Game number 2

The score (after 1 game) is: White 0, Black 4 (match to 7 points)

[First Game] [Previous Game] [Next Game] [Last Game]

Match Information

Date	août 05, 2008
Place	Slot Backgammon training match
Annotator	Fabrice Liardet
Comment	This match is played with the rules of Nack Ballard's Slot Backgammon, which state that the first move of the game must always be "a slot", which means a move that leaves a blot in direct range of the opponent's rear checkers (points 7 to 2).

Move number 1: White to play 43

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

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

Pip counts: White 167, Black 167
Position ID: 4HPwATDgc/ABMA Match ID: MADuAAAAIAAA

• White moves 13/10 13/9

#		Ply	Move	Equity
			13/10 13/9

Move number 2: Black to play 62

Pip counts: White 167, Black 167
Position ID: 4HPwATDgc/ABMA Match ID: cAnrAAAAIAAA

• Black moves 13/5

#		Ply	Move	Equity
			13/5

Annotation

This is one of the "good slots", that is only a small error in usual backgammon

Move number 3: White to play 42

Pip counts: White 167, Black 159
Position ID: 0OfgATDgc/ABMA Match ID: MAHqAAAAIAAA

• White moves 24/20* 13/11

Cube decision
2-ply cubeless equity		-0,006	(Money: -0,003)
	0,501 0,137 0,006 - 0,499 0,142 0,006
Cubeful equities:
1.	No double	+0,215
2.	Double, pass	+1,000	+0,785
3.	Double, take	+0,116	-0,099
Proper cube action:		No double, take (11,2%)

#		Ply	Move	Equity
•	1	2	24/20* 13/11	+0,516
			0,565 0,171 0,011 - 0,435 0,110 0,003
	2	2	24/22 24/20*	+0,440 ( -0,076)
			0,556 0,155 0,009 - 0,444 0,109 0,003
	3	2	24/20*/18	+0,409 ( -0,108)
			0,552 0,151 0,009 - 0,448 0,120 0,004
	4	2	24/20* 6/4	+0,367 ( -0,149)
			0,535 0,150 0,009 - 0,465 0,125 0,005
	5	2	24/20* 8/6	+0,363 ( -0,154)
			0,538 0,154 0,009 - 0,462 0,116 0,003

Move number 4: Black to play 11

Pip counts: White 161, Black 179
Position ID: 4HPkASHgc/AAWA Match ID: cInkAAAAIAAA

• Black moves bar/23 6/5*(2)

Alert: lucky roll! ( +0,375)

#		Ply	Move	Equity
•	1	2	bar/23 6/5*(2)	+0,012
			0,556 0,173 0,008 - 0,444 0,119 0,005
	2	2	bar/24 6/5*(3)	-0,077 ( -0,089)
			0,536 0,169 0,008 - 0,464 0,133 0,007
	3	2	bar/24 8/7 6/5*(2)	-0,109 ( -0,121)
			0,535 0,172 0,009 - 0,465 0,147 0,010
	4	0	bar/22 6/5*	-0,394 ( -0,406)
			0,465 0,124 0,006 - 0,535 0,178 0,014
	5	0	bar/23 24/23 6/5*	-0,398 ( -0,410)
			0,461 0,125 0,005 - 0,539 0,178 0,010

Move number 5: White to play 63

Pip counts: White 166, Black 175
Position ID: sHPwADTgc+QBUA Match ID: MAHvAAAAIAAA

• White moves bar/16

#		Ply	Move	Equity
•	1	2	bar/16	+0,062
			0,467 0,121 0,006 - 0,533 0,168 0,007
	2	2	bar/22 24/18	-0,002 ( -0,064)
			0,450 0,118 0,007 - 0,550 0,182 0,008
	3	2	bar/22 11/5	-0,092 ( -0,154)
			0,423 0,112 0,005 - 0,577 0,182 0,009
	4	0	bar/22 8/2*	-0,112 ( -0,174)
			0,415 0,118 0,007 - 0,585 0,197 0,013
	5	0	bar/22 13/7	-0,173 ( -0,235)
			0,400 0,115 0,007 - 0,600 0,217 0,015

