One SPOT or two SPOTS?

[Cacarulo]

One SPOT or two SPOTS?

Finally, I conducted the sims that recreate the optimal TC from which it is convenient to play two spots instead of one.
For this analysis, I assumed a heads-up game. Speed is not taken into account. The analyzed model was:
6D,S17,DOA,DAS,SPA1,SPL3,NS,4.5/6,50 billion rounds for each of the 18 sims carried out using CAC2 with 22 indices (R22).
The analysis was conducted on the SCORES of three different betting spreads: 1-8, 1-12, and 1-16.
Initially, the sim uses the single-spot game. Then, the game with two spots was simulated, and starting from the third sim,
various TCs ranging from +5 to -10 were evaluated. As can be observed from the analysis, for each betting spread there is an optimal TC,
resulting in a higher SCORE than if we play two spots all the time.

One spot ALWAYS

 1- 8 = 17.13
 1-12 = 23.66
 1-16 = 27.73

Two spots ALWAYS

 1- 8 = 25.42
 1-12 = 34.88
 1-16 = 40.75

Two spots at TC >= +5

 1- 8 = 22.76
 1-12 = 28.63
 1-16 = 32.12

Two spots at TC >= +4

 1- 8 = 22.84
 1-12 = 28.78
 1-16 = 32.31

Two spots at TC >= +3

 1- 8 = 23.14
 1-12 = 29.20
 1-16 = 32.79

Two spots at TC >= +2

 1- 8 = 23.56
 1-12 = 29.77
 1-16 = 33.46

Two spots at TC >= +1

 1- 8 = 24.30
 1-12 = 30.76
 1-16 = 34.60

Two spots at TC >= 0

 1- 8 = 25.45
 1-12 = 32.52
 1-16 = 36.73

Two spots at TC >= -1

 1- 8 = 26.07
 1-12 = 33.59
 1-16 = 38.09

Two spots at TC >= -2

 1- 8 = 26.37
 1-12 = 34.33
 1-16 = 39.14

Two spots at TC >= -3

 1- 8 = 26.53
 1-12 = 34.85
 1-16 = 39.89

Two spots at TC >= -4 (Optimal TC for a spread 1-8)

 1- 8 = 26.54
 1-12 = 35.13
 1-16 = 40.37

Two spots at TC >= -5

 1- 8 = 26.48
 1-12 = 35.28
 1-16 = 40.66

Two spots at TC >= -6

 1- 8 = 26.35
 1-12 = 35.32
 1-16 = 40.82

Two spots at TC >= -7 (Optimal TC for a spread 1-12)

 1- 8 = 26.26
 1-12 = 35.34
 1-16 = 40.93

Two spots at TC >= -8

 1- 8 = 26.13
 1-12 = 35.31
 1-16 = 40.97

Two spots at TC >= -9 (Optimal TC for a spread 1-16)

 1- 8 = 26.01
 1-12 = 35.27
 1-16 = 40.98

Two spots at TC >= -10

 1- 8 = 25.91
 1-12 = 35.22
 1-16 = 40.97

Sincerely,
Cac

Continuing with the previous analysis, in this case I have added a player at first base.
In the second position is the CAC2 player who can use the third position for the two-spot game.
The results have been very interesting as the optimal TCs moved upwards,
although they still remain in negative territory.

1) One spot ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  17.61  11.582
 1 - 12  24.19  10.383
 1 - 16  28.27   9.248

2) Two spots ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  25.75   8.424
 1 - 12  35.22   7.518
 1 - 16  41.08   6.673

3) Two spots at TC >= 0

 spread  score    unit
 ---------------------
 1 -  8  29.66  10.755
 1 - 12  36.94   9.090
 1 - 16  41.22   7.849

4) Two spots at TC >= -1 (Optimal TC for a spread 1-8)

 spread  score    unit
 ---------------------
 1 -  8  29.71  10.420
 1 - 12  37.40   8.885
 1 - 16  41.95   7.695

5) Two spots at TC >= -2 (Optimal TC for a spread 1-12)

 spread  score    unit
 ---------------------
 1 -  8  29.38  10.027
 1 - 12  37.47   8.644
 1 - 16  42.30   7.513

