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

BGonline.org Forums

Position of the Day 06-24-26 - You should know...

Posted By: Chuck Bower
Date: Wednesday, 1 July 2026, at 1:02 a.m.

In Response To: Position of the Day 06-24-26 - You should know... (Stick)

No, but maybe I can figure it out.

If the status quo is losing a gammon, how do wins trade with backgammons? A backgammon costs 1 extra (compared to a gammon) on a unit cube. A win gains 3. So if you can win 1 or more games for every 3 backgammons lost you will come out ahead by staying.

Assuming Blue stays, how does he win? Hitting, closing that checker out, and then bearing off 15 before White gets her one remaining checker off. Cubeless, with perfect checker distribution to start the bearoff, Blue wins right at 8.5%. Let's assume if Blue hits he can reach this perfect bearoff. (We can discuss the shortcomings of this assumption later.) So how likely is the hit?

As long as White rolls neither an ace nor doublets {2,3,4,5,6} Blue will get that shot and hit it 11/36. If he can pull all that off he'll get his 8.5% chances to win. (20/36)*(11/36)*8.5% = (220/1296)*8.5% ~ 0.17*8.5% ~ (1/6)*8.5% ~ 1.4%. So as long as he doesn't get bg'ed 3*1.4% = 5.2% he'll be better off staying.

There are multiple ways Blue can get bg'ed. Let's start with White's doublets (2,3,4,5,6} = 5/36 ~ 14%. We can stop here since 14% >> 5.2%.

As far as some things we left off, Blue owns the cube so he can gain by not playing the game to the bitter end (to get 8.5% GWC) but rather increase the stakes when an equity favorite or getting White to Pass when she still has winning chances. That's a (small) plus for Blue compared to the strawman just presented. However, Blue has yet to close his board (and could further get G'ed after hitting) nor has he acquired the perfect bearoff structure. I don't know how these counteract but my guess is overall this favors White, again by a small amount.

24/18

P.S. Is all of this in Bob Wachtel's In the Game Until the End two volume work? I need to dig into that but I'm guessing it is, or at least something that reaches the same conclusion.

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.