Late Game Containment - theory

These are mostly notes from Stick's excellent lecture on Late Game Containment.  He discusses checker play strategy and tactics, for situations where you hit a late shot in the bearoff.  I made a similar post on my old blog in reference to an online match against Mochy.  Unfortunately, I deleted the old blog and didn't save any old posts or notes from that exercise.

This is the stem position.  Idea is to play it yourself against the computer over and over, make blunders and learn.  Shown here to discuss some of the main strategical and tactical themes for late game containment.

is Player 2 score: 0 pip: 38

Unlimited Game Jacoby Beaver

pip: 181 score: 0 is Player 1

XGID=---B-aC-B----C-----AACccc-:1:1:1:00:0:0:3:0:10

on roll, cube action?

Analyzed in XG Roller+	No redouble	Redouble/Take
Player Winning Chances:	43.01% (G:0.00% B:0.00%)	42.88% (G:0.00% B:0.00%)
Opponent Winning Chances:	56.99% (G:39.43% B:1.22%)	57.12% (G:39.50% B:1.19%)
Cubeless Equities	-0.546	-1.099
Cubeful Equities
No redouble:	-0.395
Redouble/Beaver:	-2.000 (-1.605)
Redouble/Pass:	+1.000 (+1.395)
Best Cube action: No redouble / Beaver
Percentage of wrong pass needed to make the double decision right: 34.9%

eXtreme Gammon Version: 2.02

These are roughly in descending order of importance.

Structural / Static Themes

• How many checkers has the opponent borne off?
• This is very important because it impacts when you can recube.
• Less than 5 off, you can often recube before the closeout is complete.
• Even with 5 off, you may be able to recube depending on how bad the opponent's homeboard is
• It may be right to leave a key point slotted, using the power of the recube to your advantage.  For example, opponent is on bar against 5 1/2 point board.  Leave the point slotted and recube if he dances.
• Do you need a second checker?
• 5 or 6 off (or less), usually don't need it.  Would be nice to get of course, but don't need to take reckless chances going for it.  Why?  Becuase you will be a large favorite anyway if you close one man out.
• 7 off (or more), usually would like to get the second checker.  Same reasoning about risk and reward.  Now even after you close him out you may be only 50-50 or even an underdog.  Picking up a second checker has a lot of upside as you can recube him out if you get it, and sometimes just on the threat of picking up the second checker.
• How strong is the opponent's home board.  This is huge since this determines how agressive / wimpy you need to be regarding loose hits.  Note the interplay of risk and reward.
• 1 or 2 point board. Downside is low since if you get hit you are a large favorite to reenter immediately.  So you can play pure and hit loose to fight for the key points and prevent opponent from escaping. 
• 3 point board. These are iffy, and depends on the specific position.  On one hand if you get hit you are still a favorite to reenter but on the other hand 25% of the time you dance.  You can easily go from sugar to shit in one sequence so you really need to consider the specific position.  Some questions:
• How critical is it to hit? 
• What is the downside? 
• How does the roll play if you don't hit?
• 4 point board or better.  Opponent's board deserves respect so tend towards safety.  That said, sometimes you gotta man up and hit anyway . Depends on the specific position.  Same questions as 3 point board apply but keep in mind the danger is greater.
• How critical is it to hit?
• What is the downside?
• How does the roll play if you don't hit?
• Match Score considerations.    At certain lopsided scores, the takepoints and gammon values  (for both sides) may be considerably different than money.  You could be more or less sensitive to gammons, and you could be recubing earlier or later depending on...
• Gammon Value ATS
• Takepoint ATS

Strategical Themes / Priorities

• Flood the outfield with checkers to cover the escape zone.  Escape zone is where the opponent's checker lands when he partially escapes (typically 7-11 pips out).  You want to have plenty of ammunition aimed at this area so you have a double or triple shot to hit opponent's checker should he land there.
• Build a winning prime / Close opponent out.  Obvious but let's keep the main goal in sight.
• Blocking big doubles.
• Low priority.
• Generally a 'luxury' play, meaning only block the big doubles if you have the position under control already
• How good is your outfield coverage?
• If you can't improve your position much than blocking the big doubles could be right.
• Avoid getting gammoned.
• Generally a low priority and not what you should be thinking about.  You should be playing to win.  Keep in mind turning every single game you turnaround (-2 to + 2)compensates for two gammon losses (-2 to -4)  
• But, if you can't win anyway (say he has 12 checkers off and you have a busted board) then you are really on gammon save.
• Or if his board is too strong you may have to be extra cautious as the price of getting hit is too high.