6) Two spots at TC >= -3 (Optimal TC for a spread 1-16)

 spread  score    unit
 ---------------------
 1 -  8  28.97   9.692
 1 - 12  37.39   8.431
 1 - 16  42.43   7.349

7) Two spots at TC >= -4

 spread  score    unit
 ---------------------
 1 -  8  28.50   9.404
 1 - 12  37.17   8.250
 1 - 16  42.40   7.208

8) Two spots at TC >= -5

 spread  score    unit
 ---------------------
 1 -  8  28.08   9.171
 1 - 12  36.93   8.102
 1 - 16  42.30   7.092

Enjoy!

Sincerely,
Cac

[8675309]

[QUOTE=Cacarulo;313588]

Continuing with the previous analysis, in this case I have added a player at first base.
In the second position is the CAC2 player who can use the third position for the two-spot game.
The results have been very interesting as the optimal TCs moved upwards,
although they still remain in negative territory.
[SIZE=2][FONT=courier new]

1) One spot ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  17.61  11.582
 1 - 12  24.19  10.383
 1 - 16  28.27   9.248

2) Two spots ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  25.75   8.424
 1 - 12  35.22   7.518
 1 - 16  41.08   6.673

3) Two spots at TC >= 0

 spread  score    unit
 ---------------------
 1 -  8  29.66  10.755
 1 - 12  36.94   9.090
 1 - 16  41.22   7.849

4) Two spots at TC >= -1 (Optimal TC for a spread 1-8)

 spread  score    unit
 ---------------------
 1 -  8  29.71  10.420
 1 - 12  37.40   8.885
 1 - 16  41.95   7.695

5) Two spots at TC >= -2 (Optimal TC for a spread 1-12)

 spread  score    unit
 ---------------------
 1 -  8  29.38  10.027
 1 - 12  37.47   8.644
 1 - 16  42.30   7.513

6) Two spots at TC >= -3 (Optimal TC for a spread 1-16)

 spread  score    unit
 ---------------------
 1 -  8  28.97   9.692
 1 - 12  37.39   8.431
 1 - 16  42.43   7.349

7) Two spots at TC >= -4

 spread  score    unit
 ---------------------
 1 -  8  28.50   9.404
 1 - 12  37.17   8.250
 1 - 16  42.40   7.208

8) Two spots at TC >= -5

 spread  score    unit
 ---------------------
 1 -  8  28.08   9.171
 1 - 12  36.93   8.102
 1 - 16  42.30   7.092

Enjoy!

Sincerely,
I am interested if this trend will continue when you keep adding players to the table until full.

[Cacarulo]

[QUOTE=8675309;313591]

Continuing with the previous analysis, in this case I have added a player at first base.
In the second position is the CAC2 player who can use the third position for the two-spot game.
The results have been very interesting as the optimal TCs moved upwards,
although they still remain in negative territory.
[SIZE=2][FONT=courier new]

1) One spot ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  17.61  11.582
 1 - 12  24.19  10.383
 1 - 16  28.27   9.248

2) Two spots ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  25.75   8.424
 1 - 12  35.22   7.518
 1 - 16  41.08   6.673

3) Two spots at TC >= 0

 spread  score    unit
 ---------------------
 1 -  8  29.66  10.755
 1 - 12  36.94   9.090
 1 - 16  41.22   7.849

4) Two spots at TC >= -1 (Optimal TC for a spread 1-8)

 spread  score    unit
 ---------------------
 1 -  8  29.71  10.420
 1 - 12  37.40   8.885
 1 - 16  41.95   7.695

5) Two spots at TC >= -2 (Optimal TC for a spread 1-12)

 spread  score    unit
 ---------------------
 1 -  8  29.38  10.027
 1 - 12  37.47   8.644
 1 - 16  42.30   7.513

6) Two spots at TC >= -3 (Optimal TC for a spread 1-16)

 spread  score    unit
 ---------------------
 1 -  8  28.97   9.692
 1 - 12  37.39   8.431
 1 - 16  42.43   7.349

7) Two spots at TC >= -4

 spread  score    unit
 ---------------------
 1 -  8  28.50   9.404
 1 - 12  37.17   8.250
 1 - 16  42.40   7.208

8) Two spots at TC >= -5

 spread  score    unit
 ---------------------
 1 -  8  28.08   9.171
 1 - 12  36.93   8.102
 1 - 16  42.30   7.092

Enjoy!

