Hi Nack, I'll try to clarify.
Here is the original position:
| White | 6 |
|---|---|
| |
| Blue | 1 |
| GNUBg Id: IAAABAAAAAAAAA:MAGgAQAAAAAA XGID=-A-----------------a------:0:0:-1:00:0:0:0:13:16 | |
Many players would see this as a 25% position and take. I wondered what Blue's MWC would be (compared to taking the cube) if Blue passed not only this 13a13a cube, but also every similar cube at 13a12a, 13a11a, 13a10a, etc. for 8 consecutive games IF the same situation arose. At 0-8/13 Blue's MWC would be about 14%. If Blue took all 8 cubes, on average he would win 2 and lose 6 with the cube on 2. At 4-12/13 Blue's MWC is less than 6%, so I asked the question - Why not pass? (i.e., why not pass the first cube and the next seven cubes IF they are similar to the first cube). Several players have taken issue with my methodology, but the tables linked by Michael https://drive.google.com/open?id=0B7L6em2ChhMOTFY4SDFmampJcTA confirm that all 8 cubes should be passed.
To answer your specific questions, (1) Blue is not guaranteed that the same position will arise ever again. If this position comes up in the first game of the 13 point match, Blue must drop. If it comes up at 13a12a, Blue must drop. If it comes up at any 13a score through 13a6a Blue must drop. (2) Blue is free to take or drop any of the cubes, but it would be foolish to take, as shown in Michael's tables. (3) Most of the dispute about my methodology concerns my statement that ON AVERAGE Blue will win 2 times out of 8 in the 25% position. The fact that Blue could be lucky and win 6 or 7 out of 8 is irrelevant. What is relevant is that at 13a13a, 13a12a, etc. down to 13a6a Blue's best choice is to drop when doubled in this particular situation.