Part 2: Very smooth position

from: Marc Werner and Christian Liebe-Harkort

Black has an almost pefect smooth distribution with 15 checkers, three checkers on each inner point, except on the 3 point. This is almost the same distribution as in the previous chapter, the only difference is the checker from the two point, that we have moved to the three point. As you will see, little differences matter sometimes.

Position 803, Category Anchor

Black to play 6 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:55 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
The correct play is 6/off, 5/4 stripping the two highest points although the alternative 3/2 leaves no inner gap and smoothing the black checkers perfectly. This might be a surprising result, but preparing to clear the highest points still has priority. After 6/off, 5/4 black has only one horror shake (6-5) the next turn and 5-4 leaves only one blot. After 6/off, 3/2 black has 6-6, 5-5, 4-4 and 6-5- a total of five numbers which will produce a blot.

1) 6/0ff 5/4
Equity: +1.299 7 ply

Player: 80.64%17.31%51.29%12.04%
Opponent: 19.36%19.36%0.00%0.00%

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

2) 6/0ff 3/2
Equity: +1.253 (-0.046) 7 ply

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

3) 6/0ff 4/3
Equity: +1.213 (-0.086) XG Roller+

Player: 77.93%16.50%49.69%11.74%
Opponent: 22.07%22.07%0.00%0.00%

4) 6/5 6/0ff
Equity: +0.889 (-0.410) XG Roller+

Player: 68.64%16.22%42.10%10.32%
Opponent: 31.36%31.36%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 804, Category Anchor

Black to play 4 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:56 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
Trying to clear the two highest points by stripping them with 6/2, 5/4 is the best choice, even in this position. All other alternatives are considerable worse with the 4-1.
Note: Moving 6/2, 3/2 a play most player would consider as the best choice, is a big mistake here.

1) 6/2 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) 6/5 4/0ff
Equity: +1.230 (-0.041) 7 ply

Player: 78.75%17.13%50.47%11.15%
Opponent: 21.25%21.25%0.00%0.00%

3) 5/0ff
Equity: +1.209 (-0.062) 7 ply

Player: 78.33%17.50%49.95%10.88%
Opponent: 21.67%21.67%0.00%0.00%

4) 6/2 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%

5) 6/2 3/2
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%

Software: eXtreme Gammon Version: 1.13

Position 805, Category Anchor

Black to play 3 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 5:58 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
Still best to strip the 6-and 5 point with 6/2, 5/4! Though the difference between the second best move 6/5, 3/off and the third best, 6/2 here is somewhat marginal.
Note: The most surprising result of this analysis (at least for me) is that the completely safe position (no bad rolls in this position on the next turn) which will occur after black plays 3/off, 3/2 is actually the sixth(!) best move in this position (equity diff. 0.111) and it is a blunder!

1) 6/3 5/4
Equity: +1.287 7 ply

Player: 80.83%18.07%51.87%10.89%
Opponent: 19.17%19.17%0.00%0.00%

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

2) 6/5 3/0ff
Equity: +1.267 (-0.020) 7 ply

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

3) 6/2
Equity: +1.266 (-0.021) 7 ply

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

4) 5/4 3/0ff
Equity: +1.211 (-0.076) 7 ply

Player: 78.47%17.93%49.52%11.02%
Opponent: 21.53%21.53%0.00%0.00%

5) 6/3 4/3
Equity: +1.190 (-0.097) 7 ply

Player: 77.92%17.42%50.19%10.31%
Opponent: 22.08%22.08%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 806, Category Anchor

Black to play 2 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 6:07 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
Playing 6/3 and 6/4, 5/4 with the 2-1 has the same strength. Also good is moving 6/4, 3/2 (smoothing the checkers). The four best choices with this roll are all very close together.
Note: Nevertheless it seems that with a roll containing an ace trying to clear the highest points (with a roll containing an ace) quickly is always one of the best choices.