Sincerely,
I am interested if this trend will continue when you keep adding players to the table until full.

We'll have to wait and see if the trend persists, but I anticipate it will. Currently, I've included another player.
It's crucial to grasp that these simulations are quite expensive in terms of machine time. Adding each player drastically extends the duration.
My gut feeling suggests that as more players are involved, the burden of eating cards in negative counts is no longer solely on one player.
I believe that optimal TCs could potentially be consolidated into one. Of course, this is merely speculative.

Sincerely,
Cac

[Cacarulo]

Continuing with the previous analysis, in this case I have added a player at first base.
In the second position is the CAC2 player who can use the third position for the two-spot game.
The results have been very interesting as the optimal TCs moved upwards,
although they still remain in negative territory.

1) One spot ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  17.61  11.582
 1 - 12  24.19  10.383
 1 - 16  28.27   9.248

2) Two spots ALWAYS

 spread  score    unit
 ---------------------
 1 -  8  25.75   8.424
 1 - 12  35.22   7.518
 1 - 16  41.08   6.673

3) Two spots at TC >= 0

 spread  score    unit
 ---------------------
 1 -  8  29.66  10.755
 1 - 12  36.94   9.090
 1 - 16  41.22   7.849

4) Two spots at TC >= -1 (Optimal TC for a spread 1-8)

 spread  score    unit
 ---------------------
 1 -  8  29.71  10.420
 1 - 12  37.40   8.885
 1 - 16  41.95   7.695

5) Two spots at TC >= -2 (Optimal TC for a spread 1-12)

 spread  score    unit
 ---------------------
 1 -  8  29.38  10.027
 1 - 12  37.47   8.644
 1 - 16  42.30   7.513

6) Two spots at TC >= -3 (Optimal TC for a spread 1-16)

 spread  score    unit
 ---------------------
 1 -  8  28.97   9.692
 1 - 12  37.39   8.431
 1 - 16  42.43   7.349

7) Two spots at TC >= -4

 spread  score    unit
 ---------------------
 1 -  8  28.50   9.404
 1 - 12  37.17   8.250
 1 - 16  42.40   7.208

8) Two spots at TC >= -5

 spread  score    unit
 ---------------------
 1 -  8  28.08   9.171
 1 - 12  36.93   8.102
 1 - 16  42.30   7.092

Enjoy!

Sincerely,
Cac

Continuing with the previous analysis, in this case I have added two players,
one in the first position and another in the second. In the third position is the
CAC2 player who can use the fourth position for the two-spot game.

1) One spot ALWAYS

 spread  score   unit
 --------------------
 1 -  8  17.81 11.661
 1 - 12  24.39 10.432
 1 - 16  28.47  9.278

2) Two spots ALWAYS

 spread  score   unit
 --------------------
 1 -  8  26.02  8.489
 1 - 12  35.52  7.561
 1 - 16  41.40  6.712

3) Two spots at TC >= +1

 spread  score   unit
 --------------------
 1 -  8  31.82 11.576
 1 - 12  38.64  9.703
 1 - 16  42.60  8.283

4) Two spots at TC >= 0 (Optimal TC for a spread 1-8)

 spread  score   unit
 --------------------
 1 -  8  31.87 11.072
 1 - 12  39.24  9.317
 1 - 16  43.56  8.012

5) Two spots at TC >= -1 (Optimal TC for a spread 1-12)

 spread  score   unit
 --------------------
 1 -  8  31.56 10.717
 1 - 12  39.31  9.076
 1 - 16  43.87  7.851

6) Two spots at TC >= -2 (Optimal TC for a spread 1-16)

 spread  score   unit
 --------------------
 1 -  8  30.96 10.297
 1 - 12  39.12  8.823
 1 - 16  43.96  7.652

7) Two spots at TC >= -3

 spread  score   unit
 --------------------
 1 -  8  30.26  9.934
 1 - 12  38.74  8.598
 1 - 16  43.80  7.479

8) Two spots at TC >= -4

 spread  score   unit
 --------------------
 1 -  8  29.55  9.608
 1 - 12  38.26  8.392
 1 - 16  43.50  7.318

Enjoy!

