[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Will the real Bob Floyd please stand up

Posted By: Nack Ballard
Date: Saturday, 11 March 2017, at 6:50 p.m.

In Response To: Will the real Bob Floyd please stand up (Casper Van der Tak)

With 4 home boards covered on both sides, the fan - fan sequence only occurs 256/1296 times, less than 1/4. This means that the equity will be defined, because the increase in the cube value (redouble followed by redouble) is less than than the decrease in the weight of the sequence (256/1296).

[I assume you mean 4 points (not home boards).]

That may have been what Bill Kennedy had in mind, too, and it makes sense. The series is not divergent.

Tim's argument is that, divergent or not, as long as it is possible to get from any position that can be arrived at by perfect play (which includes the Smith-Jones position and almost certainly includes the Kennedy2 position currently under discussion), to a position that we all agree has undefined equity, such as the Kennedy1 position or Tanenbaum's position (with five-point boards on both sides), then any such position also has undefined equity.

In later posts, Tim (based on a suggestion by Tom Keith?) seems to be including any position that can be arrived at by LEGAL play (not just perfect play), because if equities are undefined, how can you ultimately prove that any play is better than another? It feels like a stretch, but it's hard to dispute. Anyway, even with upper/lower boundary arguments, not-too-terrible play may grant the same (or almost the same) latitude as legal play.

[I believe that any position that can be reached by perfect play can then re-reach the opening position by perfect play (at least I've never seen a case that contraindicates), so I would say that in a real sense those positions, and all normal-looking backgammon positions (and Smith-Jones is actually much closer to that end of the spectrum), are all under the same umbrella. That would also be the case if merely legal play is the criteria. In fact, even positions that can't be reached legally, such as Tim's five-point-boards position, find their way back to the opening position.]

That said, I think there's a huge difference between positions with a divergent repeat-redouble series (that directly have undefined equity), and those that merely have a chance to reach those anomalous positions. While it is fodder for a fun theoretical discussion, I would ignore the effect of undefined equity in any backgammon position that does not fall inside this slice of the pie that is so thin it could not be seen with the naked eye.

Nack

Messages In This Thread

 

Post Response

Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:

 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.