Tactical / Checker Play Themes

• Do you hit loose?  In addition to the strategical themes here are some tactical things to consider
• How key is the point?
• How does the roll play otherwise?
• How strong is your outfield coverage?
• How good is your blockade?
• What are the important points to fill in?
• Usually the 5 point, 4 point and the bar are the key points but it depends on the specific position.  So you are more likely to hit a checker loose that is sitting on one of these key points than a checker sitting on a deeper less valuable point such as 1, 2 or 3 point.
• If opponent's board is blotted you can be more aggressive in hitting loose because of the return shots
• You hit loose, opponent dances, and you don't cover.  Now what?
• If you have a lot of covers already then you don't necessarily need to bring another builder down.  Doesn't add many covers but creates the joker sequence he enters and hits and you dance - a disaster.  (Don't automatically bring more covers down.  See what your other options are)
• Generally don't move your furthest back checker as this is your last line of defence.
• Banana split hit often right when opponent has a weak board with a blot.  Or if opponent has significant enter and crack numbers (to expose a blot).
• Don't leave indirect shots if you don't have to.
• Spreading checkers in the outfield -
• outfield coverage tends to be better when checkers are adjacent to each other.
• move off points (flood the outfield for maximum coverage of escape zone)
• Dilly builders.  These guys have only one purpose - to fill in a low point.  Often right to hit loose or slot at earliest opportunity with these men.  This is especially true is opponent's board is weak and/or blotted. 

mohrp

Below are selected errors from an online match against mohrp.

First game of 7 point match.  I have already doubled and have 62 to play.

is mohrp score: 0 pip: 155

7 point match

pip: 120 score: 0 is Chutzpah

XGID=aBBAaBB-A---cC-a-bbeA-A---:1:-1:1:62:0:0:0:7:10

to play 62

1.	XG Roller+	13/7 8/6	eq: +0.551
	Player: Opponent: 66.11% (G:40.82% B:1.29%) 33.89% (G:8.16% B:0.47%)
2.	XG Roller+	22/20 13/7	eq: +0.542 (-0.009)
	Player: Opponent: 66.38% (G:37.45% B:1.19%) 33.62% (G:6.34% B:0.28%)
3.	XG Roller+	22/16 13/11	eq: +0.428 (-0.123)
	Player: Opponent: 63.78% (G:37.01% B:1.33%) 36.22% (G:10.25% B:0.92%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I moved 22/16, 13/11 which is a large mistake.

I was just trying to put my checkers in good spots should mohrp dance, but I am taking a pretty big chance.  The blot count is 5, at a time when 31, 34, 35 to enter and hit two blots.  33 appears to be really good either way.  All of his fours hit or clean up entirely while 44 becomes a super-joker.

Also, should morhrp dance then I have duplicated my own 5's, which hit on the outside but cover on the inside.

Best was 13/7, 8/6.  This cleans up one blot while diversiying my numbers should mohrp dance.  Now 5's hit on the outside while 3's and 4's cover.  Also Only 33 is a super joker for him while his entering sixes (36 46) are good rolls but also awkward.

**************
I lead 3 away 7 away and have 61 to play from the bar.

is mohrp score: 0 pip: 174

7 point match

pip: 164 score: 4 is Chutzpah

XGID=-b-a--E-CA--cD--ad-d----AA:0:0:1:61:4:0:0:7:10

to play 61

1.	XG Roller++	Bar/24 9/3*	eq: -0.261
	Player: Opponent: 48.91% (G:14.71% B:0.98%) 51.09% (G:14.47% B:0.74%)
2.	XG Roller++	Bar/18	eq: -0.321 (-0.059)
	Player: Opponent: 47.88% (G:13.20% B:0.78%) 52.12% (G:15.72% B:0.79%)
3.	3-ply	Bar/24 13/7	eq: -0.409 (-0.148)
	Player: Opponent: 45.97% (G:13.41% B:0.85%) 54.03% (G:16.89% B:1.33%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I tossed my guy to the bar point, Bar/18.

