To Hit or Not to Hit (Part 2)

In my first post regarding position 1-29 I ended with a couple of questions, lets explore the answers

The first question was what to play if the hit on the five has to come from the 8 point instead of the 6 point. This hit risk getting two blots hit. Even though the blot on the 8 is fairly safe on the first roll—only 53 will hit both blots—the odds are that if red gets hit on their 5 point again that blot on the 8 will stay there another roll giving blue another shot at it. (If red is hit there are only 9 rolls that cover the blot, red must have a 5 to cover but 56 does not work because red would have to come in with the 5). Here is the position

Pip counts: Blue 158, Red 180
Position ID: 4PPgASHgM/iAUA Match ID: cIkVAAAAAAAA

#		Ply	Move	Equity
	1	R	bar/20 8/5*	-0.105
			0.473 0.119 0.005 – 0.527 0.156 0.005 -0.092 -0.105 0.004 0.003 0.001 – 0.004 0.003 0.001 0.011 0.025
	2	R	bar/20 6/3	-0.146 ( -0.041)
			0.461 0.103 0.003 – 0.539 0.138 0.004 -0.113 -0.146 0.003 0.002 0.000 – 0.003 0.003 0.001 0.009 0.026
	3	R	bar/20 13/10	-0.169 ( -0.063)
			0.456 0.102 0.003 – 0.544 0.131 0.004 -0.118 -0.169 0.003 0.002 0.000 – 0.003 0.002 0.001 0.007 0.020
	4	R	bar/20 24/21	-0.180 ( -0.075)
			0.449 0.092 0.005 – 0.551 0.112 0.004 -0.121 -0.180 0.003 0.002 0.001 – 0.003 0.003 0.001 0.008 0.020

So the loose hit on the 5 point is still the way to go, but the equity difference between this and the second best is much less than it was in the original scenario.  The other point I find interesting here is that the safer play of bar/20 24/21 is in fourth place. All of the better plays leaves blue more shots. This is one of those positions where it seems that having more checkers back is better because red needs time  to build a blockade and establish a better home board. Once again if we look at the criteria given on page 69 more checkers back leads to bolder play.

Suppose red rolls 41 instead of 51 in the above position. Then the question is should red use the 1 to hit or to make the 20?  If red does hit they will have a good chance of making the 20 the next time.

#		Ply	Move	Equity
	1	R	bar/20	-0.132
			0.459 0.101 0.006 – 0.541 0.119 0.004 -0.099 -0.132 0.003 0.002 0.001 – 0.003 0.002 0.001 0.007 0.019
•	2	R	bar/21 6/5*	-0.196 ( -0.064)
			0.456 0.108 0.004 – 0.544 0.177 0.010 -0.162 -0.196 0.004 0.002 0.000 – 0.004 0.003 0.001 0.011 0.026
	3	R	bar/21 24/23	-0.366 ( -0.234)
			0.411 0.091 0.004 – 0.589 0.168 0.006 -0.258 -0.366 0.003 0.002 0.001 – 0.003 0.002 0.001 0.007 0.022
	4	R	bar/24 13/9	-0.378 ( -0.246)
			0.417 0.106 0.004 – 0.583 0.200 0.020 -0.275 -0.378 0.004 0.002 0.001 – 0.004 0.004 0.003 0.012 0.029

Based on the 648 game rollout bar/20 looks like the best choice, but the hit is not out of the question (given the standard errors on this one a longer rollout would be needed for a definitive answer). 

Here is another position that was developed from 1-29

Pip counts: Blue 158, Red 208
Position ID: 4PPgASHgDD5gSQ Match ID: cIkMAAAAAAAA

This addresses a position similar to the one above, the question is whether it red should hit the blot on the five one again or whether the roll would better be played to make two points in blue’s home board?

