4 for 2

[wintom]

You are too lazy to make endless calculations over the board? You
don't want to memorize huge tables that you will need only a very few
times? But what will you do in a position like this?

GNU Backgammon Position ID: YAAAAAMAAAAAAA
Match ID : QYkEAAAAAAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg (Cube: 2)
| | | O | OOO 0 points
| | | O | OOO
| | | | OOO
| | | | OO
| | | | OO
v| |BAR| |
| | | | XX
| | | | XX
| | | | XXX
| | | X | XXX Rolled 11
| | | X | XXX 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: wintom
Pip counts: O 12, X 12

For these two-chequer positions you only have to memorize the following
four rules:
1. Avoid to leave the two chequers on the same point.
2. If you can bear off one of the chequers, that's what you are
supposed to do.
3. If you cannot bear off one chequer then put one chequer on the
5-point.
4. If you cannot put a chequer on the 5-point put one on the 4-point.

If you have a good look at one of those probability tables you will
find out that in doubt a combination where there is a chequer on the
5-point is always best. There are only two exceptions: when you have to
decide between 3-2 and 4-1 or when the decision is 6-1 or 4-3. In both
cases the one with a chequer on the 4-point is better.

Applying this to the position noted above we now know that 6/5 6/3 is
the best move.

This concept is also useful for the bear-in.

Comments welcome,
Thomas Koch

[robadams]

I think one should memorize the 2 checker positions. Your rules
wouldn't help you play a 2,1 from that position correctly for instance.

with 4 pips, 3,1 is better than 2,2

with 5 pips, 4,1 is better than 3,2

with 6 pips 5,1 and 4,2 are equal and better than 3,3

with 7 pips, 5,2 is better than 4,3 is better than 6,1

with 8 pips 5,3 is better than 6,2 is better than 4,4

with 9 pips 6,3 is better then 5,4

with 10 pips 6,4 is better than 5,5

That's about it. Not a huge chart.

[wintom]

robadams wrote:
> I think one should memorize the 2 checker positions. Your rules
> wouldn't help you play a 2,1 from that position correctly for instance.

As far as I know there are 10 combinations for 6,3 and 10 combinations
for 5,4 so my rules would not be mistaken. To move 6/5 6/4 would be ok.

> with 9 pips 6,3 is better then 5,4

Though there is an equal number of combinations that bear off on the
next roll there is a slight difference on the second roll: If you move
to 6,3 even if you throw 21 there will be only one chequer left wich
makes bearing off easier at that state (as stated in the second rule).
That is the reason why 6,3 is supposed to be slightly better. A rollout
with gnubg showed that the difference in equity is 0.003. Rather small.
But thanks for pointing this out. I hadn't realized it before.

> That's about it. Not a huge chart.

Oh, for me that's big enough. You don't know how bad my brain works
sometimes ;-) I guess I will stick to my rules loosing an equity of
0.003 in one of about 20 cases or I will just remember 6,3 as an
exception :-/ But I understand, that this might disqualify my rules for
common use :-(

Thanks anyway!
Thomas Koch

[neilkaz]

If I may chime in with the Rule I have used for 30 years, and I
certainly cannot take credit for it as it is so simple that I doubt I
and the founder.

Rule of 2 or 3..." Play to have your last two pieces two or three pips
apart and if that is not possible have them as close to 2 or 3 as
possible"

ie..with 7 pips..43 (one apart) is closer to 2 than 61 (5 apart) is to
three.

Note that there is no difference between 42 (2 apart) and 51 (4 apart)

The rule can be amended to 2.5 but why bother ? .. neilkaz ..

[wintom]

Simple! Works! Perfect!

Why didn't I ask the pros in the first place ;-)

Thanks!!

Thomas Koch