This post examines what the odds of winning at blackjack are if a player never busts. If the dealer must hit on 16 and stand on 17, the odds of the dealer busting is 28.37%. The player will automatically win 28.37% of the time if he doesn’t hit.
Next, the probability of a dealer getting a final hand of 17 or above is 71.63%. The probability of a player receiving a two card hand of 17 or above is 34.8%. Therefore, the player will push 34.8% of the time with just a two card hand.
We still have to account for receiving a hand of 17 or above by hitting on decision hands (2-11) and no bust hands. A decision hand (2-16) occurs 38.7% of the time and a no bust hand will occur 26.5% of the time. Let’s assume that 10% of the time hitting on decision hands or no bust hands will result in a final hand of 17 or higher. This suggests that the player will push 44.8% of the time.
Adding the probability of winning because of the dealer busting to the probability of pushing equals 73.5%. Recall that a dealer pushes or wins 71.63% of the time. Therefore, the player has a 1.87% advantage over the dealer.