#		Ply	Move	Equity
	1	R	bar/22 6/5*	-0.002
			0.522 0.110 0.005 – 0.478 0.224 0.011 -0.076 -0.002 0.004 0.003 0.001 – 0.004 0.003 0.002 0.012 0.026
•	2	R	bar/21	-0.041 ( -0.039)
			0.502 0.108 0.003 – 0.498 0.189 0.005 -0.079 -0.041 0.004 0.003 0.001 – 0.004 0.003 0.002 0.011 0.025
	3	R	bar/22 23/22	-0.079 ( -0.077)
			0.496 0.108 0.004 – 0.504 0.200 0.007 -0.102 -0.079 0.003 0.002 0.000 – 0.003 0.003 0.001 0.010 0.024
	4	R	bar/24 13/10	-0.165 ( -0.164)
			0.479 0.100 0.004 – 0.521 0.223 0.010 -0.172 -0.165 0.003 0.002 0.000 – 0.003 0.003 0.001 0.009 0.021
	5	0	bar/24 21/18	-0.267 ( -0.265)
			0.446 0.084 0.002 – 0.554 0.200 0.008
			0-ply cubeful prune [expert]

The above rollout is based on 1296 games, the bar/22 6/5* play is once again the best, but only by a little.  (Note that this position has been corrected since the original post, thanks Timothy for pointing out the error)

I happen to run into very similar positions playing a match online earlier today, and because of my study of this position I repeated the loose hit on the 5 with a great deal more confidence that I had in the past.

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To Hit or Not to Hit (Part 1)

The Blots, Shots, and Odds chapter does not really lend itself to a posting, not to say that the contents of the chapter are not important. To make it useful though is simply a matter of practice, practice, practice.

I personally find many of the hit or not to hit decisions to be very difficult in real play. This is especially true of the loose hits in my home board plays. Position 1-29 in Trice is exactly one of the positions that it took me a while to play right, and even knowing that the loose hit in the home board is the right play by a large margin I still have to fight the nagging feeling that I am doing the wrong thing when I make it. Even more so is when the basic position repeats itself on the next roll and I am faced with making the play again. Getting all those checkers sent back can’t be right can it? Let’s see.

Pip counts: Blue 158, Red 180
Position ID: 4PPgASHgM/iAUA Match ID: cIkUAAAAAAAA

#		Ply	Move	Equity
	1	R	bar/20 6/5*	-0.005
			0.492 0.123 0.003 – 0.508 0.140 0.009 -0.038 -0.005 0.004 0.003 0.001 – 0.004 0.003 0.002 0.013 0.023
	2	R	bar/20 24/23	-0.180 ( -0.176)
			0.451 0.096 0.003 – 0.549 0.122 0.004 -0.125 -0.180 0.003 0.002 0.001 – 0.003 0.002 0.000 0.007 0.019

The rollout (as usual 648 games, expert level) confirms what Trice has already told us, anything other than hitting the blue blot on the 5 is a big mistake. But what happens if blue hits back on the 5—a likely outcome—and red once again gets the option to hit? Given the reason for making the hit it would seem that hitting again is the way to go,  but the cost is risking a fifth checker back. (Of course this is one Magriel’s criteria for leaving the blot that Trice discusses.)  After a blue hit (say with 51) and another red 51 we have the following the position:

Pip counts: Blue 157, Red 194
Position ID: 4PPgARHgGXzAUA Match ID: cIkUAAAAAAAA

#		Ply	Move	Equity
	1	R	bar/20 6/5*	-0.092
			0.486 0.112 0.004 – 0.514 0.174 0.008 -0.095 -0.092 0.004 0.003 0.000 – 0.004 0.003 0.001 0.010 0.023
	2	R	bar/24 13/8	-0.171 ( -0.079)
			0.459 0.103 0.004 – 0.541 0.156 0.009 -0.140 -0.171 0.003 0.002 0.001 – 0.003 0.003 0.001 0.009 0.022

So hitting again is the right play, even though it may send back a fifth checker.  In fact if the situation repeats again another lose hit is called for:

Pip counts: Blue 155, Red 208
Position ID: 4PPgAQXgDD7gUA Match ID: cIkQAAAAAAAA

#		Ply	Move	Equity
	1	R	bar/21 6/5*	-0.119
			0.491 0.100 0.005 – 0.509 0.227 0.011 -0.151 -0.119 0.005 0.004 0.001 – 0.005 0.005 0.002 0.016 0.037
	2	R	bar/24 13/9	-0.172 ( -0.053)
			0.471 0.097 0.004 – 0.529 0.219 0.021 -0.196 -0.172 0.005 0.003 0.001 – 0.005 0.004 0.004 0.016 0.035

There are numerous other question that arise from this position, for example if your hit is with a 3 instead of a 1 is hitting off the 8 still the play, leaving two blots? If we give red something more constructive to do with the roll, like make a point in blue’s home board is that a better play?

