Hi all...

During training with XG occurred this position:


XGID=---AB-------------------c-:1:-1:1:61:10:17:3:0:10 It's ok mike?

The two questions are:

1) What's the best way to play 6-1, and why?
2) By how much in your opinion (in points, without rolling out the position lol) is the second move worse (more or less) than the correct one?

Obv the second question is far more interesting than the first one.

Gl

My spinal cord would play 4/off 3/2.
After the counter intuitive (and very likely wrong) 4/off 3/2 white has a double/take which complicate the equity calculation (it is possible to manually count every roll

After 6/0 3/2: 23 rolls will win the game (assuming White doesn't roll a double), which is around 64%.

After 6/0 4/3: 17 rolls win, around 47%.

So it's a huge error.

Question 1:

for bear-off

• Rule #1: always bear-off a checker if you can. Does not apply here
• Rule #2: spread out your checkers. So without even counting 3/2 is better than stacking with 4/3

There is one exception to rule 1 and 2: if you are far behind in the bear-off you need to maximize your winning doubles, this often mean stacking on a point to get the extra double. it does not applies here

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Question 2:

1. After 4/off 3/2: You cannot bear off the remain checker with any roll with a 1 and also 32. that's 13 rolls
2. After 4/off 4/3: you cannot bear off with any roll with a 1 or a 2 (20 rolls) except 22, so 19 rolls are bad.

for the cubeless equities, first you see that opponent win 1/6 time with a double. so the respective winning chances are

1. W1= 5/6*(36-13)/36 = 53.24%
2. W2= 5/6*(36-19)/36 = 39.35%

Your question just ask the difference, in that case there are 6 roll difference between 1 and 2. so dW=5/6*6/36=5/36=13.9%. (note: to calculate that OTB remember 6/36=16.7% and each 1/36 is 2.8%)

So the stacking play lose a whopping 13.9% of winning chance.

Now cubeful: pretty easy in that case. After play 1, opp cannot cube, after play 2 he will and you will not redouble if he does not win as you are only 17/36 favorite.

1. E1= W1-(1-W1) = 2W1-1 = 0.065
2. E2= (2W2-1)*2= -0.426

So the bad move loses almost 0.5 point of normalized equity (1 full point as the cube is at 2)... Remembering rule #2 of bear-off pays off

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These calculation are not important for the checker play, but for the upcoming double after 4/3, they are, so it is good thing to practice these.

Black to Play 5-2

XGID=----A-A------------a-a----:0:0:1:52:0:0:0:0:10

I have more than 15,000 positions like this one where your Rule #1 does not apply. Of course, there are over 54,000 different bear-off positions, and 21 different rolls that might come up in each one, so 15,000 is a very small number of exceptions.

Your rules handle the overwhelming majority of cases very well!

More more such positions, see:
http://forumserver.twoplustwo.com/13...44/index2.html

Mike

For the record:

After playing a long session with good PR this was the last game, and I played 4/0 4/3 trying to maximize doubles, but missing completely the point well exposed by extreme gammon (the 2+2 user).

After that XG doubled, and I went wrong another time: I thought that any double would have win instantly the game for the bot, and even in the case of normal roll I would still have 2 missing number, completely forgetting about the fact that I could double myself. So I dropped its cube.

After analyzing the game, I was surprised because I thought that the error would be small. The PR was horrible: 29 (casual player).

MORAL: write 100 time "I will study backgammon endgames"

You can't double because you are still an underdog. But you can still take the double because you win more than 25%.

yes, but I should have thought about that, and I didn't. I simply played automatically because one think that during bearoff nothing special can happen.

During my first times in BG, reading books, I laughed at top player's warning about studying endgames and 2 checkers cube action and so on... Now I learned that the more you play the more that positions occur.

Instructive thread! I like it.