Part 1: Totally smooth position

from: Marc Werner and Christian Liebe-Harkort

Black has a perfect distribution with his 15 checker, three checkers on every inner board point.

You might think that the checker plays for this position are very simple and equity swings for different plays are small, you will see that this is not the case.

In all these positions shown here, White's timing is so good that, trying to crunch him makes no sense. (Black´s only consideration is safety). White most likely (>90%) will be gammoned if he doesn´t hit a shot. On the other hand, White has an excellent timing and a strong offensive position so hitting an early shot really hurts Black (depending of course how many checkers black is able to bear off). Because the equity-swing between getting hit, (loosing two points or facing an unpleasant redouble by White) or avoiding a shot and wining most likely a gammon is huge, accurate play is required. All interesting moves for this position will be considered in this chapter and usually Black has at least two reasonable choices for his move.

Position 796, Category Anchor

Black to play 6 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:42 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
The correct play here is 6/off, 5/4 preparing to clear the two highest points as quickly as possible, leaving only one horror-shake (6-5) next turn. This is right by a wide margin, since the two other alternatives (4/3, 3/2) each leave inner gaps and this formation is very dangerous against an ace-point anchor. Even by risking the double blotter 6-5 the next roll.
Note: after playing 6/off, 5-4 black has only 6-5 and 5-4 as bad rolls. His chances getting hit are: 62 (2x20+2x11 shots) / 1296 = 5,09% in a cross section of 1296 (36x 36)

1) 6/0ff 5/4
Equity: +1.261 7 ply

Player: 79.58%17.05%51.00%11.53%
Opponent: 20.42%20.42%0.00%0.00%

Pipcount: 53(-130) - 183(+130)

2) 6/0ff 4/3
Equity: +1.207 (-0.054) 7 ply

Player: 77.92%16.37%50.63%10.92%
Opponent: 22.08%22.08%0.00%0.00%

3) 6/0ff 3/2
Equity: +1.119 (-0.142) XG Roller+

Player: 75.58%16.26%49.48%9.84%
Opponent: 24.42%24.42%0.00%0.00%

4) 6/5 6/0ff
Equity: +0.858 (-0.403) XG Roller+

Player: 67.89%16.96%40.94%9.99%
Opponent: 32.11%32.11%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 797, Category Anchor

Black to play 4 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:44 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
The correct play is 6/2, 5/4 although the difference between the two other alternatives
(6/5, 4/off and 5/off) is very marginal.
Note: after playing 6/2, 5-4 black has only 6-5 and 5-4 as bad rolls. His chances getting hit are: 62 (2x20+2x11 shots) / 1296 = 5,09% in a cross section of 1296 (36x 36).

1) 6/2 5/4
Equity: +1.202 7 ply

Player: 78.50%17.51%51.31%9.68%
Opponent: 21.50%21.50%0.00%0.00%

Pipcount: 55(-128) - 183(+128)

2) 6/5 4/0ff
Equity: +1.189 (-0.013) 7 ply

Player: 77.71%16.97%50.30%10.44%
Opponent: 22.29%22.29%0.00%0.00%

3) 5/0ff
Equity: +1.184 (-0.018) 7 ply

Player: 77.55%17.00%49.99%10.56%
Opponent: 22.45%22.45%0.00%0.00%

4) 6/2 4/3
Equity: +1.153 (-0.049) XG Roller+

Player: 76.74%16.47%50.68%9.59%
Opponent: 23.26%23.22%0.04%0.00%

5) 6/2 3/2
Equity: +1.044 (-0.158) XG Roller+

Player: 73.77%16.14%49.13%8.50%
Opponent: 26.23%26.19%0.04%0.00%

Software: eXtreme Gammon Version: 1.13

Position 798, Category Anchor

Black to play 3 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:45 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
Still right to try to prepare clearing the two highest points by a wide margin, since the alternative (6/3, 4/3) leave an inner gap on the 4 point. Playing 6/2 with the 3-1 is a big mistake in this position, even the number of hits in 1296 is smaller compared to the best move.
Note: After 6/2 black will get hit: 44 (1x11+1x11+2x11 shots) / 1296 = 3,39% in a cross section of 1296 (36x 36).

