Backgammon Boot Camp Discussion

Duplication and Diversification

Posted on October 29, 2009 by wrwomack

Between my daughter’s wedding and the SHG dice issue I have not been posting much on the subject of Backgammon Boot Camp. Of course I have also not been getting very far with the book. Hopefully I will get back on track now, and I will start with a rather simply post.

Neither duplication or diversification are difficult concepts to grasp. The real difficulty seems to come in seeing and applying them in the course of a game. It seems the other clear warning, from Trice and others as well, is not to go “duplication happy.” I am thinking that the best way to do this is to follow the general rule that you should not make a play simply because of duplication. However, if you are either stuck with having to leave blots, or have a play that has several advantages but presents some risk than duplication can be very helpful.

There are some articles on duplication at http://www.bkgm.com/articles/page03.html#duplication, I think the one by Kit Woolsey is the most helpful.

Gaining Time Part 3

Posted on October 17, 2009October 17, 2009 by wrwomack

Positions 2-19 and 2-20 present two varaitions of a position. In the first position the best move is to forego the loose hit and make the 16 point. Trice gives two reasons for not hitting. One is that blue’s position does not need consolidating, the other is that blue position is not likely to become significantly stronger than it already is. It seems to be that blue would very much like to make another home board in this position, but this does not give blue that much greater of an advantage. I thought part of the reason that bar/16 was the better play in this position might be making the 16 point. But as the rollout shows 16/11 also comes out ahead.

+-24-23-22-21-20-19-+---+-18-17-16-15-14-13-+

+--1--2--3--4--5--6-+---+--7--8--9-10-11-12-+

Pip counts: Blue 139, Red 165
Position ID: hnOOAyBsOwDhRA Match ID: cAkWAAAAAAAA

• Red moves bar/16

Ply

Move

Equity

•

bar/16

-0.212

0.439	0.117	0.004	–	0.561	0.099	0.003	-0.103	-0.212
0.002	0.001	0.000	–	0.002	0.001	0.000	0.005	0.011

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/21 16/11

-0.227 ( -0.015)

0.437	0.124	0.004	–	0.563	0.122	0.004	-0.124	-0.227
0.002	0.002	0.000	–	0.002	0.002	0.000	0.005	0.013

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/21 6/1*

-0.251 ( -0.039)

0.439	0.124	0.004	–	0.561	0.147	0.005	-0.147	-0.251
0.002	0.002	0.000	–	0.002	0.002	0.000	0.006	0.014

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

The next position is 2-20, this is followed by the positions that Trice mentions but does not show.

Pip counts: Blue 132, Red 165
Position ID: DeeMCSBsOwDhRA Match ID: cAkWAAAAAAAA

• Red moves bar/16

Cube decision
2-ply cubeless equity		+0.288
Cubeful equities:
1.	No double	+0.404
2.	Double, pass	+1.000	+0.596
3.	Double, take	+0.290	-0.114
Proper cube action:		No double, take (16.0%)

Ply

Move

Equity

•

bar/21 6/1*

+0.340

0.567	0.239	0.013	–	0.433	0.144	0.005	+0.236	+0.340
0.002	0.002	0.001	–	0.002	0.002	0.001	0.006	0.016

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/16

+0.144 ( -0.196)

0.523	0.185	0.008	–	0.477	0.114	0.003	+0.124	+0.144
0.002	0.002	0.001	–	0.002	0.001	0.000	0.005	0.012

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/21 16/11

+0.003 ( -0.338)

0.498	0.173	0.009	–	0.502	0.160	0.005	+0.013	+0.003
0.002	0.002	0.001	–	0.002	0.001	0.000	0.005	0.013

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

Pip counts: Blue 130, Red 165
Position ID: DeeMAyBsOwDhRA Match ID: cAkWAAAAAAAA

• Red moves bar/16

Ply

Move

Equity

•

bar/21 6/1*

-0.042

0.483	0.154	0.007	–	0.517	0.147	0.004	-0.026	-0.042
0.002	0.002	0.000	–	0.002	0.002	0.001	0.006	0.014

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/21 16/11

-0.085 ( -0.044)

0.474	0.152	0.006	–	0.526	0.146	0.004	-0.043	-0.085
0.002	0.002	0.000	–	0.002	0.001	0.000	0.005	0.013

