Summary - Winning idea for blackjack (Wouldn't it be fun to beat the casino?)


Optimal strategy - Table of Content


Decision Table (dealer has an estimated 0.72% advantage)

Optimal Strategy for Hard Total

HARD

8

9

10

A

12

13

14

15

16

17

2

hit

hit

2/h

2/h

hit

sta

sta

sta

sta

sta

3

hit

2/h

2/h

2/h

hit

sta

sta

sta

sta

sta

4

hit

2/h

2/h

2/h

sta

sta

sta

sta

sta

sta

5

hit

2/h

2/h

2/h

sta

sta

sta

sta

sta

sta

6

hit

2/h

2/h

2/h

sta

sta

sta

sta

sta

sta

7

hit

hit

2/h

2/h

hit

hit

hit

hit

hit

sta

8

hit

hit

2/h

2/h

hit

hit

hit

hit

hit

sta

9

hit

hit

2/h

2/h

hit

hit

hit

hit

hit

sta

10

hit

hit

hit

2/h

hit

hit

hit

hit

hit

sta

A

hit

hit

hit

2/h

hit

hit

hit

hit

hit

sta

Optimal Strategy for Soft Total

SOFT

A2

A3

A4

A5

A6

A7

A8

A9

2

hit

hit

hit

hit

hit

2/s

sta

sta

3

hit

hit

hit

hit

2/h

2/s

sta

sta

4

hit

hit

2/h

2/h

2/h

2/s

sta

sta

5

hit

2/h

2/h

2/h

2/h

2/s

sta

sta

6

2/h

2/h

2/h

2/h

2/h

2/s

2/s

sta

7

hit

hit

hit

hit

hit

sta

sta

sta

8

hit

hit

hit

hit

hit

sta

sta

sta

9

hit

hit

hit

hit

hit

hit

sta

sta

10

hit

hit

hit

hit

hit

hit

sta

sta

A

hit

hit

hit

hit

hit

hit

sta

sta

Optimal Strategy for Decision on Split

SPLT

2

3

4

5

6

7

8

9

10

A

2

N

N

N

N

N

Y

Y

Y

N

Y

3

N

N

N

N

Y

Y

Y

Y

N

Y

4

Y

Y

N

N

Y

Y

Y

Y

N

Y

5

Y

Y

N

N

Y

Y

Y

Y

N

Y

6

Y

Y

N

N

Y

Y

Y

Y

N

Y

7

Y

Y

N

N

N

Y

Y

N

N

Y

8

N

N

N

N

N

N

Y

Y

N

Y

9

N

N

N

N

N

N

Y

Y

N

Y

10

N

N

N

N

N

N

Y

N

N

Y

A

N

N

N

N

N

N

Y

N

N

Y


Algorithm - How do I generated the table above? (Technical/Statistical)

