Blackjack Mathematical Approach

December 21st, 2008

Here are some mathematical Blackjack formulas, considered to be the best and easiest approaches to adopt and remember in order to maximize your chances of winning.

Case I. Soft Hands
A-8 or A-9: In this case, the player must always stand.
A-7: If the dealer has 3 thru 6, probably the best thing to do is to double down. While stand on 2, 7, or 8, otherwise hit.
A-6: If the dealer has 3 thru 6, probably the best thing to do is to double down, otherwise hit.
A-4 or A-5: If the dealer has 4 thru 6, probably the best thing to do is to double down, otherwise hit.
A-2 or A-3: If the dealer has 5 or 6, probably the best thing to do is to double down, otherwise hit.

Case II. Hard Hands
17 to 21: You have a more chance to win if you stand always.
13 to 16: If the dealer has 2 thru 6, you must stand, otherwise hit.
12: If the dealer has 4 thru 6, you must stand. But if the dealer has 2 or 3, then you must hit.
11: If dealer has 2 thru 10, you must double down. Otherwise, hit.
10: If dealer has 2 thru 9, you must double down. Otherwise, hit.
9: If dealer has 3 thru 6, you must double down. Otherwise, hit.
8 or less: You should always hit.

Case III. Splitting
10-10: the player should always stand in order to have the higher chance of winning.
9-9: If the dealer has 2 thru 6, 8, or 9, you must split. And you must stand on anything else.
8-8 or Ace- Ace: In this situation, the player must always split.
7-7: If the dealer has 2 thru 7, you must split. Otherwise you must hit.
6-6: If the dealer has 2 thru 6, you must split. Otherwise you must hit.
5-5: If the dealer has 2 thru 9, you double down. Otherwise you must hit.
4-4: If the dealer has 4 or 5, you must split. Otherwise you must hit.
2-2 or 3-3: If the dealer has 2 thru 7, you must split. Otherwise you must hit.