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/16

-0.095 ( -0.053)

0.466	0.140	0.005	–	0.534	0.122	0.003	-0.047	-0.095
0.002	0.002	0.000	–	0.002	0.002	0.000	0.005	0.013

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

Pip counts: Blue 141, Red 165
Position ID: hnOOCSBsOwDhRA Match ID: cAkWAAAAAAAA

• Red moves bar/16

Alert: doubtful move ( -0.044)

Ply

Move

Equity

bar/21 6/1*

+0.049

0.503	0.192	0.009	–	0.497	0.143	0.006	+0.059	+0.049
0.002	0.002	0.001	–	0.002	0.002	0.001	0.006	0.014

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

•

bar/16

+0.004 ( -0.044)

0.485	0.155	0.005	–	0.515	0.096	0.003	+0.031	+0.004
0.002	0.002	0.001	–	0.002	0.001	0.000	0.005	0.012

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/21 16/11

-0.217 ( -0.265)

0.444	0.133	0.006	–	0.556	0.135	0.005	-0.114	-0.217
0.002	0.002	0.001	–	0.002	0.002	0.000	0.005	0.013

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871966697 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

Gaining Time (Part 2)

Posted on October 11, 2009October 11, 2009 by wrwomack

For me making the right play in a position like 2-18 is hard because leaving the blot just seems “wrong.” Understanding the big picture and to what you are accomplishing with a play goes a long way in helping to overcome that. The position Trice gives is:

Pip counts: Blue 139, Red 158
Position ID: 4LuFAyCMx+EBUA Match ID: cIkVAAAAAAAA

I am not sure what I would have done in this position before reading Trice. You are going to have to create another blot here no matter what, so I would have probably gone with bar/22 13/8 or bar/20 13/10 trying to leave as few direct shots as I could.

I explored some variations on this position to try and determine when to hit or not hit. One of the problems with doing this from this position is that it is easy to end up with positions where the reason for hitting or not hitting is something other than gaining time. However I found the differences in the following two positions interesting.

Pip counts: Blue 119, Red 155
Position ID: bLuBAyCM5+ABUA Match ID: cInmAGAAMAAA

• Red moves bar/24 6/1*

Ply

Move

Equity

bar/24 13/8

-0.619

0.191	0.029	0.002	–	0.809	0.369	0.102	-0.619	-0.619
0.002	0.002	0.001	–	0.002	0.007	0.005	0.005	0.005

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871233900 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

•

bar/24 6/1*

-0.637 ( -0.018)

0.182	0.025	0.001	–	0.818	0.445	0.144	-0.637	-0.637
0.003	0.002	0.000	–	0.003	0.008	0.007	0.005	0.005

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 871233900 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

bar/24 8/3

-0.643 ( -0.024)

0.179	0.027	0.002	–	0.821	0.390	0.102	-0.643	-0.643
0.003	0.003	0.001	–	0.003	0.010	0.008	0.006	0.006

Full cubeful rollout with var.redn.

648 games, Mersenne Twister dice gen. with seed 871233900 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 2-ply cubeful prune [world class]

The above was my attempt to answer the question about whether or not the hit was still correct if blue had a more closed board. In this position hitting loses to 13/8, but only by a small amount. But the issue does not seem to be just the closed board but the threat blue has to make another point. If you move 3 checkers back so that blue is not as likely to make another home board point in the next couple of rolls then the hit comes out on top. In both cases however the equities between the two moves is very close, a longer or world class rollout could well give different results. So hitting in either case would not be a particular bad move.

Pip counts: Blue 131, Red 155
Position ID: bBuaAyCM5+ABUA Match ID: cInmAGAAMAAA

Ply

Move

Equity

•

bar/24 6/1*

-0.538

0.231	0.054	0.005	–	0.769	0.413	0.145	-0.538	-0.538
0.003	0.003	0.001	–	0.003	0.007	0.007	0.005	0.005

bar/24 13/8

-0.540 ( -0.002)

0.230	0.058	0.005	–	0.770	0.379	0.086	-0.540	-0.540
0.002	0.003	0.001	–	0.002	0.007	0.005	0.005	0.005

bar/24 8/3

-0.576 ( -0.038)

0.212	0.051	0.003	–	0.788	0.398	0.103	-0.576	-0.576
0.003	0.003	0.001	–	0.003	0.007	0.006	0.006	0.006

Gaining Time (Part 1)

Posted on October 4, 2009October 4, 2009 by wrwomack

Position 2-17 and the related discussion covers some of the opening replies where hitting deep in your home board is the best – or at least a very good – play. These types of positions are an exception to the usual rule of not burying a checker. The real question for us lower level players is when to decide if this is the right play?