Dealer's ending total -- Result only

Dealer stands at 17 or more

Dealer's-up-card

17

18

19

20

21

Bust

2

0.139809

0.134907

0.129655

0.124027

0.117994

0.353608

3

0.135034

0.130482

0.125581

0.120329

0.114700

0.373875

4

0.130490

0.125938

0.121386

0.116485

0.111233

0.394468

5

0.122251

0.122251

0.117700

0.113148

0.108246

0.416404

6

0.165438

0.106267

0.106267

0.101715

0.097163

0.423151

7

0.368566

0.137797

0.078625

0.078625

0.074074

0.262312

8

0.128567

0.359336

0.128567

0.069395

0.069395

0.244741

9

0.119995

0.119995

0.350765

0.119995

0.060824

0.228425

10

0.111424

0.111424

0.111424

0.342194

0.111424

0.212109

A

0.130789

0.130789

0.130789

0.130789

0.361558

0.115286

Overall

0.145126

0.139497

0.133464

0.180252

0.120068

0.280000


Dealer stands at 17 or more, except hits on soft 17

Dealer's-up-card

17

18

19

20

21

Bust

2

0.130134

0.136546

0.131294

0.125665

0.119632

0.356728

3

0.126328

0.131957

0.127055

0.121803

0.116174

0.376682

4

0.122406

0.127307

0.122756

0.117854

0.112602

0.397075

5

0.118359

0.122911

0.118359

0.113807

0.108906

0.417659

6

0.114838

0.114838

0.114838

0.110286

0.105734

0.439467

7

0.368566

0.137797

0.078625

0.078625

0.074074

0.262312

8

0.128567

0.359336

0.128567

0.069395

0.069395

0.244741

9

0.119995

0.119995

0.350765

0.119995

0.060824

0.228425

10

0.111424

0.111424

0.111424

0.342194

0.111424

0.212109

A

0.057493

0.143204

0.143204

0.143204

0.373974

0.138920

Overall

0.133260

0.141507

0.135474

0.182262

0.122078

0.285419


Expectation Table

The expectation table for hard total

HARD

4

5

6

7

8

9

10

A

12

13

14

15

16

17

18

19

20

21

2

-0.29;-0.11;-0.57

-0.29;-0.13;-0.57

-0.29;-0.14;-0.55

-0.29;-0.11;-0.43

-0.29;-0.02;-0.21

-0.29;+0.07;+0.06

-0.29;+0.18;+0.36

-0.29;+0.24;+0.47

-0.29;-0.25;-0.51

-0.29;-0.31;-0.62

-0.29;-0.36;-0.73

-0.29;-0.42;-0.84

-0.29;-0.47;-0.95

-0.16;-0.54;-1.08

+0.11;-0.62;-1.25

+0.38;-0.73;-1.46

+0.64;-0.86;-1.71

+0.88;-1.00;-2.00

3

-0.25;-0.08;-0.49

-0.25;-0.09;-0.49

-0.25;-0.10;-0.47

-0.25;-0.08;-0.36

-0.25;+0.01;-0.14

-0.25;+0.10;+0.12

-0.25;+0.20;+0.41

-0.25;+0.26;+0.52

-0.25;-0.23;-0.47

-0.25;-0.29;-0.58

-0.25;-0.35;-0.70

-0.25;-0.41;-0.82

-0.25;-0.47;-0.93

-0.12;-0.53;-1.07

+0.14;-0.62;-1.24

+0.40;-0.73;-1.46

+0.65;-0.86;-1.71

+0.88;-1.00;-2.00

4

-0.21;-0.05;-0.41

-0.21;-0.06;-0.41

-0.21;-0.07;-0.39

-0.21;-0.04;-0.28

-0.21;+0.04;-0.07

-0.21;+0.13;+0.18

-0.21;+0.23;+0.46

-0.21;+0.28;+0.57

-0.21;-0.21;-0.43

-0.21;-0.27;-0.55

-0.21;-0.34;-0.67

-0.21;-0.40;-0.79

-0.21;-0.46;-0.92

-0.08;-0.53;-1.06

+0.17;-0.62;-1.24

+0.42;-0.73;-1.45

+0.66;-0.85;-1.71

+0.89;-1.00;-2.00

5

-0.16;-0.01;-0.33

-0.16;-0.02;-0.33

-0.16;-0.03;-0.31

-0.16;-0.01;-0.20

-0.16;+0.07;+0.00

-0.16;+0.16;+0.24

-0.16;+0.26;+0.51

-0.16;+0.31;+0.61

-0.16;-0.19;-0.39

-0.16;-0.26;-0.52

-0.16;-0.32;-0.64

-0.16;-0.39;-0.77

-0.16;-0.45;-0.90

-0.05;-0.52;-1.05

+0.19;-0.62;-1.23