I will look at a couple of these questions in the next post.

The Passing of Walter Trice

 

Since this blog is dedicated to learning from his book I thought readers might want to know that Walter Trice recently passed away. More details at the link below.

 

http://www.gammonvillage.com/backgammon/news/article_display.cfm?resourceid=5919

Opening Rolls

 

I am not going to spend time on the opening rolls chapter at this point, although I would recommend reading this chapter carefully as there are some conceptual points that are interesting.

There is a great deal of information on opening rolls at http://www.bkgm.com/openings.html.  So if you want to explore this area in more depth take a look there.

Position 1-21 (Part 4)

 

Before wrapping up this position there are a couple of other interesting questions to explore. Suppose instead of 54 red rolls 53, now playing 13/8 13/10 leaves blue 2 additional shots over 13/8 13/9.

#		Ply	Move	Equity
	1	R	6/1 4/1	+0.460
			0.652 0.014 0.000 – 0.348 0.014 0.000 +0.304 +0.460 0.001 0.000 0.000 – 0.001 0.001 0.000 0.002 0.006
	2	R	6/1 5/2	+0.443 ( -0.017)
			0.648 0.013 0.000 – 0.352 0.019 0.001 +0.289 +0.443 0.001 0.000 0.000 – 0.001 0.001 0.000 0.002 0.006
	3	R	8/5 8/3	+0.420 ( -0.040)
			0.637 0.017 0.001 – 0.363 0.009 0.000 +0.282 +0.420 0.001 0.001 0.000 – 0.001 0.001 0.000 0.002 0.006
	4	R	6/3 6/1	+0.407 ( -0.053)
			0.634 0.014 0.000 – 0.366 0.020 0.000 +0.263 +0.407 0.001 0.001 0.000 – 0.001 0.001 0.000 0.003 0.006
	5	R	13/10 13/8	+0.319 ( -0.142)
			0.606 0.020 0.001 – 0.394 0.016 0.000 +0.217 +0.319 0.000 0.001 0.000 – 0.000 0.000 0.000 0.001 0.002

While 13/9 13/8 is worth considering 13/9 13/10 seems pretty clearly inferior to other options.

What if the relative pip count is the same, but the race is longer? For example:

Pip counts: Blue 109, Red 93
Position ID: bnZwwADcbQ4GAA Match ID: cAkWAAAAAAAA

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.596
			0.691 0.013 0.000 – 0.309 0.016 0.000 +0.378 +0.596 0.002 0.003 0.000 – 0.002 0.001 0.000 0.004 0.009
	2	R	6/2 6/1	+0.589 ( -0.007)
			0.687 0.019 0.001 – 0.313 0.016 0.000 +0.377 +0.589 0.002 0.001 0.000 – 0.002 0.001 0.000 0.004 0.010
	3	R	8/4 6/1	+0.547 ( -0.049)
			0.681 0.020 0.000 – 0.319 0.018 0.000 +0.366 +0.547 0.002 0.001 0.000 – 0.002 0.001 0.000 0.004 0.008
	4	R	13/9 13/8	+0.547 ( -0.050)
			0.696 0.025 0.001 – 0.304 0.012 0.000 +0.406 +0.547 0.001 0.001 0.000 – 0.001 0.001 0.000 0.003 0.006
	5	R	8/3 6/2	+0.533 ( -0.064)
			0.682 0.021 0.001 – 0.318 0.015 0.000 +0.371 +0.533 0.001 0.001 0.000 – 0.001 0.001 0.000 0.003 0.007

As in the rollouts of the original position 13/9 13/8 is best in terms of game winning chances and cubeless equity, but losses out to other positions in terms of cubeful equity.

Wrapping It Up

So does all of this lead to anything useful, or have I just spent a lot of time doing meaningless rollouts?

For one thing spending the time on this position has helped me to remember the position, so it will be useful for reference. I also think that I will spend fewer games in similar positions hoping my opponent is forced to break a point before I am, and hopefully in that process win more often.

Position 1-21 (Part 3)

 

At the end of part 2 on Position 1-21 I asked several questions regarding how changes to the position might impact red’s play in this case. Despite some of the issues I noted in Part 2 with the rollouts I have decided to stick with the 648 game expert level rollouts for this analysis. My goal is to determine the relative differences created by variations in this position and I believe that this level of analysis will allow us to do that.