The computer likes Bar/24, 9/3*

Even though the 3 point is deep and I am using the wrong builder (I would rather attack by unstacking the 6 point) it looks like White's position is just too strong to leave alone.  I need to hit to try and slow him down.

By leaving him alone, mohrp is bound to do something good next turn. 
Also, my play abandons my anchor.  The ace point isn't much, but it is all I have at the moment so it may be prudent to hold it to cut down on the gammons a bit.

*************
I lead 3 away 6 away and have 44 to play.

is mohrp score: 1 pip: 137

7 point match

pip: 153 score: 4 is Chutzpah

XGID=----BcDAC---bB---bacB-bbA-:0:0:1:44:4:1:0:7:10

to play 44

1.	XG Roller++	24/20 13/9(2) 7/3	eq: -0.084
	Player: Opponent: 49.56% (G:7.00% B:0.21%) 50.44% (G:6.36% B:0.17%)
2.	XG Roller++	24/20 7/3 6/2(2)	eq: -0.114 (-0.031)
	Player: Opponent: 49.29% (G:8.75% B:0.26%) 50.71% (G:8.67% B:0.23%)
3.	4-ply	24/20 8/4 7/3 6/2	eq: -0.143 (-0.059)
	Player: Opponent: 48.68% (G:8.66% B:0.26%) 51.32% (G:9.26% B:0.29%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I made the second best play here, 24/20, 7/3, 6/2(2).  While it isn't the worst play I've ever made, I think the error is instructive. 

Best was 24/20, 13/9(2), 7/3.  13/9(2) is a useful play for several reasons.  First it forms a min-block agsint his anchor - The 6-point, 8-point, 9-point is often annoying for the opponent and I may be able to hold it for a while.  Second, I have an advanced anchor already so I don't need the midpoint anymore.  Third, holding the midpoint strips my position a bit.  By moving to the 9-point instead I keep more checkers above his anchor (for now) and also allow myself some time to move checkers for several rolls while I await a double to move off the anchor.  Finally, note the race is close which I is related to the above but reinforces the point that I form a position I can hold for a while while hoping to roll a double.

***********
Same game.  I have 32 to play.

is mohrp score: 1 pip: 107

7 point match

pip: 123 score: 4 is Chutzpah

XGID=--BBCbB-A---bB-A-b-bB-bbc-:0:0:1:32:4:1:0:7:10

to play 32

1.	XG Roller++	8/6 4/1	eq: -0.188
	Player: Opponent: 47.82% (G:12.54% B:0.36%) 52.18% (G:12.00% B:0.21%)
2.	XG Roller++	8/3	eq: -0.219 (-0.030)
	Player: Opponent: 46.49% (G:10.96% B:0.35%) 53.51% (G:10.52% B:0.14%)
3.	XG Roller++	15/13 4/1	eq: -0.257 (-0.068)
	Player: Opponent: 46.13% (G:10.87% B:0.21%) 53.87% (G:11.68% B:0.17%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I made the poor checker play, 15/31, 4/1.

Best was 8/6, 4/1 while also bad, but superior to my play would have been 8/3.

I think the idea is place your blot where opponent has to pay the biggest price to hit.

8/6 goes to a good spot as does 4/1 which is a small bonus.  The only use for my man on the 4 point is to fill in the ace so let's just go there now.  But again I think the key is to make him hit me from the midpoint.  This way, (1) I will have more jokers which enter and enter and hit - I may have aces to hit as extras.  (2) When opponent hits, at least he is not escaping his back men at the same time.  When he hits on his side of the board, he is no closer to escaping from the back anchor.  Compare to when he hits on my side of the board, and he is moving from the back anchor at the same time.  I think this small detail is important, and probably the strategical reason why my pay is wrong.  #1 is the tactical reason why it is wrong.