Move number 6: Black to play 54

Pip counts: White 157, Black 175
Position ID: 4HPkESCwc/AANA Match ID: cInyAAAAIAAA

• Black moves 23/18 13/9*

#		Ply	Move	Equity
	1	2	23/14*	+0,126
			0,585 0,188 0,011 - 0,415 0,109 0,004
•	2	2	23/18 13/9*	+0,121 ( -0,005)
			0,588 0,200 0,013 - 0,412 0,119 0,006
	3	2	13/9* 13/8	+0,062 ( -0,064)
			0,569 0,200 0,011 - 0,431 0,121 0,006
	4	0	13/9* 6/1*	-0,017 ( -0,142)
			0,554 0,204 0,011 - 0,446 0,138 0,010
	5	0	13/9*/4	-0,037 ( -0,163)
			0,551 0,187 0,011 - 0,449 0,140 0,009

Annotation

Actually I think I played the four first, then looked for a five and missed the outfield hit altogether. Luckily for me, the outfield hit left more returns than usual and the game move was pretty strong anyway.
Note that it would have been the slightly better move at an even match score, but that it is a bit more gammonish (in both ways), since it is bringing a builder and doesn't develop the back checkers.

Move number 7: White to play 63

Pip counts: White 166, Black 166
Position ID: sHPhIDDgc+QBUA Match ID: MAHvAAAAIAAA

• White moves bar/16*

#		Ply	Move	Equity
•	1	0	bar/16*	+0,226
			0,500 0,149 0,010 - 0,500 0,149 0,007
	2	0	bar/22 13/7*	-0,001 ( -0,227)
			0,441 0,135 0,009 - 0,559 0,194 0,013
	3	0	bar/22 11/5	-0,178 ( -0,404)
			0,400 0,110 0,006 - 0,600 0,212 0,013
	4	0	bar/22 24/18	-0,266 ( -0,492)
			0,386 0,097 0,006 - 0,614 0,251 0,012
	5	0	bar/22 8/2	-0,345 ( -0,570)
			0,360 0,097 0,005 - 0,640 0,251 0,019

Move number 8: Black to play 32

Pip counts: White 157, Black 182
Position ID: 4HPkESCwc3AQWA Match ID: cInpAAAAIAAA

• Black moves bar/22 24/22

#		Ply	Move	Equity
•	1	2	bar/22 24/22	-0,272
			0,481 0,138 0,005 - 0,519 0,141 0,005
	2	2	bar/23 24/21	-0,355 ( -0,083)
			0,472 0,137 0,006 - 0,528 0,169 0,010
	3	2	bar/23 8/5	-0,356 ( -0,084)
			0,470 0,142 0,005 - 0,530 0,162 0,010
	4	2	bar/22 18/16	-0,368 ( -0,096)
			0,471 0,137 0,006 - 0,529 0,167 0,011
	5	2	bar/23 13/10	-0,383 ( -0,111)
			0,474 0,139 0,006 - 0,526 0,183 0,015

Annotation

There is nothing else to be achieved with this roll

Move number 9: White to play 53

Pip counts: White 157, Black 177
Position ID: sHNwECbgc+QRIA Match ID: MIHuAAAAIAAA

• White moves 24/21 16/11

Cube decision
2-ply cubeless equity		+0,038	(Money: +0,041)
	0,519 0,141 0,005 - 0,481 0,138 0,005
Cubeful equities:
1.	No double	+0,272
2.	Double, pass	+1,000	+0,728
3.	Double, take	+0,201	-0,071
Proper cube action:		No double, take (8,9%)

#		Ply	Move	Equity
•	1	2	24/21 16/11	+0,334
			0,541 0,138 0,006 - 0,459 0,131 0,003
	2	2	24/16	+0,310 ( -0,023)
			0,545 0,113 0,003 - 0,455 0,124 0,003
	3	2	16/11 13/10	+0,163 ( -0,171)
			0,493 0,129 0,005 - 0,507 0,147 0,005
	4	2	16/13 11/6	+0,151 ( -0,183)
			0,494 0,120 0,003 - 0,506 0,143 0,003
	5	0	16/8	+0,112 ( -0,222)
			0,479 0,124 0,004 - 0,521 0,146 0,004

Annotation

Being 4-0 down, White wants some offense (translate : some gammons), and the 11 point is a good one to have. Anchoring on the 16 is good but not as threatening.