One of the questions I asked  was how a weaker home board for blue and a higher pip count for red might change the play.  Let’s begin with the rollout for the position as given in Trice:

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.464
			0.659 0.014 0.000 – 0.341 0.014 0.000 +0.318 +0.464 0.001 0.001 0.000 – 0.001 0.001 0.001 0.002 0.006
	2	R	13/9 13/8	+0.421 ( -0.043)
			0.650 0.019 0.001 – 0.350 0.014 0.000 +0.307 +0.421 0.000 0.001 0.000 – 0.000 0.000 0.000 0.002 0.002

(See part 2 for a discussion of 13/9 13/8 not being the best play in this rollout)

For starters lets weaken blue’s board and leave the pip count the same:

Pip counts: Blue 99, Red 85
Position ID: 23E4wAB22wwGAA Match ID: cAkWAAAAAAAA

#		Ply	Move	Equity
	1	R	13/9 13/8	+0.572
			0.711 0.019 0.000 – 0.289 0.005 0.000 +0.437 +0.572 0.001 0.001 0.000 – 0.001 0.000 0.000 0.002 0.004
	2	R	6/1 5/1	+0.563 ( -0.009)
			0.690 0.016 0.001 – 0.310 0.011 0.000 +0.386 +0.563 0.001 0.001 0.000 – 0.001 0.001 0.000 0.003 0.009

One of the issues with variation on a theme in backgammon positions is that changes can have more consequences than you desire. The change here has significantly (in the informal sense not the statistical sense) reduced blue’s chances in the game. But our goal is to study why a particular play would be good for red in these positions, and here 13/9 13/8 comes out a pretty clear winner. If reds blot on the 9 is hit it should be fairly easy for red to escape with the 20 and 21 points open. Of course 41, 42, and 51 do leave blue a shot at pointing on red and making another home board point. But even then, with red’s strong home board it is not going to be easy for blue to close the other point on red because slotting the empty point is extremely risky.

Now let’s make this a little more difficult for red:

Pip counts: Blue 99, Red 85
Position ID: 3mxGwAB22wwGAA Match ID: cAkWAAAAAAAA

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.588
			0.693 0.017 0.001 – 0.307 0.010 0.000 +0.393 +0.588 0.002 0.001 0.000 – 0.002 0.001 0.000 0.003 0.010
	2	R	8/4 8/3	+0.539 ( -0.049)
			0.681 0.023 0.000 – 0.319 0.009 0.000 +0.377 +0.539 0.001 0.001 0.000 – 0.001 0.001 0.000 0.003 0.010
	3	R	13/9 13/8	+0.537 ( -0.051)
			0.698 0.015 0.000 – 0.302 0.005 0.000 +0.406 +0.537 0.001 0.001 0.000 – 0.001 0.001 0.000 0.002 0.005
	4	R	6/2 6/1	+0.517 ( -0.072)
			0.678 0.019 0.001 – 0.322 0.014 0.000 +0.361 +0.517 0.002 0.001 0.000 – 0.002 0.001 0.000 0.004 0.010

This is another one of the cases where in terms of game winning chances and cubeless equity 13/9 13/8 is the best play, but in terms of the cubeful equity it rates in 3rd place.  Still the move gives us more chance of winning the game with the extra open point.

While the extra open point seems to make the 13/9 13/8 play better, shifting the pip count just a little once again demonstrates how close this play really is:

Pip counts: Blue 99, Red 88
Position ID: 3mwcwAC27QwGAA Match ID: cAkWAAAAAAAA

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.586
			0.693 0.018 0.000 – 0.307 0.008 0.000 +0.395 +0.586 0.002 0.001 0.000 – 0.002 0.000 0.000 0.003 0.009
	2	R	6/2 6/1	+0.566 ( -0.020)
			0.686 0.018 0.000 – 0.314 0.009 0.000 +0.382 +0.566 0.002 0.001 0.000 – 0.002 0.001 0.000 0.003 0.010
	3	R	8/4 8/3	+0.528 ( -0.057)
			0.677 0.025 0.000 – 0.323 0.006 0.000 +0.374 +0.528 0.001 0.001 0.001 – 0.001 0.000 0.000 0.003 0.009
	4	R	13/9 13/8	+0.513 ( -0.073)
			0.673 0.016 0.000 – 0.327 0.004 0.000 +0.357 +0.513 0.001 0.001 0.000 – 0.001 0.001 0.000 0.002 0.005