***********
I lead 3 away 4 away and am on roll.  Cube action?

is mohrp score: 3 pip: 135

7 point match

pip: 124 score: 4 is Chutzpah

XGID=-----CC-CBA-fC---bbbc-----:0:0:1:00:4:3:0:7:10

on roll, cube action?

Analyzed in XG Roller++	No double	Double/Take
Player Winning Chances:	74.64% (G:0.04% B:0.00%)	74.72% (G:0.05% B:0.00%)
Opponent Winning Chances:	25.36% (G:0.00% B:0.00%)	25.28% (G:0.00% B:0.00%)
Cubeless Equities	+0.493	+1.487
Cubeful Equities
No double:	+0.822 (-0.061)
Double/Take:	+0.882
Double/Pass:	+1.000 (+0.118)
Best Cube action: Double / Take

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

This one still confuses me.   I didn't double, thinking this is an easy money take and his take point at this score is lower than money so I should be more conservative with the cube and wait.

And yet, this is a small double for a money and a larger double at this score.  What is going on?  The short answer is I don't know but here is a guess.  Opponent's low takepoint is based on the power of his recube leverage.  In a contact position the trailer will have more opportunity to rewhip than in a straight race. 

The above makes some sense to me - but isn't my takepoint on a rewhip a very high 40%?  Even though a race with no contact where I can win two points is exactly what I want, don't I still need to be careful since he can turn around a long race very easily and all of a sudden I am dropping or playing for the match?  I still don't get it.

************
I lead 2 away 4 away and have 23 to play.

is mohrp score: 3 pip: 128

7 point match

pip: 121 score: 5 is Chutzpah

XGID=--bC-CB-B---bD---Abcc-c---:0:0:1:32:5:3:0:7:10

to play 32

1.	XG Roller++	17/14 13/11	eq: +0.210
	Player: Opponent: 62.76% (G:12.67% B:0.62%) 37.24% (G:9.85% B:0.24%)
2.	XG Roller++	13/8	eq: +0.154 (-0.056)
	Player: Opponent: 62.04% (G:11.65% B:0.58%) 37.96% (G:9.73% B:0.18%)
3.	XG Roller++	17/14 3/1	eq: +0.153 (-0.057)
	Player: Opponent: 61.07% (G:14.19% B:0.58%) 38.93% (G:10.62% B:0.23%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I noticed the duplication of 5's to hit and escape and so played 13/8 which balances my builders.

Apparently this was a situation where the most important factor is not getting hit and thus 17/14, 13/11 is the better play.

13/8 leaves 15 hitters - and mohrp certainly won't hesitate to hit.  The other play (17/14,13/11) leaves 13 hitters. 

bjfarquhar

I joined a gym for the first time in my life about a month ago and discovered the 7-10 hours per week I spend exercising has discplaced my time available to blog.  I still hope to continue blogging, but it looks like I will be less active, at least for a while.

Good news.  Paul Money has resumed his blogging.  Please check his excellent work at dorbel daily.

Below are selected errors from an online match against bjfarquhar.

Opening game of 11 point match.  I have 43 to play.

is bjfarquhar score: 0 pip: 131

11 point match

pip: 109 score: 0 is Chutzpah

XGID=---BBcDBBB--b------bccbA--:1:1:1:43:0:0:0:11:10

to play 43

1.	XG Roller+	7/4 7/3	eq: -0.053
	Player: Opponent: 40.29% (G:9.32% B:0.26%) 59.71% (G:9.76% B:0.18%)
2.	XG Roller+	6/3 6/2	eq: -0.144 (-0.090)
	Player: Opponent: 38.67% (G:10.21% B:0.32%) 61.33% (G:14.76% B:0.35%)
3.	2-ply	6/2 4/1	eq: -0.240 (-0.186)
	Player: Opponent: 35.44% (G:8.13% B:0.23%) 64.56% (G:15.27% B:0.33%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I moved 6/3, 6/2.  This holds my baby prime but why?  I am not trying to prime him here.  Moreover, waht is the opponent going to do next time?  He is going to hit me loose.  Having a homeboard blot is not constructive at this time.  Better was 7/4,7/3 which leaves the homeboard clean in aticipation of getting hit next time.  Another point is that my move leaves me very brittle next time.  I have no spares to play.  The computer's play on the other hand gives me sixes out (if I don't get hit) and small numbers to maybe make a point next time.