Sincerely,
Cac

[8675309]

Very good information. Thanks so much.

[Cacarulo]

Very good information. Thanks so much.

Stay tuned. I'm analyzing what happens when there are already three players seated at the table.

Sincerely,
Cac

[DSchles]

You know it will only keep going in the same direction, right?. To stop and reverse wouldn't make any sense.

Don

[Cacarulo]

You know it will only keep going in the same direction, right?. To stop and reverse wouldn't make any sense.

Don

That's right, it will keep going in the same direction, but what I want to see is at what point the TC stops being negative or if,
by increasing the players, the three TCs converge into one. Just simple curiosity.

Sincerely,
Cac

[Cacarulo]

Continuing with the previous analysis, in this case I have added two players,
one in the first position and another in the second. In the third position is the
CAC2 player who can use the fourth position for the two-spot game.

1) One spot ALWAYS

 spread  score   unit
 --------------------
 1 -  8  17.81 11.661
 1 - 12  24.39 10.432
 1 - 16  28.47  9.278

2) Two spots ALWAYS

 spread  score   unit
 --------------------
 1 -  8  26.02  8.489
 1 - 12  35.52  7.561
 1 - 16  41.40  6.712

3) Two spots at TC >= +1

 spread  score   unit
 --------------------
 1 -  8  31.82 11.576
 1 - 12  38.64  9.703
 1 - 16  42.60  8.283

4) Two spots at TC >= 0 (Optimal TC for a spread 1-8)

 spread  score   unit
 --------------------
 1 -  8  31.87 11.072
 1 - 12  39.24  9.317
 1 - 16  43.56  8.012

5) Two spots at TC >= -1 (Optimal TC for a spread 1-12)

 spread  score   unit
 --------------------
 1 -  8  31.56 10.717
 1 - 12  39.31  9.076
 1 - 16  43.87  7.851

6) Two spots at TC >= -2 (Optimal TC for a spread 1-16)

 spread  score   unit
 --------------------
 1 -  8  30.96 10.297
 1 - 12  39.12  8.823
 1 - 16  43.96  7.652

7) Two spots at TC >= -3

 spread  score   unit
 --------------------
 1 -  8  30.26  9.934
 1 - 12  38.74  8.598
 1 - 16  43.80  7.479

8) Two spots at TC >= -4

 spread  score   unit
 --------------------
 1 -  8  29.55  9.608
 1 - 12  38.26  8.392
 1 - 16  43.50  7.318

Enjoy!

Sincerely,
Cac

For this simulation, I placed three players located in the first, second, and third positions.
In the fourth position is the CAC2 player, who can take the fifth position to play the second hand.

1) One spot ALWAYS

 spread  score   unit
 --------------------
 1 -  8  18.07 11.767
 1 - 12  24.67 10.496
 1 - 16  28.77  9.335

2) Two spots ALWAYS

 spread  score   unit
 --------------------
 1 -  8  26.39  8.557
 1 - 12  35.92  7.614
 1 - 16  41.80  6.752

3) Two spots at TC >= +2

 spread  score   unit
 --------------------
 1 -  8  33.27 12.014
 1 - 12  40.01  9.965
 1 - 16  43.90  8.466

4) Two spots at TC >= +1 (Optimal TC for a spread 1-8)

 spread  score   unit
 --------------------
 1 -  8  33.71 11.912
 1 - 12  40.61  9.921
 1 - 16  44.60  8.450

5) Two spots at TC >= 0 (Optimal TC for a spread 1-12)

 spread  score   unit
 --------------------
 1 -  8  33.42 11.290
 1 - 12  40.87  9.483
 1 - 16  45.21  8.122

6) Two spots at TC >= -1 (Optimal TC for a spread 1-16)

 spread  score   unit
 --------------------
 1 -  8  32.90 10.924
 1 - 12  40.71  9.216
 1 - 16  45.29  7.958

7) Two spots at TC >= -2

 spread  score   unit
 --------------------
 1 -  8  32.05 10.486
 1 - 12  40.26  8.949
 1 - 16  45.11  7.753

Sincerely,
Cac

[LT Isaac]

What would happen if you play more than two spots, for example, four?