Pip counts: Blue 159, Red 167
Position ID: 4HPkQSDgc/ABMA Match ID: cAkWAAAAAAAA

The “automatic” play here is 24/20 13/8, but as Trice points out there is an issue with this. With blue bringing the checker down to the 14 point 61 and 66 now make the 20 point for blue on the red blot in addition to 31 that would normally make this point. Any 6, 3, or 1 can slot the 20 point for blue and that would be the likely play for most of the rolls. So by hitting on the ace red reduces the rolls that point on the 5 to 11 and 33.

There are a couple of other opening reply positions that Trice says should be played with the deep hit. These are:

Pip counts: Blue 157, Red 167
Position ID: 4HPhQSDgc/ABMA Match ID: cAkVAAAAAAAA

This creates a similar situation to 2-17, in this case with the checker on the 22 there are a number rolls that make the 22 point on top of red. 24/22 6/1* is the best play here by quite a bit according to a quick gnubg rollout.

The other position Trice mentions for the deep hit is:

Pip counts: Blue 162, Red 167
Position ID: 4HPhASjgc/ABMA Match ID: cIkRAAAAAAAA

And a short rollout of this position supports Trice’s statement that 6/2* 24/21 is likely the best play here.

I was curious if Trice really had all of the opening replies where the deep hit was best. I used Timothy Chow’s handy table of opening replies (http://www-math.mit.edu/~tchow/2ndmove.shtml) to look for others and found

Pip counts: Blue 158, Red 167
Position ID: 4HPiQSDgc/ABMA Match ID: cAkVAAAAAAAA

• Red moves 24/22 6/1*

This is a little different than the positions above because the split to the 22 in this position is not as likely to be pointed on as in the positions Trice mentions. The table gives two possible plays here the hit and 24/22 13/8. This is not one of the replies rolled out in the BGONLINE positions so these moves would be based on GNUBG 4-ply, which does give a nod to the hitting play.

I did a much larger rollout of the two options than I normally would to see if this move held up to closer scrutiny. The conclusion is that the 13/8 play came out with a slight edge, but the equity difference is so small that the hit on the ace point is certainly a viable option and depending upon your style might be well worth considering.

Ply

Move

Equity

24/22 13/8

-0.208

0.447	0.108	0.004	–	0.553	0.137	0.006	-0.136	-0.208
0.001	0.001	0.000	–	0.001	0.001	0.000	0.002	0.005

Full cubeful rollout with var.redn.

5004 games, Mersenne Twister dice gen. with seed 870508992 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

•

24/22 6/1*

-0.217 ( -0.009)

0.445	0.114	0.004	–	0.555	0.139	0.007	-0.138	-0.217
0.001	0.001	0.000	–	0.001	0.001	0.000	0.002	0.006

Full cubeful rollout with var.redn.

5004 games, Mersenne Twister dice gen. with seed 870508992 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

13/8 6/4

-0.196 ( +0.011)

0.446 0.114 0.003 – 0.554 0.149 0.007

2-ply cubeful prune [world class]

13/11 6/1*

-0.234 ( -0.026)

0.439 0.123 0.004 – 0.561 0.166 0.010

2-ply cubeful prune [world class]

13/11 13/8

-0.249 ( -0.042)

0.432 0.114 0.003 – 0.568 0.159 0.007

2-ply cubeful prune [world class]

Bringing It Home (Part 2)

Posted on September 25, 2009September 25, 2009 by wrwomack

The following position is not from Trice but fits will with the subject of the this chapter and is a point well worth exploring.

