## Dealer Up Card Odds

To be a good blackjack player, you need to know and understand blackjack basic strategy. Beyond memorizing a simple chart, it is a good idea to know why certain decisions are made. In the past I have posted series of blogs that delve deep into the reasoning behind basic strategy decisions. One of many things that basic strategy takes into account is the probability of busting when drawing a card. This morning, I posted a blog discussing the probability of busting when you (or the dealer) have a certain hand total.

However, one of the difficult things about blackjack is that you don’t know what hand the dealer has. Since the dealer has a hole card face down, you can only guess what his hand is. Luckily, mathematicians a whole lot smarter than me have already calculated the likelihood of the dealer busting based on what his up card is. These statistics are found by determining, based on what up card the dealer has, what hands he is likely to have, and from there determining how likely he is to bust with that hand. A full chart follows.

When looking at these numbers, you may be surprised because the highest hands have the lost bust percentage. That is because the dealer in those cases is likely to have a hand high enough that he would stand rather than drawing again. For example, if the dealer shows a ten-value card, he is not likely to bust because he would stand on a hand of 17-21. If he shows a 10, that means 8 cards (7, 8, 9, 10, J, Q, K, ace) would give the dealer a hand in the 17-21 range and only 5 cards (2, 3, 4, 5, 6) would give him a stiff hand that is likely (31-62%) to bust when he hits.

The following list has 3 numbers. The first is the dealer’s up card. The second number is the dealer’s bust percentage, or the likelihood that the dealer will bust when he has that up card. The third number is the player’s odds when the dealer has that up card. It should be noted that those odds take into account that the player plays perfect strategy. Also, because this doesn’t take into account what hand the player has, the odds will change based on the player’s cards. A percentage in parenthesis means the odds favor the dealer.

Up Card – Dealer Bust % — Player Odds %
2 – 35.3% — 9.8%
3 – 37.56% — 13.4%
4 – 40.28% — 18%
5 – 42.89% – 23.2%
6 – 42.08% – 23.9%
7 – 25.99% — 14.3%
8 – 23.86% — 5.4%
9 – 23.34% — (4.3%)
10 – 21.43% — (16.9%)
Ace – 11.65% — (16%)