This page presents the optimal play for blackjack
when the following rules apply:
Dealer hits up to sixteen, dealer sticks on 17.
A tie is a push -- no win, no loss.
Player wins 1.5 times bet on blackjack.
No surrender
Only one split allowed.
Player gets only one more card when splitting Aces.
The analysis is for an infinite, well-mixed deck.
(For card-counting, this assumes count is 0).
We may eventually provide the optimal play and payoffs for
when a simple card-counting strategy is employed.
Key:
H Hit
S Stick
D Double down
DH Double down if you can, else hit
DS Double down if you can, else stick
The numbers across the top of a table give the dealer's up card (1=Ace)
The numbers down the left hand column is the sum of the cards in the player's
(hard) hand.
Best move matrix
1 2 3 4 5 6 7 8 9 10
1
2 H H H H H H H H H H
3 H H H H H H H H H H
4 H H H H H H H H H H
5 H H H H H H H H H H
6 H H H H H H H H H H
7 H H H H H H H H H H
8 H H H H H H H H H H
9 H H DH DH DH DH H H H H
10 H DH DH DH DH DH DH DH DH H
11 H DH DH DH DH DH DH DH DH DH
12 H H H S S S H H H H
13 H S S S S S H H H H
14 H S S S S S H H H H
15 H S S S S S H H H H
16 H S S S S S H H H H
17 S S S S S S S S S S
18 S S S S S S S S S S
19 S S S S S S S S S S
20 S S S S S S S S S S
21 S S S S S S S S S S
Again the numbers across the top represent the dealer's up card.
The numbers down the left hand column represent a hand in which the
player has an Ace plus this value -- e.g. for a hand of A,2,5 look
in the row starting with 7
Best move matrix aces
1 2 3 4 5 6 7 8 9 10
1 H H H H H H H H H H
2 H H H H H DH H H H H
3 H H H H DH DH H H H H
4 H H H H DH DH H H H H
5 H H H DH DH DH H H H H
6 H H DH DH DH DH H H H H
7 H S DS DS DS DS S S H H
8 S S S S S S S S S S
9 S S S S S S S S S S
10 S S S S S S S S S S
The table that follows provides strategy when you have a pair.
Again the numbers across the top represent the dealer's up card.
The numbers down the left mean that the player has a pair of that
number.
Split (yes=Y; no=N)
1 2 3 4 5 6 7 8 9 10
1 Y Y Y Y Y Y Y Y Y Y
2 N Y Y Y Y Y Y N N N
3 N Y Y Y Y Y Y N N N
4 N N N N Y Y N N N N
5 N N N N N N N N N N
6 N Y Y Y Y Y N N N N
7 N Y Y Y Y Y Y N N N
8 Y Y Y Y Y Y Y Y Y Y
9 N Y Y Y Y Y N Y Y N
10 N N N N N N N N N N
The numbers below give the probability of the dealer ending with the number
on the left or blackjack (BJ) or busting when the up card is the number on the top of
the column.For example, if the dealer has a 6 showing, he/she has a 16.54%
chance of ending with a 17, a 10.17% chance of winding up with a 20 and nearly
10% chance of ending up with a 21, but 0.0% chance of getting blackjack and over
42% chance of busting.
1 2 3 4 5 6 7 8 9 10
17 0.1308 0.1398 0.1350 0.1305 0.1223 0.1654 0.3686 0.1286 0.1200 0.1114
18 0.1308 0.1349 0.1305 0.1259 0.1223 0.1063 0.1378 0.3593 0.1200 0.1114
19 0.1308 0.1297 0.1256 0.1214 0.1177 0.1063 0.0786 0.1286 0.3508 0.1114
20 0.1308 0.1240 0.1203 0.1165 0.1131 0.1017 0.0786 0.0694 0.1200 0.3422
21 0.0539 0.1180 0.1147 0.1112 0.1082 0.0972 0.0741 0.0694 0.0608 0.0345
BJ 0.3077 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0769
BUST 0.1153 0.3536 0.3739 0.3945 0.4164 0.4232 0.2623 0.2447 0.2284 0.2121
If you play the above strategy under the conditions denoted above, over the
long run for each dollar wagered at the start of a hand, you should expect to
lose 0.58 cents.
Expected value of it all is -0.005804
(Simple card counting can help, but that's for another page).
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