1) 6/3 5/4
Equity: +1.271 7 ply

Player: 80.36%17.78%52.02%10.56%
Opponent: 19.64%19.64%0.00%0.00%

Pipcount: 56(-127) - 183(+127)

2) 6/3 4/3
Equity: +1.203 (-0.068) 7 ply

Player: 78.22%16.95%51.23%10.04%
Opponent: 21.78%21.78%0.00%0.00%

3) 6/2
Equity: +1.196 (-0.075) 7 ply

Player: 78.30%17.54%51.07%9.69%
Opponent: 21.70%21.70%0.00%0.00%

4) 6/5 3/0ff
Equity: +1.180 (-0.091) 7 ply

Player: 77.36%16.88%49.96%10.52%
Opponent: 22.64%22.64%0.00%0.00%

5) 4/0ff
Equity: +1.152 (-0.119) XG Roller+

Player: 76.58%16.61%49.77%10.20%
Opponent: 23.42%23.42%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 799, Category Anchor

Black to play 2 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:46 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
Here 6/5, 2/off and 6/3 has the same strength. Surprisingly stripping the two highest points now seems to be a slight mistake.
Maybe one reason could be that the formation 6 (point)/ 2 (checkers), 5 (2), 4 (5) on the three highest points is not as safe as the 6(2), 5(2), 4(4) formation.

1) 6/5 2/0ff
Equity: +1.267 7 ply

Player: 79.96%17.92%50.45%11.59%
Opponent: 20.04%20.04%0.00%0.00%

Pipcount: 57(-126) - 183(+126)

2) 6/3
Equity: +1.266 (-0.001) 7 ply

Player: 80.18%17.86%51.64%10.68%
Opponent: 19.82%19.82%0.00%0.00%

3) 6/4 5/4
Equity: +1.236 (-0.031) 7 ply

Player: 79.59%18.61%50.45%10.53%
Opponent: 20.41%20.41%0.00%0.00%

4) 5/4 2/0ff
Equity: +1.216 (-0.051) XG Roller+

Player: 78.36%17.59%49.17%11.60%
Opponent: 21.64%21.64%0.00%0.00%

5) 4/3 2/0ff
Equity: +1.204 (-0.063) XG Roller+

Player: 77.96%17.11%49.63%11.22%
Opponent: 22.04%22.04%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 800, Category Anchor

Black to play 3 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:48 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
Best here is 6/3, 2off; second choice is stripping the two highest points with 6/3, 5/3 resulting in the 6(2), 5(2), 4(3) formation on the three highest points which seems better than the 6(2), 5(2), 4(4) formation now.
Note: Very bad now is playing 6/4, 5/2 with the 3-2 resulting in the same position as moving the 4-1. But with the roll 4-1, 6/4, 5/2 is the best choice. Also it seems that bearing off one checker also has merits.

1) 6/3 2/0ff
Equity: +1.286 7 ply

Player: 80.28%17.32%51.07%11.89%
Opponent: 19.72%19.72%0.00%0.00%

Pipcount: 55(-128) - 183(+128)

2) 6/3 5/3
Equity: +1.250 (-0.036) 7 ply

Player: 79.59%16.98%52.32%10.29%
Opponent: 20.41%20.41%0.00%0.00%

3) 3/0ff 2/0ff
Equity: +1.208 (-0.078) 7 ply

Player: 77.82%16.97%48.89%11.96%
Opponent: 22.18%22.18%0.00%0.00%

4) 6/4 5/2
Equity: +1.202 (-0.084) 7 ply

Player: 78.50%17.51%51.31%9.68%
Opponent: 21.50%21.50%0.00%0.00%

5) 6/4 3/0ff
Equity: +1.198 (-0.088) XG Roller+

Player: 77.73%16.79%49.66%11.28%
Opponent: 22.27%22.27%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 801, Category Anchor

Black to play 4 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:49 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
6/off is top choice here. Playing 6/2, 5/3 (resulting in the 6(2), 5(2), 4(3) formation on the three highest points) is even more inferior then moving two checkers off (4/off, 2/off).
Note: Again it seems that bearing off one checker (whenever it is possible with one number) is considerable superior than trying to clear the two highest points by stripping them.