Pip counts: Blue 142, Red 76
Position ID: 2O4GABzZ3TYAAA Match ID: cInoAGAAMAAA

The “obvious” play with this is 8/7 8/6, clearing form the back of the prime and avoiding gaps. The problem with this play is that it creates an issue with clearing reds bar point. The big problem are 5’s, which would have to be played form the 6 point leaving a gap in the home board. If the 6 point is cleared before the bar point 5’s than have the potential to force red to leave a blot on the bar point.

While 7/5 7/6 leaves a gap on the bar point it allows much more flexibility in this position. This problem is an example of looking for problem numbers in the bear in and playing to minimize their impact. It comes from an article by Kit Woolsey that discusses this topic with several other examples. The article may be found at http://www.bkgm.com/articles/GOL/Nov02/safe.htm.

Bringing It Home (Part 1)

Posted on September 21, 2009September 25, 2009 by wrwomack

Whenever I am getting to the end of the game with my opponent still having checkers back I am never really sure that I am playing things right. That is where the chapter on Bringing It Home comes in. One of my issues was to simply rush into my home board and then try to bear off from there. Trice’s examples of playing to allow for the big doubles has already helped me in these positions and I am sure that as I work through more examples of the end game I will get better at seeing the potential problems in these kinds of positions and hopefully avoiding them much more often.

The other situations are those like Trice illustrates in position 2-16. The loose hit in positions like this feels really risky, so it takes some study to realize that hitting is often the right play in these positions.

The position below presents a similar situation as 2-16, but in analyzing it I came up with a couple of interesting things.

Pip counts: Blue 134, Red 73
Position ID: bDuJAUiz3TkAAA Match ID: cAnxAGAAMAAA

Unlike 2-16 at DMP in this position the correct play is not to hit, but to make a safe play 8/4 5/3 coming out on top (although 8/2* only gives up a little over 0.01 equity so it is hardly a terrible choice).

As you would expect at 2-away 1-away Crawford 8/2* becomes the clear choice because it gives more gammon chances giving red a better chance to win the match without another game.

What I found surprising was the results at 3-away 1-away. I expected the answer to be the same as DMP because a gammon does not really gain anything for red since if they have to win two games anyway. One though I had on this is that the possibility of a backgammon is what drives the play in this situation. However, even at 0-0 in a 7 point match the hit comes out ahead. I found this even more surprising. Looking at the equities in the rollouts this position demonstrates the complexity of match play and the differences that can occur depending upon the match score. Getting into the details of this is getting quite a bit ahead of ourselves, but it is something to keep in mind.

Without getting to wrapped up in the details my take away from this is that I should consider hitting the blot in these situations a lot more than I would have in the past. Even if it is wrong as a DMP it is not wrong by that much. Of course, I am sure that I now run the risk of over generalizing this and hitting when I should not. That will take more learning.

Rollouts

DMP

Ply

Move

Equity

8/4 5/3

+0.747

0.874	0.682	0.046	–	0.126	0.007	0.000	+0.747	+0.747
0.002	0.012	0.005	–	0.002	0.002	0.000	0.004	0.004

8/6 8/4

+0.746 ( -0.001)

0.873	0.706	0.044	–	0.127	0.004	0.001	+0.746	+0.746
0.002	0.011	0.005	–	0.002	0.001	0.000	0.004	0.004

8/4 6/4

+0.739 ( -0.008)

0.870	0.668	0.047	–	0.130	0.004	0.000	+0.739	+0.739
0.002	0.011	0.005	–	0.002	0.001	0.000	0.004	0.004

•

8/2*

+0.733 ( -0.014)

0.866	0.757	0.029	–	0.134	0.023	0.001	+0.733	+0.733
0.002	0.009	0.004	–	0.002	0.003	0.000	0.004	0.004

8/6 5/1

+0.661 ( -0.087)

0.830	0.623	0.042	–	0.170	0.010	0.001	+0.661	+0.661
0.002	0.012	0.005	–	0.002	0.002	0.000	0.005	0.005

2-away, 1-away Crawford

Ply

Move

Equity

•

8/2*

+2.161

0.867	0.713	0.048	–	0.133	0.017	0.000	+2.161	+2.161
0.002	0.003	0.005	–	0.002	0.003	0.001	0.009	0.009

8/6 8/4

+1.880 ( -0.281)