+0.44;-0.73;-1.45

+0.67;-0.85;-1.71

+0.89;-1.00;-2.00

6

-0.12;+0.03;-0.24

-0.12;+0.02;-0.24

-0.12;+0.00;-0.22

-0.12;+0.03;-0.12

-0.12;+0.10;+0.08

-0.12;+0.19;+0.30

-0.12;+0.28;+0.56

-0.12;+0.33;+0.66

-0.12;-0.17;-0.34

-0.12;-0.24;-0.48

-0.12;-0.31;-0.62

-0.12;-0.38;-0.75

-0.12;-0.44;-0.89

-0.01;-0.52;-1.04

+0.22;-0.61;-1.23

+0.45;-0.73;-1.45

+0.68;-0.85;-1.71

+0.89;-1.00;-2.00

7

-0.48;-0.09;-0.95

-0.48;-0.12;-0.95

-0.48;-0.15;-0.89

-0.48;-0.07;-0.59

-0.48;+0.08;-0.19

-0.48;+0.17;+0.10

-0.48;+0.26;+0.39

-0.48;+0.29;+0.46

-0.48;-0.21;-0.51

-0.48;-0.27;-0.59

-0.48;-0.32;-0.67

-0.48;-0.37;-0.75

-0.48;-0.41;-0.83

-0.11;-0.48;-0.97

+0.40;-0.59;-1.18

+0.62;-0.72;-1.43

+0.77;-0.85;-1.70

+0.93;-1.00;-2.00

8

-0.51;-0.16;-1.02

-0.51;-0.19;-1.02

-0.51;-0.22;-1.00

-0.51;-0.21;-0.85

-0.51;-0.06;-0.45

-0.51;+0.10;-0.03

-0.51;+0.20;+0.29

-0.51;+0.23;+0.35

-0.51;-0.27;-0.62

-0.51;-0.32;-0.69

-0.51;-0.37;-0.77

-0.51;-0.42;-0.84

-0.51;-0.46;-0.92

-0.38;-0.51;-1.01

+0.11;-0.59;-1.18

+0.59;-0.71;-1.43

+0.79;-0.85;-1.70

+0.93;-1.00;-2.00

9

-0.54;-0.24;-1.09

-0.54;-0.27;-1.09

-0.54;-0.29;-1.07

-0.54;-0.29;-0.96

-0.54;-0.21;-0.72

-0.54;-0.05;-0.30

-0.54;+0.12;+0.14

-0.54;+0.16;+0.23

-0.54;-0.34;-0.74

-0.54;-0.39;-0.81

-0.54;-0.43;-0.88

-0.54;-0.47;-0.95

-0.54;-0.51;-1.02

-0.42;-0.55;-1.11

-0.18;-0.62;-1.23

+0.29;-0.72;-1.43

+0.76;-0.85;-1.70

+0.94;-1.00;-2.00

10

-0.54;-0.29;-1.08

-0.54;-0.31;-1.08

-0.54;-0.34;-1.06

-0.54;-0.32;-0.95

-0.54;-0.25;-0.75

-0.54;-0.15;-0.47

-0.54;+0.03;-0.01

-0.54;+0.12;+0.18

-0.54;-0.38;-0.80

-0.54;-0.43;-0.87

-0.54;-0.47;-0.94

-0.54;-0.50;-1.01

-0.54;-0.54;-1.08

-0.42;-0.58;-1.17

-0.18;-0.65;-1.30

+0.06;-0.73;-1.46

+0.55;-0.85;-1.70

+0.96;-1.00;-2.00

A

-0.60;-0.29;-1.20

-0.60;-0.32;-1.20

-0.60;-0.34;-1.18

-0.60;-0.35;-1.09

-0.60;-0.26;-0.83

-0.60;-0.12;-0.46

-0.60;+0.03;-0.04

-0.60;+0.10;+0.10

-0.60;-0.38;-0.84

-0.60;-0.43;-0.90

-0.60;-0.47;-0.96

-0.60;-0.51;-1.02

-0.60;-0.54;-1.08

-0.52;-0.58;-1.16

-0.23;-0.64;-1.28

+0.19;-0.73;-1.46

+0.60;-0.85;-1.71

+0.90;-1.00;-2.00

The expectation table for soft total

SOFT

AA

A2

A3

A4

A5

A6

A7

A8

A9

A10

2

-0.29;+0.08;-0.07

-0.29;+0.05;-0.07

-0.29;+0.02;-0.07

-0.29;+0.00;-0.07

-0.29;-0.02;-0.07

-0.16;-0.00;-0.01

+0.11;+0.06;+0.11

+0.38;+0.12;+0.24

+0.64;+0.18;+0.36

+0.88;+0.24;+0.47

3

-0.25;+0.10;-0.00

-0.25;+0.07;-0.00

-0.25;+0.05;-0.00

-0.25;+0.03;-0.00

-0.25;+0.01;-0.00

-0.12;+0.03;+0.05

+0.14;+0.09;+0.17

+0.40;+0.15;+0.29

+0.65;+0.20;+0.41

+0.88;+0.26;+0.52

4

-0.21;+0.13;+0.06

-0.21;+0.10;+0.06

-0.21;+0.08;+0.06

-0.21;+0.06;+0.06

-0.21;+0.04;+0.06

-0.08;+0.06;+0.12

+0.17;+0.12;+0.23

+0.42;+0.17;+0.35

+0.66;+0.23;+0.46

+0.89;+0.28;+0.57

5

-0.16;+0.16;+0.13

-0.16;+0.13;+0.13

-0.16;+0.11;+0.13

-0.16;+0.09;+0.13

-0.16;+0.07;+0.13

-0.05;+0.09;+0.18

+0.19;+0.15;+0.29

+0.44;+0.20;+0.40

+0.67;+0.26;+0.51

+0.89;+0.31;+0.61

6

-0.12;+0.19;+0.20

-0.12;+0.17;+0.20

-0.12;+0.14;+0.20