Move number 10: Black to play 31

Pip counts: White 149, Black 177
Position ID: 4HPMAwSwc3AQJg Match ID: cInlAAAAIAAA

• Black moves 8/4*

#		Ply	Move	Equity
•	1	2	8/4*	-0,355
			0,472 0,134 0,004 - 0,528 0,162 0,008
	2	2	22/18	-0,366 ( -0,011)
			0,448 0,112 0,002 - 0,552 0,128 0,004
	3	2	24/21 22/21	-0,414 ( -0,059)
			0,439 0,107 0,003 - 0,561 0,131 0,004
	4	2	24/23 8/5	-0,484 ( -0,129)
			0,424 0,110 0,003 - 0,576 0,141 0,005
	5	2	18/15 8/7	-0,495 ( -0,140)
			0,433 0,110 0,002 - 0,567 0,157 0,008

Annotation

A close call between two radically different moves. The game move is by far the best to win the game, because it starts a prime against White's back checker and Black is still OK if hit. But the score is so gammon-safeish that upgrading the anchor with 22/18 is almost correct, by virtue of losing 3.4% less gammons.

Move number 11: White to play 11

Pip counts: White 153, Black 173
Position ID: aGdwECbgc8wDQA Match ID: MIHkAAAAIAAA

• White moves bar/24 8/7* 6/5(2)

Cube decision
2-ply cubeless equity		+0,085	(Money: +0,087)
	0,528 0,162 0,008 - 0,472 0,134 0,004
Cubeful equities:
1.	No double	+0,355
2.	Double, pass	+1,000	+0,645
3.	Double, take	+0,299	-0,056
Proper cube action:		No double, take (8,0%)

Alert: lucky roll! ( +0,337)

#		Ply	Move	Equity
•	1	0	bar/24 8/7* 6/5(2)	+0,781
			0,633 0,233 0,016 - 0,367 0,101 0,003
	2	0	bar/21*	+0,581 ( -0,201)
			0,590 0,191 0,011 - 0,410 0,102 0,002
	3	0	bar/23 6/5(2)	+0,559 ( -0,223)
			0,601 0,163 0,007 - 0,399 0,111 0,002
	4	0	bar/24 6/5(3)	+0,549 ( -0,232)
			0,597 0,164 0,007 - 0,403 0,111 0,002
	5	0	bar/24 8/7*(3)	+0,453 ( -0,328)
			0,558 0,178 0,009 - 0,442 0,121 0,003

Annotation

White is already knocking at the door of a double, because winning a doubled gammon is huge when trailing by far.

Move number 12: Black to play 55

Pip counts: White 149, Black 180
Position ID: sGvMAyBoZ3AAUw Match ID: cIn2AAAAIAAA

• Black cannot move

#		Ply	Move	Equity
			Cannot move

Annotation

Given a match equity table, the calculation of a take point is rather simple. From the doublee's point of view, the three possible outcomes are losing a doubled game (LD), passing (P) and winning a doubled game (WD). From the "universal" formula risk / (risk + reward), the take point is (P-LD) / (WD-LD). Unfortunately, two further considerations can shift that take point by a significant amount : gammons and the redouble potential.

While the doublee's gammons are usually sparse, the doubler's gammons are an important consideration and make for a fourth possible outcome. That outcome has to be merged into the LD equity, like it will be shown below. I will spare the redouble considerations for a later annotation, since here Black get very low equity from his redoubles : if he wins he will be 6-0 ahead anyway with a 91% of winning chances, while a redouble to 4 would allow White an automatic redouble to 8, making the game a double match point.

