[Bug-gnubg] Bearoff database

[isambard mews]

I tried to recreate the bearoff database and noticed some differences which could be due to rounding, but already at position #47 there were some significant differences. My workings for position 47 are given below. Have I made a mistake in the calculation methodology?

Each section shows possible rolls, the best move from the roll, the cumulative probability of bearoffs for a given x number of rolls (these are divided by 36 at the end).

The last 2 lines show the divided by 36 number and the 16 bit hex representation. Below is also an extract from dumpbearoff for this position.

Position number : 47 (gnubg)

    0   100.000   0.000         n/a     n/a

    1     0.000   5.556         n/a     n/a

    2     0.000  68.673         n/a     n/a

    3     0.000  25.458         n/a     n/a

    4     0.000   0.313

Position number : 47 (my calc)

    0   100.000   0.000         n/a     n/a    

    1     0.000   5.556         n/a     n/a    

    2     0.000  67.825         n/a     n/a    

    3     0.000  26.308         n/a     n/a    

    4     0.000   0.313 

Make Bearoff Database

Position # 47: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

1,1: 

 17: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 20: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 22: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 0.361111 0.626543 0.012346 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 17 

1,2: 

 21: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 23: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 0.916667 2.007716 0.075617 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 21 

1,3: 

 17: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 20: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 1.638889 3.260802 0.100309 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 17 

1,4: 

 12: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 16: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 2.472222 4.421296 0.106481 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 12 

1,5: 

  6: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 14 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 11: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 3.972222 4.921296 0.106481 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  6 

1,6: 

  5: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 14 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 10: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 11: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 5.694444 5.199074 0.106481 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  5 

2,2: 

  9: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 29: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 6.638889 5.254630 0.106481 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  9 

2,3: 

 12: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 7.472222 6.415123 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 12 

2,4: 

 11: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 35: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 8.750000 7.137346 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 11 

2,5: 

 10: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 30: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 10.361111 7.526235 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 10 

2,6: 

  9: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 10: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 12.250000 7.637346 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  9 

3,3: 

  1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 14 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 13.250000 7.637346 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  1 

3,4: 

 30: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 34: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 13.527778 9.359568 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move: 30 

3,5: 

  9: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 29: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 15.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  9 

3,6: 

  8: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

  9: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 17.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  8 

4,4: 

  1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 14 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 18.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  1 

4,5: 

  8: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

 28: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 20.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  8 

4,6: 

  7: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

  8: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 0 22.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  7 

5,5: 

  0: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 1.000000 22.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  0 

5,6: 

  1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 14 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

  7: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 13 13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 1.000000 24.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  1 

6,6: 

  0: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Σ probs: 2.000000 24.416667 9.470679 0.112654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Best move:  0 

Final probs: 0 0.055556 0.678241 0.263074 0.003129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

Integer probs: 0 e39 ada1 4359 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0