Sincerely,
Isaac

[Cacarulo]

For this simulation, I placed three players located in the first, second, and third positions.
In the fourth position is the CAC2 player, who can take the fifth position to play the second hand.

1) One spot ALWAYS

 spread  score   unit
 --------------------
 1 -  8  18.07 11.767
 1 - 12  24.67 10.496
 1 - 16  28.77  9.335

2) Two spots ALWAYS

 spread  score   unit
 --------------------
 1 -  8  26.39  8.557
 1 - 12  35.92  7.614
 1 - 16  41.80  6.752

3) Two spots at TC >= +2

 spread  score   unit
 --------------------
 1 -  8  33.27 12.014
 1 - 12  40.01  9.965
 1 - 16  43.90  8.466

4) Two spots at TC >= +1 (Optimal TC for a spread 1-8)

 spread  score   unit
 --------------------
 1 -  8  33.71 11.912
 1 - 12  40.61  9.921
 1 - 16  44.60  8.450

5) Two spots at TC >= 0 (Optimal TC for a spread 1-12)

 spread  score   unit
 --------------------
 1 -  8  33.42 11.290
 1 - 12  40.87  9.483
 1 - 16  45.21  8.122

6) Two spots at TC >= -1 (Optimal TC for a spread 1-16)

 spread  score   unit
 --------------------
 1 -  8  32.90 10.924
 1 - 12  40.71  9.216
 1 - 16  45.29  7.958

7) Two spots at TC >= -2

 spread  score   unit
 --------------------
 1 -  8  32.05 10.486
 1 - 12  40.26  8.949
 1 - 16  45.11  7.753

Sincerely,
Cac

To complete the study of when it is most convenient to play two hands, I have added this last simulation
in which I placed four players located in the first, second, third, and fourth positions. In the fifth
position is the CAC2 player, who can occupy the sixth position to play the second hand.
Clearly, the idea of this study can be used with other counting systems.
If I remember correctly, such a possibility exists in CVCX.

1) One spot ALWAYS
 
 spread  score   unit
 --------------------
 1 -  8  18.26 11.857
 1 - 12  24.89 10.572 
 1 - 16  28.99  9.393
 
2) Two spots ALWAYS
 
 spread  score   unit
 --------------------
 1 -  8  26.64  8.610
 1 - 12  36.18  7.648 
 1 - 16  42.06  6.779
 
3) Two spots at TC >= +3
 
 spread  score   unit
 --------------------
 1 -  8  34.41 12.290
 1 - 12  41.16 10.144
 1 - 16  45.04  8.621

4) Two spots at TC >= +2

 spread  score   unit
 --------------------
 1 -  8  34.78 12.278
 1 - 12  41.58 10.148
 1 - 16  45.50  8.615

5) Two spots at TC >= +1 (Optimal TC for a spread 1-8)

 spread  score   unit
 --------------------
 1 -  8  35.09 12.151
 1 - 12  42.03 10.076
 1 - 16  46.02  8.578

6) Two spots at TC >= 0 (Optimal TC for a spread 1-12 and 1-16)

 spread  score   unit
 --------------------
 1 -  8  34.53 11.446
 1 - 12  42.05  9.634
 1 - 16  46.43  8.249

7) Two spots at TC >= -1

 spread  score   unit
 --------------------
 1 -  8  33.81 11.061
 1 - 12  41.67  9.307
 1 - 16  46.26  8.031

8) Two spots at TC >= -2

 spread  score   unit
 --------------------
 1 -  8  32.87 10.608
 1 - 12  41.10  9.029
 1 - 16  45.95  7.821

Enjoy!

Sincerely,
Cac

[LT Isaac]

Invaluable

[Cacarulo]

Invaluable

It is, thank you!

Sincerely,
Cac