**********
Same game.  I won the cube and have 15 to play from the air.

is bjfarquhar score: 0 pip: 106

11 point match

pip: 104 score: 0 is Chutzpah

XGID=-aACB-BBBBaa------acbbbb-A:1:1:1:51:0:0:0:11:10

to play 51

1.	XG Roller++	Bar/24 7/2	eq: -0.866
	Player: Opponent: 18.66% (G:5.70% B:0.45%) 81.34% (G:34.23% B:0.71%)
2.	XG Roller++	Bar/24 9/4	eq: -0.945 (-0.078)
	Player: Opponent: 18.29% (G:5.00% B:0.40%) 81.71% (G:39.80% B:1.57%)
3.	2-ply	Bar/24 8/3	eq: -1.072 (-0.206)
	Player: Opponent: 16.84% (G:4.46% B:0.33%) 83.16% (G:48.26% B:2.27%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

This one I don't understand.  I moved Bar/24, 9/4 while the correct play is Bar/24, 7/2. 

I suppose the computer's play covers the 2 point and best positions me should my opponent miss.  His sixes are duplicated after all.  But the details show that this move gets you gammoned more while winning only a smidge more so I am not sure why this is the better play - looking at the numbers.

****************
I trail 11 away 9 away and have 41 to play.

is bjfarquhar score: 2 pip: 145

11 point match

pip: 146 score: 0 is Chutzpah

XGID=---b-BDBC---cB---d-d--b-B-:0:0:1:41:0:2:0:11:10

to play 41

1.	XG Roller+	24/20 6/5	eq: +0.367
	Player: Opponent: 59.27% (G:13.44% B:0.51%) 40.73% (G:11.18% B:0.30%)
2.	XG Roller+	8/4 6/5	eq: +0.291 (-0.076)
	Player: Opponent: 57.09% (G:14.93% B:0.59%) 42.91% (G:12.68% B:0.68%)
3.	4-ply	24/23 24/20	eq: +0.327 (-0.040)
	Player: Opponent: 58.30% (G:12.67% B:0.46%) 41.70% (G:11.45% B:0.35%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

The obvious play is 24/20,6/5 splitting for an advanced anchor while diversifying on the other side of the board, and it is indeed correct.

I moved 8/4, 6/5.  My thinking was that my opponent has an attacking structure (rather than a priming structure) so I don't want to split into his stacks.  I guess this was a case of overthinking.  He has an anchor, I don't which favors splitting.  I am short on timing, argues for moving the back guys now.  I have a solid prime already, so it will be difficult for opponent to attack and escape at the same time.  Meanwhile, getting a third checker behind my 4 prime is bad for him, also argues for splitting.

*************
Here is a simple 3rd roll position.  65R-63S-65??

is bjfarquhar score: 2 pip: 158

11 point match

pip: 156 score: 3 is Chutzpah

XGID=-a----EaC---dF-a-c-e----A-:0:0:1:65:3:2:0:11:10

to play 65

1.	XG Roller+	24/13	eq: +0.308
	Player: Opponent: 58.87% (G:6.98% B:0.19%) 41.13% (G:5.77% B:0.14%)
2.	XG Roller+	13/7* 6/1*	eq: +0.225 (-0.084)
	Player: Opponent: 54.85% (G:16.49% B:0.56%) 45.15% (G:11.08% B:0.39%)
3.	3-ply	13/8 13/7*	eq: +0.171 (-0.138)
	Player: Opponent: 54.11% (G:14.20% B:0.62%) 45.89% (G:10.65% B:0.41%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I made the 2nd roll play, 13/7*, 6/1* which is a large error in this exact position.

Since I have escaped one man already, I should be thinking 'up in the race, race.'  Simply 24/13 is correct and then hope to roll smooth and bring the position home from there.