After the g11 MET, Black's equity after winning a doubled game is 91%, his equity after losing a single one is 71.5%. For figuring his equity after winning a doubled one, White's gammon rate (percentage of gammons among his won games) is crucial here, and its estimation is difficult. I went with 40% in the game, which was not too bad. That means that White's equity after winning a doubled game is 60% of the equity at 4-2 up (65%), plus 40% of the equity at a 4-4 tie (50%), which is 59%. So the take point is (71.5-59) / (91-59), about 39%. A very high take point, which is generally the case when one is leading and there are many gammons in the air. 39% is obviously too much to ask for in this position, even with good chances of a backgame and a healthy front position.

Move number 13: White doubles to 2

Pip counts: White 149, Black 180
Position ID: aGdwAFOwa8wDIA Match ID: MBngAAAAIAAA

• Black rejects

Alert: wrong double ( -0,006)!

Cube decision

Rollout cubeless equity

+0,564

(Money: +0,544)

Cubeful equities:

No double

+1,006

Double, take

+1,334

+0,328

Double, pass

+1,000

-0,006

Proper cube action:

Too good to double, pass (1,9%)

Rollout details

	Win	W g	W bg		Lose	L g	L bg	Cubeless	Cubeful
Centered 1-cube	0,652	0,291	0,022	-	0,348	0,071	0,002	+0,564	+1,006
Standard error	0,001	0,001	0,000	-	0,001	0,000	0,000	0,003	0,003
Player Black owns 2-cube	0,673	0,310	0,021	-	0,327	0,071	0,003	+1,379	+1,334
Standard error	0,001	0,001	0,000	-	0,001	0,001	0,000	0,005	0,005

Truncated cubeful rollout (depth 11) with var.redn.

1296 games, Mersenne Twister dice gen. with seed 837397995 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]

Annotation

Great mental arithmetic job I did here, you think ? Not really. In fact I got one of the match equities wrong, which butchered the entire job and gave me a take point of 32% instead of 39%. But fortunately, in the same time I underestimated Black's chances and thought it was still a borderline pass. In fact, even though Black's chances are better than that, it is a big pass and at the borderline of too good to double for White !

Apart from the lucky side, what that shows is that if one wants to make match equity computations, one had better do them right...

White wins 1 point

Game statistics for game 2
Player	White	Black
Checker play statistics
Total moves	6	6
Unforced moves	5	4
Unmarked moves	1	1
Moves marked good	5	5
Moves marked doubtful	0	0
Moves marked bad	0	0
Moves marked very bad	0	0
Error rate (total)	+0,000	-0,005 ( -0,030%)
Error rate (per move)	+0,0	-1,2 ( -0,008%)
Chequerplay rating	Supernatural	Supernatural
Luck statistics
Rolls marked very lucky	0	0
Rolls marked lucky	1	1
Rolls unmarked	4	4
Rolls marked unlucky	0	0
Rolls marked very unlucky	0	0
Luck rate (total)	+0,749 ( +4,873%)	+0,006 ( +0,040%)
Luck rate (per move)	+124,9 ( +0,812%)	+1,0 ( +0,007%)
Luck rating	Go to Las Vegas immediately	None
Cube statistics
Total cube decisions	6	6
Close or actual cube decisions	4	1
Doubles	1	0
Takes	0	0
Passes	0	1
Missed doubles (below CP)	0	0
Missed doubles (above CP)	0	0
Wrong doubles (below DP)	0	0
Wrong doubles (above TG)	1 (-0,006 ( -0,042%))	0
Wrong takes	0	0
Wrong passes	0	0
Error rate (total)	-0,006 ( -0,042%)	+0,000
Error rate (per cube decision)	-1,6 ( -0,010%)	+0,0
Cube decision rating	Supernatural	Supernatural
Overall statistics
Error rate (total)	-0,006 ( -0,042%)	-0,005 ( -0,030%)
Error rate (per decision)	-0,7 ( -0,005%)	-0,9 ( -0,006%)
Equiv. Snowie error rate	-0,5	-0,4
Overall rating	Supernatural	Supernatural
Actual result	+5,09%	-5,09%
Luck adjusted result	+0,26%	-0,26%

[First Game] [Previous Game] [Next Game] [Last Game]

Output generated Tue Sep 09 12:27:47 2008 by GNU Backgammon 0.16-mingw (HTML Export version 1.172)