1) 6/3
Equity: +1.277 7 ply

Player: 80.56%18.16%51.52%10.88%
Opponent: 19.44%19.44%0.00%0.00%

Pipcount: 58(-125) - 183(+125)

2) 6/4 5/4
Equity: +1.273 (-0.004) 7 ply

Player: 80.65%18.91%50.78%10.96%
Opponent: 19.35%19.35%0.00%0.00%

3) 6/4 3/2
Equity: +1.262 (-0.015) 7 ply

Player: 80.27%18.66%50.86%10.75%
Opponent: 19.73%19.73%0.00%0.00%

4) 3/0ff
Equity: +1.244 (-0.033) 7 ply

Player: 79.38%17.79%50.46%11.13%
Opponent: 20.62%20.62%0.00%0.00%

5) 6/5 4/2
Equity: +1.208 (-0.069) 7 ply

Player: 78.59%17.69%50.91%9.99%
Opponent: 21.41%21.41%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 807, Category Anchor

Black to play 4 3

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 6:08 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
Cleary the best move here is 6/2, 3/off. All other candidates are considerably inferior to the top choice.
Note: Playing 6/2, 5/2 here (resulting in the well known 6(2), 5(2), 4(3) formation) would be a big mistake. Again it seems that bearing off one checker (like in position A) is clearly superior compared to the play of stripping the 5-and 6 points.

1) 6/2 3/0ff
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) 6/3 4/0ff
Equity: +1.209 (-0.044) 7 ply

Player: 78.00%16.77%49.94%11.29%
Opponent: 22.00%22.00%0.00%0.00%

3) 4/0ff 3/0ff
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%

4) 6/2 5/2
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%

5) 5/2 4/0ff
Equity: +1.087 (-0.166) XG Roller+

Player: 74.61%16.10%48.45%10.06%
Opponent: 25.39%25.39%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 808, Category Anchor

Black to play 3 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/8/2010 6:09 PM, from dongbang

Pipcount: 61(-122) - 183(+122)

Comment:
The difference between the top choice 6/4, 3/off and the second best move 6/4, 5/2 is tiny.
Once again it looks like, whenever it is possible, that bearing off one checker- and smoothing the points with the other number- is best.

1) 6/4 3/0ff
Equity: +1.290 7 ply

Player: 80.53%17.94%50.58%12.01%
Opponent: 19.47%19.47%0.00%0.00%

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

2) 6/4 5/2
Equity: +1.271 (-0.019) 7 ply

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

3) 6/3 5/3
Equity: +1.257 (-0.033) 7 ply

Player: 79.82%17.40%51.77%10.65%
Opponent: 20.18%20.18%0.00%0.00%

4) 6/3 4/2
Equity: +1.211 (-0.079) XG Roller+

Player: 78.11%16.30%51.30%10.51%
Opponent: 21.89%21.86%0.03%0.00%

5) 5/0ff
Equity: +1.208 (-0.082) XG Roller+

Player: 77.79%16.50%49.67%11.62%
Opponent: 22.21%22.21%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 819, Category Anchor

Black to play 1 1

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 9:58 AM, from admin

Pipcount: 61(-122) - 183(+122)

Comment:
There are some interesting choices: Obviously you can clear the 6-point, but where should you play the last ace? It turns out, that playing 3/2 (smoothing and remaining even on the 5-point) is already a serious mistake, you should play 5/4. Also pay attention to the second best move, clearing the 5-point. Opposed to position 814 (totally smooth) it is not best, but very close.

1) 6/5(2) 6/4
Equity: +1.333 7 ply

Player: 82.05%18.47%51.90%11.68%
Opponent: 17.95%17.95%0.00%0.00%

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

2) 5/4(2) 5/3
Equity: +1.315 (-0.018) 7 ply

Player: 82.03%19.19%52.12%10.72%
Opponent: 17.97%17.97%0.00%0.00%

3) 5/4(3) 3/2
Equity: +1.291 (-0.042) 7 ply

Player: 81.38%19.44%51.20%10.74%
Opponent: 18.62%18.62%0.00%0.00%

4) 6/5(3) 3/2
Equity: +1.251 (-0.082) 7 ply

Player: 79.74%17.82%51.28%10.64%
Opponent: 20.26%20.26%0.00%0.00%

5) 6/2
Equity: +1.175 (-0.158) 3 ply

Player: 79.49%18.59%50.77%10.13%
Opponent: 20.51%20.46%0.05%0.00%

Software: eXtreme Gammon Version: 1.13

Position 820, Category Anchor

Black to play 3 3

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 10:03 AM, from admin

Pipcount: 61(-122) - 183(+122)

Comment:
Two candidates, that have almost the same equity, bearing off wins by a hair.