Position 1-21 (Part 2)

Pip counts: Blue 99, Red 85
Position ID: 22xMwAB22wwGAA Match ID: cAkWAAAAAAAA

My first thought was to look at Position 1-21 and then vary it some to see when in similar positions breaking the 13 made sense. As usual I started by setting up the position in GNUBG and taking a look at what the analysis has to say about the position, this is where things got a little interesting:

#		Ply	Move	Equity
	1	2	6/1 5/1	+0.490
			0.673 0.016 0.000 – 0.327 0.014 0.000
			2-ply cubeful prune [world class]
	2	2	6/2 6/1	+0.446 ( -0.044)
			0.660 0.014 0.000 – 0.340 0.017 0.000
			2-ply cubeful prune [world class]
	3	2	8/4 8/3	+0.443 ( -0.047)
			0.659 0.017 0.000 – 0.341 0.012 0.000
			2-ply cubeful prune [world class]
	4	2	13/9 13/8	+0.424 ( -0.066)
			0.666 0.014 0.000 – 0.334 0.013 0.000
			2-ply cubeful prune [world class]
	5	2	13/4	+0.152 ( -0.338)
			0.553 0.021 0.000 – 0.447 0.017 0.000
			2-ply cubeful prune [world class]

The 2 ply evaluation puts the 13/9 13/8 play in fourth place, note that this is due to the cubeful equities, in terms of straight wins it is second place, winning 0.8% less than the 6/1 5/1. Of course to really get at the answer we need a rollout. I started with my now typical 648 game expert rollout. This gave  6/1 5/1 0.9% more winning chances than 13/9 13/8, so just to be safe I ran it to 1296 games with the following results:

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.459
			0.659 0.013 0.000 – 0.341 0.015 0.000 +0.317 +0.459 0.001 0.000 0.000 – 0.001 0.001 0.000 0.002 0.005
	2	R	13/9 13/8	+0.423 ( -0.036)
			0.650 0.019 0.001 – 0.350 0.013 0.000 +0.306 +0.423 0.000 0.000 0.000 – 0.000 0.000 0.000 0.001 0.002
	3	R	6/2 6/1	+0.409 ( -0.050)
			0.639 0.014 0.000 – 0.361 0.019 0.000 +0.273 +0.409 0.001 0.000 0.000 – 0.001 0.001 0.000 0.002 0.005

Now these results are just the opposite of what Trice says they should be, so I decided to try a 1296 game rollout at world class level:

#		Ply	Move	Equity
	1	R	6/1 5/1	+0.460
			0.659 0.011 0.000 – 0.341 0.015 0.000 +0.314 +0.460 0.001 0.000 0.000 – 0.001 0.000 0.000 0.002 0.003
	2	R	13/9 13/8	+0.424 ( -0.036)
			0.663 0.017 0.001 – 0.337 0.013 0.000 +0.330 +0.424 0.000 0.000 0.000 – 0.000 0.000 0.000 0.001 0.001

Here 6/1 5/1 still comes our on top, but only because of the cubeful equity. In terms of won games and cubeless equity 13/9 13/8 is best, BUT only if you play the rest of the game out with world class skill!

What does this say for us normal players? I decided to try a rollout having GNUBG play at intermediate level.

#		Ply	Move	Equity
	1	R	13/9 13/8	+0.589
			0.648 0.063 0.005 – 0.352 0.033 0.001 +0.330 +0.589 0.006 0.002 0.000 – 0.006 0.001 0.001 0.013 0.023
	2	R	6/1 5/1	+0.576 ( -0.013)
			0.647 0.037 0.001 – 0.353 0.025 0.001 +0.306 +0.576 0.006 0.002 0.000 – 0.006 0.001 0.000 0.012 0.021
	3	R	8/4 8/3	+0.506 ( -0.083)
			0.628 0.046 0.002 – 0.372 0.016 0.000 +0.287 +0.506 0.006 0.002 0.000 – 0.006 0.001 0.000 0.013 0.023
	4	R	6/2 6/1	+0.486 ( -0.104)
			0.642 0.043 0.002 – 0.358 0.032 0.001 +0.296 +0.486 0.006 0.002 0.001 – 0.006 0.001 0.003 0.012 0.022

Keeping in mind that this is with both sides playing at an intermediate level the 13/9 13/8 and 6/1 5/1 play are virtually equal. (Given the larger standard error for this rollout it is probably safe to say that it is a statistical dead heat).

