The only change is when we hold a 'soft' total, which means we hold an ace that can be either a 1 or an 11. When the upcard is 7 through A, our probability of winning is more than the 10-25% chance of the dealer busting, so we hit until we reach 17 or higher. On 13 and above, the higher chance of busting means that it will be more profitable to stand when the upcard is less than 6 and take the dealer's 35-40% chance of busting. This happens between 29 and 31% of the time, as the upcards 4, 5, and 6 were found to be profitable stands while 2 and 3 remained hits. We could bust on the next hit, or the dealer could get a higher total than us. However, we are not going to win every time this happens.

On 12, we have a 69% chance of not busting when we hit. We will decide to stand when our probability of winning through hitting is less than the dealer busting. As you can see, the higher total we have, the greater the likelihood that we bust. Here are the player bust out rates for each (hard) starting hand total. In contrast, the lower upcards will almost always require an additional two cards and thus there are more chances to bust. Conceptually, this makes sense because with these higher upcards give the dealer a much greater chance of landing within the safe zone of 17 or higher, often with just one additional card. As you can see, they vary drastically with 2, 3, 4, 5, and 6 making the dealer 1.5-2 times more likely to bust than 7, 8, 9, T/J/Q/K, or A. Here is the dealer bust out rates for each starting card, or upcard. Why, you ask? Let's take a look at the math. This will depend on what card the dealer holds. Here we have a chance of busting, so we must evaluate whether it is +EV (positive expected value) to take another card. When we reach 12 and higher, it starts to get interesting. On 11 and below, we have no chance of busting, so it makes sense to take another card. The dealer stands on 17 and above, and hits on anything else. Our goal is to get blackjack, or closer to it than the dealer, or for him to bust. Well as you know there are thirteen different cards in the deck: ranging in value from 1 to 10 (or 11 with a soft ace).

Blackjack strategy for every table