-0.12;+0.13;+0.20

-0.12;+0.11;+0.20

-0.01;+0.12;+0.25

+0.22;+0.18;+0.36

+0.45;+0.23;+0.46

+0.68;+0.28;+0.56

+0.89;+0.33;+0.66

7

-0.48;+0.17;-0.18

-0.48;+0.12;-0.18

-0.48;+0.08;-0.18

-0.48;+0.04;-0.18

-0.48;-0.00;-0.18

-0.11;+0.05;-0.01

+0.40;+0.17;+0.22

+0.62;+0.22;+0.32

+0.77;+0.26;+0.39

+0.93;+0.29;+0.46

8

-0.51;+0.10;-0.31

-0.51;+0.05;-0.31

-0.51;+0.01;-0.31

-0.51;-0.03;-0.31

-0.51;-0.07;-0.31

-0.38;-0.07;-0.26

+0.11;+0.04;-0.03

+0.59;+0.15;+0.20

+0.79;+0.20;+0.29

+0.93;+0.23;+0.35

9

-0.54;+0.00;-0.46

-0.54;-0.04;-0.46

-0.54;-0.08;-0.46

-0.54;-0.11;-0.46

-0.54;-0.15;-0.46

-0.42;-0.15;-0.40

-0.18;-0.10;-0.29

+0.29;+0.01;-0.07

+0.76;+0.12;+0.14

+0.94;+0.16;+0.23

10

-0.54;-0.07;-0.51

-0.54;-0.10;-0.51

-0.54;-0.14;-0.51

-0.54;-0.17;-0.51

-0.54;-0.21;-0.51

-0.42;-0.20;-0.46

-0.18;-0.14;-0.35

+0.06;-0.09;-0.24

+0.55;+0.03;-0.01

+0.96;+0.12;+0.18

A

-0.60;-0.06;-0.59

-0.60;-0.10;-0.59

-0.60;-0.13;-0.59

-0.60;-0.17;-0.59

-0.60;-0.20;-0.59

-0.52;-0.22;-0.55

-0.23;-0.16;-0.42

+0.19;-0.06;-0.23

+0.60;+0.03;-0.04

+0.90;+0.10;+0.10

The expectation table for split

SPLT

2,2

3,3

4,4

5,5

6,6

7,7

8,8

9,9

10,10

A,A

2

-0.11;-0.15

-0.14;-0.20

-0.02;-0.23

+0.36;-0.25

-0.25;-0.28

-0.29;-0.22

-0.29;-0.05

+0.11;+0.14

+0.64;+0.36

+0.08;+0.73

3

-0.08;-0.10

-0.10;-0.13

+0.01;-0.16

+0.41;-0.19

-0.23;-0.21

-0.25;-0.15

-0.25;+0.01

+0.14;+0.20

+0.65;+0.41

+0.10;+0.77

4

-0.05;-0.04

-0.07;-0.07

+0.04;-0.09

+0.46;-0.12

-0.21;-0.14

-0.21;-0.09

-0.21;+0.07

+0.17;+0.26

+0.66;+0.46

+0.13;+0.81

5

-0.01;+0.03

-0.03;+0.00

+0.07;-0.02

+0.51;-0.05

-0.16;-0.07

-0.16;-0.01

-0.16;+0.14

+0.19;+0.31

+0.67;+0.51

+0.16;+0.85

6

+0.03;+0.10

+0.00;+0.08

+0.10;+0.05

+0.56;+0.03

-0.12;+0.01

-0.12;+0.06

-0.12;+0.21

+0.22;+0.37

+0.68;+0.56

+0.20;+0.89

7

-0.09;-0.05

-0.15;-0.11

+0.08;-0.18

+0.39;-0.24

-0.21;-0.30

-0.32;-0.14

-0.41;+0.16

+0.40;+0.34

+0.77;+0.51

+0.17;+0.91

8

-0.16;-0.21

-0.22;-0.26

-0.06;-0.32

+0.29;-0.38

-0.27;-0.43

-0.37;-0.42

-0.46;-0.12

+0.11;+0.20

+0.79;+0.40

+0.10;+0.80

9

-0.24;-0.38

-0.29;-0.43

-0.21;-0.48

+0.14;-0.53

-0.34;-0.59

-0.43;-0.57

-0.51;-0.42

-0.18;-0.10

+0.76;+0.23

+0.00;+0.64

10

-0.29;-0.48

-0.34;-0.53

-0.25;-0.58

+0.03;-0.63

-0.38;-0.68

-0.47;-0.64

-0.54;-0.50

-0.18;-0.31

+0.55;+0.05

-0.07;+0.53

A

-0.29;-0.49

-0.34;-0.54

-0.26;-0.58

+0.03;-0.63

-0.38;-0.68

-0.47;-0.70

-0.54;-0.53

-0.23;-0.25

+0.60;+0.07

-0.06;+0.52


Simulation (without changing bet)


Variable bet

COUNT

Result (Bet = 1)

Occurance

Average

Bet

Result (Bet Vary)

-4

-7.0

17

-0.41

1

-7.0

-3

-6.0

29

-0.21

1

-6.0

-2

-4.5

47

-0.10

1

-4.5

-1

2.5

125

0.02

1

2.5

0

6.0

518

0.01

1

6.0

1

-0.5

147

-0.00

1

-0.5

2

0.5

68

0.01

2

1.0

3

-9.0

32

-0.28

3

-27.0

4

3.0

6

0.50

4

12.0

5

-1.0

3

-0.33

5

-5.0

6

6.0

6

1.00

6

36.0

7

1.0

2

0.50

7

7.0

Sum

-9.0

1000

-0.09


14.5


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