1) 6/0ff
Equity: +1.253 7 ply

Player: 79.36%17.11%50.78%11.47%
Opponent: 20.64%20.64%0.00%0.00%

Pipcount: 54(-129) - 183(+129)

2) 4/0ff 2/0ff
Equity: +1.203 (-0.050) 7 ply

Player: 77.74%16.74%49.48%11.52%
Opponent: 22.26%22.26%0.00%0.00%

3) 6/2 5/3
Equity: +1.195 (-0.058) 7 ply

Player: 78.10%16.58%52.07%9.45%
Opponent: 21.90%21.90%0.00%0.00%

4) 5/3 4/0ff
Equity: +1.105 (-0.148) XG Roller+

Player: 75.19%16.31%48.76%10.12%
Opponent: 24.81%24.81%0.00%0.00%

5) 6/2 4/2
Equity: +1.046 (-0.207) XG Roller+

Player: 73.81%15.75%49.83%8.23%
Opponent: 26.19%26.15%0.04%0.00%

Software: eXtreme Gammon Version: 1.13

Position 802, Category Anchor

Black to play 4 3

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:50 PM, from dongbang

Pipcount: 60(-123) - 183(+123)

Comment:
The best move here is 6/3, 4/off. Once again bearing off one checker and prepare to clear the six-point beats 6/2, 5/2 by a wide margin. This position was really suprising me, I never would have made that move, because it looks so ugly if you are used to see even numbers as good.
Note: In fact the two other moves bearing off one checker (6/2, 3/off and 4/off, 3/off) are better than 6/2, 5/3.

1) 6/3 4/0ff
Equity: +1.207 7 ply

Player: 77.93%16.38%50.63%10.92%
Opponent: 22.07%22.07%0.00%0.00%

Pipcount: 53(-130) - 183(+130)

2) 6/2 3/0ff
Equity: +1.112 (-0.095) 7 ply

Player: 75.41%16.37%49.23%9.81%
Opponent: 24.59%24.59%0.00%0.00%

3) 4/0ff 3/0ff
Equity: +1.110 (-0.097) 7 ply

Player: 75.14%16.21%48.49%10.44%
Opponent: 24.86%24.86%0.00%0.00%

4) 6/2 5/2
Equity: +1.109 (-0.098) 7 ply

Player: 75.81%16.39%51.09%8.33%
Opponent: 24.19%24.19%0.00%0.00%

5) 5/2 4/0ff
Equity: +1.022 (-0.185) XG Roller+

Player: 72.92%15.91%48.22%8.79%
Opponent: 27.08%27.08%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 814, Category Anchor

Black to play 1 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/10/2010 1:18 PM, from admin

Pipcount: 60(-123) - 183(+123)

Comment:
The best move is to clear the 5-point. This somewhat surprising result (I guess most people would clear from the rear and not create a gap), leaves NO bad numbers next turn and also clears a point. The resulting formation is actually very safe.

1) 5/4(2) 5/3
Equity: +1.314 7 ply

Player: 81.84%18.70%52.44%10.70%
Opponent: 18.16%18.16%0.00%0.00%

Pipcount: 56(-127) - 183(+127)

2) 6/5(2) 6/4
Equity: +1.302 (-0.012) 7 ply

Player: 81.14%18.08%51.79%11.27%
Opponent: 18.86%18.86%0.00%0.00%

3) 6/3 5/4
Equity: +1.271 (-0.043) 7 ply

Player: 80.36%17.79%52.01%10.56%
Opponent: 19.64%19.64%0.00%0.00%

4) 6/5(3) 4/3
Equity: +1.189 (-0.125) XG Roller+

Player: 77.82%17.60%49.57%10.65%
Opponent: 22.18%22.17%0.01%0.00%

5) 6/5(3) 3/2
Equity: +1.139 (-0.175) XG Roller+

Player: 76.51%16.80%50.37%9.34%
Opponent: 23.49%23.47%0.02%0.00%

Software: eXtreme Gammon Version: 1.13

Position 815, Category Anchor

Black to play 2 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 9:29 AM, from admin

Pipcount: 60(-123) - 183(+123)

Comment:
Best to clear the 6-point and prepare to clear the 5-point.