0.867	0.573	0.037	–	0.133	0.007	0.000	+1.880	+1.880
0.002	0.003	0.004	–	0.002	0.003	0.000	0.008	0.008

8/4 5/3

+1.851 ( -0.310)

0.874	0.552	0.027	–	0.126	0.010	0.000	+1.851	+1.851
0.002	0.004	0.003	–	0.002	0.002	0.000	0.008	0.008

8/4 6/4

+1.808 ( -0.353)

0.873	0.531	0.033	–	0.127	0.011	0.000	+1.808	+1.808
0.002	0.004	0.004	–	0.002	0.002	0.000	0.008	0.008

8/6 5/1

+1.664 ( -0.498)

0.837	0.495	0.023	–	0.163	0.017	0.000	+1.664	+1.664
0.002	0.004	0.003	–	0.002	0.002	0.000	0.009	0.009

3-away 1-away Crawford

Ply

Move

Equity

•

8/2*

+0.809

0.861	0.705	0.021	–	0.139	0.023	0.001	+0.809	+0.809
0.002	0.003	0.002	–	0.002	0.003	0.000	0.006	0.006

8/4 5/3

+0.798 ( -0.011)

0.873	0.578	0.008	–	0.127	0.006	0.000	+0.798	+0.798
0.002	0.004	0.001	–	0.002	0.003	0.000	0.004	0.004

8/6 8/4

+0.794 ( -0.015)

0.869	0.601	0.009	–	0.131	0.006	0.001	+0.794	+0.794
0.002	0.004	0.001	–	0.002	0.001	0.000	0.004	0.004

8/4 6/4

+0.788 ( -0.021)

0.869	0.560	0.007	–	0.131	0.007	0.000	+0.788	+0.788
0.002	0.004	0.001	–	0.002	0.001	0.000	0.004	0.004

8/6 5/1

+0.702 ( -0.107)

0.830	0.518	0.005	–	0.170	0.011	0.001	+0.702	+0.702
0.002	0.004	0.001	–	0.002	0.002	0.000	0.005	0.005

0-0 to 7

Ply

Move

Equity

•

8/2*

+1.545

0.861	0.715	0.019	–	0.139	0.015	0.001	+1.556	+1.545
0.002	0.003	0.002	–	0.002	0.001	0.000	0.007	0.011

8/4 5/3

+1.456 ( -0.089)

0.867	0.559	0.009	–	0.133	0.008	0.000	+1.385	+1.456
0.001	0.003	0.001	–	0.001	0.000	0.000	0.005	0.007

8/4 6/4

+1.434 ( -0.111)

0.864	0.537	0.009	–	0.136	0.008	0.000	+1.351	+1.434
0.001	0.003	0.001	–	0.001	0.000	0.000	0.005	0.008

8/6 8/4

+1.391 ( -0.154)

0.868	0.574	0.010	–	0.132	0.005	0.000	+1.408	+1.391
0.002	0.003	0.001	–	0.002	0.000	0.000	0.006	0.010

8/6 5/1

+1.319 ( -0.226)

0.826	0.494	0.008	–	0.174	0.010	0.000	+1.224	+1.319
0.002	0.003	0.001	–	0.002	0.000	0.000	0.006	0.009

Staying Connected

Posted on September 17, 2009September 17, 2009 by wrwomack

At this point I don’t have any positions to discuss on this topic. The positions in Trice seem pretty self explanatory and I am not sure at this point that I can correctly apply this concept to a match position for discussion. I have, however, after reading this chapter been attempting to keep the whole concept of connectivity in mind during actual play. I will come back to this subject when I feel like I have something more to add.

Premature Burial

Posted on September 10, 2009September 13, 2009 by wrwomack

The concepts in this chapter are fairly easy to grasp, I think for us lower level players there are really two issues we have to come to grips with when dealing with this topic, one is the fear of leaving a blot or blots and the other is knowing when to make an exception to the general rule and place a checker on the one or two point.

Pip counts: Blue 157, Red 167
Position ID: 4HPhQSDgc/ABMA Match ID: cAkVAAAAAAAA

Hits in the home board are sometimes an exception to the premature burial rule. In the above position I would be inclined to play 13/8 24/22 or 13/8 13/11 to avoid burying a checker on the ace point. However a rollout (648 games, expert) gives the best play as 5/1* 24/22 followed by 5/1* 13/11.