1) 6/3(2) 6/0ff
Equity: +1.397 7 ply

Player: 82.50%15.43%53.47%13.60%
Opponent: 17.50%17.50%0.00%0.00%

Pipcount: 49(-134) - 183(+134)

2) 6/3(3) 5/2
Equity: +1.396 (-0.001) 7 ply

Player: 82.91%15.24%55.65%12.02%
Opponent: 17.09%17.09%0.00%0.00%

3) 6/0ff 5/2 3/0ff
Equity: +1.239 (-0.158) 7 ply

Player: 78.44%15.97%50.39%12.08%
Opponent: 21.56%21.56%0.00%0.00%

4) 6/0ff 3/0ff(2)
Equity: +1.227 (-0.170) XG Roller

Player: 77.76%16.65%47.61%13.50%
Opponent: 22.24%22.24%0.00%0.00%

5) 6/3 5/2(3)
Equity: +1.209 (-0.188) XG Roller

Player: 78.17%15.18%53.92%9.07%
Opponent: 21.83%21.83%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 821, Category Anchor

Black to play 4 2

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 10:06 AM, from admin

Pipcount: 61(-122) - 183(+122)

Comment:
The best move is simply 6/off. The resulting formation of your checkers is pretty safe. Following the "rule of even" would lead you to the wrong move.

1) 6/0ff
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) 6/2 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) 6/2 4/2
Equity: +1.157 (-0.129) XG Roller

Player: 76.97%16.61%51.11%9.25%
Opponent: 23.03%23.03%0.00%0.00%

4) 5/3 4/0ff
Equity: +1.109 (-0.177) XG Roller

Player: 75.31%16.95%48.16%10.20%
Opponent: 24.69%24.69%0.00%0.00%

5) 6/4 6/2
Equity: +0.874 (-0.412) XG Roller

Player: 69.32%16.96%43.43%8.93%
Opponent: 30.68%28.89%1.76%0.03%

Software: eXtreme Gammon Version: 1.13

Position 822, Category Anchor

Black to play 4 4

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 10:09 AM, from admin

Pipcount: 61(-122) - 183(+122)

Comment:
Both plays have the almost same equity. Opposed to position 817, taking 3 checkers off wins by a hair.

1) 6/2 4/0ff(3)
Equity: +1.122 7 ply

Player: 75.21%16.25%47.55%11.41%
Opponent: 24.79%24.79%0.00%0.00%

Pipcount: 45(-138) - 183(+138)

2) 6/2(3) 4/0ff
Equity: +1.121 (-0.001) 7 ply

Player: 75.35%14.60%51.48%9.27%
Opponent: 24.65%24.65%0.00%0.00%

3) 6/2(2) 4/0ff(2)
Equity: +0.328 (-0.794) 1 ply

Player: 52.62%14.71%32.20%5.71%
Opponent: 47.38%47.38%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Position 823, Category Anchor

Black to play 6 3

Black vs White

Moneygame: Jacoby and Beaver

added at 4/11/2010 10:16 AM, from admin

Pipcount: 61(-122) - 183(+122)

Comment:
The best move is to bear off two checkers. This play beats 6/off 5/2 clearly. The reason is, that the resulting position is much safer then then other.

1) 6/0ff 3/0ff
Equity: +1.285 7 ply

Player: 79.76%16.82%50.01%12.93%
Opponent: 20.24%20.24%0.00%0.00%

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

2) 6/0ff 5/2
Equity: +1.251 (-0.034) 7 ply

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

3) 6/3 6/0ff
Equity: +0.905 (-0.380) XG Roller+

Player: 68.94%15.78%42.69%10.47%
Opponent: 31.06%31.06%0.00%0.00%

Software: eXtreme Gammon Version: 1.13

Even in this position playing the rolls containing an ace are nearly identical to those in part 1 . Again 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 quickly The same is true for the other rolls containing no ace. Like in position part 1 it is best to bear off one checker (here of course from the heavy 3 point) and move the other checker from the 6 point try to clear the highest point fast.

updated: Thursday, April 15, 2010