1) 6/4(3) 5/3
Equity: +1.397 7 ply

Player: 83.30%17.32%53.20%12.78%
Opponent: 16.70%16.70%0.00%0.00%

Pipcount: 52(-131) - 183(+131)

2) 6/4(3) 2/0ff
Equity: +1.356 (-0.041) 7 ply

Player: 81.96%17.85%50.38%13.73%
Opponent: 18.04%18.04%0.00%0.00%

3) 6/4 5/3(3)
Equity: +1.326 (-0.071) XG Roller+

Player: 81.27%16.46%52.96%11.85%
Opponent: 18.73%18.71%0.02%0.00%

4) 6/4(2) 6/2
Equity: +1.291 (-0.106) XG Roller+

Player: 80.04%16.22%51.76%12.06%
Opponent: 19.96%19.95%0.01%0.00%

5) 6/0ff 2/0ff
Equity: +1.276 (-0.121) XG Roller+

Player: 79.55%16.72%49.98%12.85%
Opponent: 20.45%20.45%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 816, Category Anchor

Black to play 3 3

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 9:31 AM, from admin

Pipcount: 60(-123) - 183(+123)

Comment:
No surprises here. Best to clear the 6-point and bear a checker off.

1) 6/3(2) 6/0ff
Equity: +1.392 7 ply

Player: 82.39%15.25%53.86%13.28%
Opponent: 17.61%17.61%0.00%0.00%

Pipcount: 48(-135) - 183(+135)

2) 6/3(3) 5/2
Equity: +1.363 (-0.029) 7 ply

Player: 82.02%14.81%56.05%11.16%
Opponent: 17.98%17.98%0.00%0.00%

3) 6/3 5/2(3)
Equity: +1.122 (-0.270) XG Roller+

Player: 75.69%14.77%52.66%8.26%
Opponent: 24.31%24.29%0.02%0.00%

4) 6/0ff 5/2 3/0ff
Equity: +1.121 (-0.271) XG Roller+

Player: 75.51%15.53%50.02%9.96%
Opponent: 24.49%24.49%0.00%0.00%

5) 6/0ff(2)
Equity: +0.888 (-0.504) XG Roller+

Player: 68.63%16.27%42.28%10.08%
Opponent: 31.37%31.37%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 817, Category Anchor

Black to play 4 4

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 9:34 AM, from admin

Pipcount: 60(-123) - 183(+123)

Comment:
Both possibilities have almost the same equity. Both resulting positions are not very safe.

1) 6/2(3) 4/0ff
Equity: +1.025 7 ply

Player: 72.81%14.21%50.70%7.90%
Opponent: 27.19%27.19%0.00%0.00%

Pipcount: 44(-139) - 183(+139)

2) 6/2 4/0ff(3)
Equity: +1.023 (-0.002) 7 ply

Player: 72.67%15.94%46.92%9.81%
Opponent: 27.33%27.33%0.00%0.00%

3) 6/2(2) 4/0ff(2)
Equity: +0.130 (-0.895) XG Roller+

Player: 47.43%14.04%28.80%4.59%
Opponent: 52.57%52.57%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 818, Category Anchor

Black to play 6 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 9:46 AM, from admin

Pipcount: 60(-123) - 183(+123)

Comment:
The best move is to bear off two checkers. It might be tempting to prepare to clear the 5-point, but this leaves too many shots.
Note: After 6/off, 5/3 black will get hit: 73 times ( 1x11 + 2x11+ 2x20) / 1296 = 5,63% in the next roll, but after 6/off, 2/off only 65 and 44 leave single shots.

1) 6/0ff 2/0ff
Equity: +1.284 7 ply

Player: 79.76%16.87%49.96%12.93%
Opponent: 20.24%20.24%0.00%0.00%

Pipcount: 52(-131) - 183(+131)

2) 6/0ff 5/3
Equity: +1.251 (-0.033) 7 ply

Player: 79.11%16.23%51.59%11.29%
Opponent: 20.89%20.89%0.00%0.00%

3) 6/0ff 4/2
Equity: +1.117 (-0.167) XG Roller+

Player: 75.43%15.62%50.37%9.44%
Opponent: 24.57%24.57%0.00%0.00%

4) 6/4 6/0ff
Equity: +0.892 (-0.392) XG Roller+

Player: 68.84%16.65%42.27%9.92%
Opponent: 31.16%31.16%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

It is nearly impossible to give general rules for every single position that eventually can occur against an ace-point anchor but some useful hints look all right. With all numbers containing an ace (6-1, 4-1 and 3-1) except for the 2-1 it is best to strip the 6- and 5 points trying to clear them as quickly as possible. With all other rolls containing no ace (3-2, 4-2 and 4-3) it is best to take one checker off and strip the 6 point in order to clear the highest point quickly.

updated: Thursday, April 15, 2010