Game Plan

Posted on September 6, 2009 by wrwomack

This is another of those areas where the real trick for me at least is learning to think in terms of a game plan as the game progresses. I often find myself making a move that seems right only to realize that I have created some long term issues for myself. I think this is often due to failing to make the play with a view to an overall game plan. For example in position 2-1 I might well have continued to try a priming approach without really thinking about the long term problems with that play. Hopefully I will begin to think in terms of a game plan when playing in the future.

For further study on game plans Gammon Life has a series of articles by Mary Hickey devoted to the topic of game plans. You can find them at http://www.gammonlife.com/writers/maryhickey.htm.

There are also several articles by Walter Trice that deal with game plan issues on the same site http://www.gammonlife.com/writers/waltertrice.htm.

To Hit or Not to Hit (Part 3)

Posted on September 5, 2009September 5, 2009 by wrwomack

Positions 1-30 through 1-33 illustrate the 6 criteria Trice discusses for deciding between safe and bold plays. I find that remembering “boards, backs, blots, anchors” is a good way to keep in mind what needs to be considered in these situations. The real trick is remember to apply this criteria in the course of play. One of the the things I am struggling with right now is making sure I am thinking about all of this in the course of a match. Position 1-30 is really close, so playing the hit while not the best move is not a devastating error.

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Ply

Move

Equity

•

15/13 6/5

-0.314

0.416	0.086	0.004	–	0.584	0.144	0.004	-0.227	-0.314
0.002	0.002	0.001	–	0.002	0.002	0.000	0.006	0.017

8/7*/5

-0.342 ( -0.028)

0.415	0.130	0.008	–	0.585	0.211	0.012	-0.256	-0.342
0.003	0.002	0.001	–	0.003	0.003	0.001	0.007	0.021

Before I leave the subject of To Hit or Not to Hit I would like to show a position I encountered playing GNUBG the other day. I was surprised at the best play in this position, and I am still not sure I can articulate why this is best. But here is the position:

Pip counts: Blue 71, Red 82
Position ID: t+0GABBz20ZAAA Match ID: QokIAAAAAAAA

My play was 10/7. If red gets hit at this point it is pretty much game over, so my thought was that I had to play it safe. Even though I am behind in the race blue still has to roll a 6 to get their back checker moving, and even then with the exception of 66 I am still likely to get a shot and maybe a direct shot at it. 10/7 gives me a chance to make the 2 point on the next roll (although a slim one). After 10/7 the next roll seemed pretty safe, although their are rolls that would leave an indirect shot for blue or force red to break a point in their home board.

The surprising (at least to me answer) is:

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Ply

Move

Equity

17/15 3/2*

+0.313

0.705	0.021	0.000	–	0.295	0.081	0.001	+0.350	+0.313
0.001	0.001	0.000	–	0.001	0.001	0.000	0.003	0.005

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 868089133 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 0-ply cubeful [expert]

10/8 3/2*

+0.296 ( -0.017)

0.739	0.022	0.000	–	0.261	0.124	0.003	+0.373	+0.296
0.001	0.001	0.000	–	0.001	0.001	0.000	0.003	0.006

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 868089133 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 0-ply cubeful [expert]

•

10/7

+0.152 ( -0.162)

0.628	0.015	0.000	–	0.372	0.013	0.000	+0.258	+0.152
0.001	0.001	0.000	–	0.001	0.001	0.000	0.002	0.004

Full cubeful rollout with var.redn.

1296 games, Mersenne Twister dice gen. with seed 868089133 and quasi-random dice

Play: 0-ply cubeful [expert]

Cube: 0-ply cubeful [expert]

After 3/2* red as just over a 30% chance of getting hit. Virtually all of these will be wins for blue (given the winning percentages from the roll out red will run a few games even after being hit).

So what is wrong with the “safe” 10/7. After playing out the position a few times the problem for red is that if blue rolls a 6 fairly quick there are a lot rolls where blue gets a shot at the red checker as it comes around from the 17 point. Blue may get a few chances at the red checker, so the hit comes out to be the best play.