Given these various results it seems we have indeed found something of a critical point in this kind of position. So we can see that if we find ourselves in this position the 13/9 13/8 play is certainly sound, but we may not often find ourselves in exactly this position, but we will likely see similar positions with some regularity. Trice has already told us that adding one more pip to reds position changes the play. It seems obvious then that if red was slightly further in this race 13/9 13/8 would be even better. But what about similar positions, for example suppose the pip count difference was the same but with a longer race for both? What if reds pip count is slightly higher but blues board is weaker? What is the tipping point for leaving a slightly higher probability shot? These are all questions worth exploring.

Position 1-21 (Part 1)

 

I am skipping ahead a fair amount, the chapter on the Defensive Ace Point seemed fairly straight forward. Position 1-21 however seemed anything but straight forward to me, but it also seems like I find myself in positions like this with some regularity so it is certainly one worth pursuing.

Pip counts: Blue 99, Red 85
Position ID: 22xMwAB22wwGAA Match ID: cAkWAAAAAAAA

The first problem I ran into working through this position was Trice’s analysis of the winning chances for red. Once you read this section carefully it makes since what he is saying, but there are still a couple of numbers that he seems to create out of thin air. For example, that if red gets hit after 13/9 13/8 they will lose 5 out of 6 games, or if red plays safe on this roll they will still get hit about 25% of the time later in the game.  I am guessing that Trice can estimate these numbers with a great deal of accuracy because he has studied and played these types of positions thousands of times. Since I, and most of you reading this, do not have this store of mental data to draw on we are left with trying to sort out this position in other ways. Of course, Trice gives us a hint at the end of the chapter by telling us that this makes a good reference position.

If we know the right move in this position then if it comes up in a game we will not need to know all the other details to make the correct play. Of course this assumes that we have a mental database tuned to the point that we can pull this answer out at a moments notice! I have already noticed that some of the positions I have studied earlier are coming in handy in game play. Not that the positions are necessarily identical, but they have been close enough to allow me to make better decisions than I would have had I not studied the similar position.

Trice says that changing the pip count by just one for red in this position changes the correct play. That might make it a good reference position for the world class player, but for me it raises a lot of questions. I am sure that I can remember the basics of the position because as I said it comes up a lot. But changing the pip count by one changing the decision, that is one I will have to work on a lot to remember. And what happens at different pip counts with the same relative difference, and what happens if blue’s board is a weaker with similar pip counts?

All of these questions lead me to conclude that studying some variations of this position would be worth the effort. Perhaps I can develop some guidance and a better feel for when to break the 13 point. I know that right now I frequently hold it too long and end up losing games I should win because I do. So if I can get this play right more often I should win more games. However, as I started to analyze this position with GNUBG I noticed some funny things happening. That will be the staring point for my next post.

Pip Counting

 

Since I play mostly online pip counting is not something I do a lot of. However, there is a part of me that says everyone backgammon player should be able to do it, so I have played around with methods. Trice mentions Jack Kissane’s Cluster Counting method. The method I find the easiest (but remember I don’t do it a lot so take it for what is worth) is Douglas Zare’s Half-Crossover method. This nice thing about this method is you can get a really good estimate of where you stand in the race without doing the full pip count (handy for some of those checker play decision that depend on whether you are ahead or behind) and you can arrive at the exact pip count with only a little bit of math that you can do fairly easily in your head.

You can find details on both of these methods as well as several others at http://www.bkgm.com/articles/page04.html#pip_counting.

Anchors Part 3 (Pos 1-14)

Pip counts: Blue 156, Red 164
Position ID: 4HPwAyDgc+QBKA Match ID: cIkRAAAAAAAA

 

To finish up this chapter a quick look at pos 1-14. This is fairly east to see, but the interesting point is the difference between and the position that Trice gives earlier were blue has another checker on the 13 rather than the checker on the 24. In that case making the 20 point is not the right play. Red wants to keep the back checkers deep and increase the chances of getting a hit. While this is easy to see in studying the position it is the kind of thing that is easy to miss in the course of a real game. This type of thing points out an issue that I have with my game and others may have as well, that is I often play without really giving consideration to where I stand in the race. I am trying to hard to make it a habit to think about where the race stands before I make any move.