Strategy-wise, I don't want to attack here nor do I want to be hit myself, so hitting is simply the wrong gameplan.

************
Here is another related 3rd roll position that I blundered.  65R-64S-55?

is bjfarquhar score: 2 pip: 157

11 point match

pip: 156 score: 7 is Chutzpah

XGID=-a----EaC---dF--ac-e----A-:0:0:1:55:7:2:0:11:10

to play 55

1.	XG Roller+	13/8(2) 6/1*(2)	eq: +0.452
	Player: Opponent: 61.49% (G:22.60% B:0.77%) 38.51% (G:7.66% B:0.24%)
2.	XG Roller+	8/3(2) 6/1*(2)	eq: +0.370 (-0.082)
	Player: Opponent: 58.65% (G:27.34% B:0.88%) 41.35% (G:9.44% B:0.41%)
3.	2-ply	13/3(2)	eq: +0.213 (-0.239)
	Player: Opponent: 57.06% (G:14.50% B:0.36%) 42.94% (G:8.00% B:0.26%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

Once again, I am up in the race and don't want to get hit, nor do I really want to attack/blitz.

My play 8/3*(2), 6/1(2)* leaves me blotted on the 8 point, while not really greatly placed for conducting a blitz anyway even in the best scenario.

The quiet and blotless 13/8(2), 6/1*(2) is the way to go.  Put him on the bar, gain 20 pips, and leave no blots.

****************
Here is another early game position.  I lead 2 away 9 away and have 41 to play.

is bjfarquhar score: 2 pip: 155

11 point match

pip: 155 score: 9 is Chutzpah

XGID=----bBE-B---cDa-ac-e---AA-:0:0:1:41:9:2:0:11:10

to play 41

1.	XG Roller+	23/18	eq: -0.302
	Player: Opponent: 48.41% (G:10.60% B:0.41%) 51.59% (G:13.99% B:0.39%)
2.	XG Roller+	13/9 6/5	eq: -0.360 (-0.058)
	Player: Opponent: 46.64% (G:10.87% B:0.42%) 53.36% (G:14.06% B:0.50%)
3.	4-ply	24/20 6/5	eq: -0.304 (-0.002)
	Player: Opponent: 47.85% (G:8.90% B:0.29%) 52.15% (G:13.05% B:0.41%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I made the 'creative play' 13/9, 6/5 slotting the best blocking point and sort of duplicating some of his hitting 5's.

The correct play 23/18 looks obvious in retrospect.  This is a classic disctraction play.  Opponent has an anchor and I don't so splitting is a priority.  I have him outboarded right now 2 to 1 so action favors me at the moment.  If I go for a high split I would rather get hit outside than inside where he may point on my head making a homebard point at the same time.  So the bar poinr is the place to split to.

************
I lead 2 away 4 away and have 51 to play.

is bjfarquhar score: 7 pip: 161

11 point match

pip: 149 score: 9 is Chutzpah

XGID=----abDCC---dB-B-a-eb---A-:0:0:1:51:9:7:0:11:10

to play 51

1.	XG Roller+	24/18	eq: +0.025
	Player: Opponent: 57.63% (G:8.50% B:0.28%) 42.37% (G:9.18% B:0.19%)
2.	XG Roller+	24/23 8/3	eq: -0.123 (-0.148)
	Player: Opponent: 54.87% (G:11.09% B:0.41%) 45.13% (G:11.98% B:0.29%)
3.	2-ply	8/2	eq: -0.177 (-0.203)
	Player: Opponent: 52.43% (G:8.72% B:0.21%) 47.57% (G:12.19% B:0.43%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I scooted up on pip and dumped behind him, 24/23, 8/3.

Best was to simply try and escape 24/18.

I am up the race and my back blot is my big liability so running is good.  He only hits sixes (minus 33) and aces which means he misses a significant portion of the time.  If I do get hit I am not much worse off than before, only losing 7 pips.  He only has a 2 point board so getting hit is not fatal. And I may get return shots from the bar, which is good.  Also, dumping checkers behind him is not really what you want to do.