| |
BGonline.org Forums
Example of play prediction method
Posted By: Rick Janowski In Response To: Gammon Go (GG) and Gammon Save (GS) Considerations (Rick Janowski)
Date: Friday, 17 May 2013, at 9:00 a.m.
Here I will try to provide an example of the proposed methodology for predicting correct checker play at post-Crawford scores, in this case for the opening 32, using rollout data from the opening book:
GG+ = 32D (S28.2). So GG+ margin = 0.0282
GS- = 32S (D31.9). So GS+ margin = 0.0319
Play Aggression Index (PAI) = GG+ margin / GS+ margin = 0.79. As this is less than 1.2, the GS+ play, 32S, should be correct at most even match scores, which is correct.
If we define A as the points needed by the player on roll and B has the points needed by the opponent, and the ratio, B/A as R. From calibration of XG++ evaluations for opening rolls the following formula was derived for PAI values less than 1.2:
R = 0.92*PAI^0.67. Where PAI = 0.79, R = 0.79 too.
We can check this against known rollouts at 8 away scores (carried out by Dmitriy). Where the player on roll needs 8 points to win (A =8), the score where the plays switch from GG+ to GS+ is where the opponent needs A*R points, in this case 6.3. So, at 8 away 6 away 32D is predicted as the correct play but at 8 away 7 away the correct play is predicted to be 32S. The actual rollout results are as follows:
At 8away, 4 away, 32D is correct by a margin of 0.001
At 8away 5 away, 32D and 32S are equally strong (ie, no margin)
At 8 away 6 away and 8 away 7 away, 32S is correct with margins of 0.001 and 0.003 respectively.
So the prediction of the switch-point is wrong by one place, but the error of 0.001, is negligible.
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.