Would you expose more blots when faced with a 4 ½ point backgammon board ?

image006

The match score and factors to take into account : : 0-0 to 3, cube is in the middle. This is slightly different than in a real money backgammon game, but not by much.

The important features of this position are:

The position is nearly symmetrical, although the blot in White’s board is both a builder to make a 5-point board and subject to an immediate return shot.

Black has to make a decision whether to volunteer a shot now, or to collapse his board

What occured at the table: Black held the anchor, playing 6-5 6-3.

The results:

play-to-win-2

There are three possible options that are all sensible here.

1. 21-17 is taking the bull by the horns.

Black cannot sit on the position, and even his slight racing lead is going to force him to either leave the anchor or to give up his board.

2. 5-2 3-2 leaves a blot but does not bury any new checkers

Black will still have 13 checkers “in play” to block and hold his board.

3. 6-3 6-5 is safe for this roll, but gives up the 6-point, which Black will probably never make again.

First, let us take a look at the rollout results, then discuss each of the three possible plays.

21-17 certainly seems like a risk. . It gives White some very strong rolls.

The safe play will leave no killing shots. But let us look at the equities for White after each of his rolls following each of the 3 options we are analysing

After 21-17:

image006

Roll Equity
55 1.306
21 1.125
53 1.056
33 0.762
66 0.718
54 0.586
44 0.505
52 0.493
65 0.452
51 0.389
11 0.367
32 0.326
41 0.305
22 0.236
62 0.210
43 0.152
63 0.151
31 0.038
42 -0.067
61 -0.130
64 -0.153

After 5-2 5-3

image008

Roll Equity
31 1.002
21 0.597
11 0.582
51 0.571
61 0.569
66 0.543
55 0.537
44 0.517
64 0.512
41 0.493
33 0.446
22 0.442
53 0.424
62 0.411
32 0.385
63 0.375
43 0.353
52 0.223
42 0.127
65 0.104
54 -0.059

After 6-3 6-5

image010

Roll Equity
55 0.688
33 0.668
44 0.641
32 0.640
21 0.640
66 0.601
22 0.596
63 0.584
43 0.557
53 0.553
64 0.542
62 0.535
52 0.426
61 0.407
65 0.402
41 0.383
42 0.378
51 0.371
31 0.356
54 0.266
11 0.039

What is the key? Clearing the 6-point simply does not leave White with any bad possible rolls.. Black’s lack of direct shots at the 6 and 14 points create relatively safe landing points.

Moreover, when White is hit, Black cannot contain him – now or in the futurer. Black has a 3-point board and will very likely not get a stronger position later.

It is my opinion that it would be hard to do this kind of analysis over the board. Setting up each of the 3 positions and then looking at White’s 21 possible shakes.

Conventional backgammon strategy teaches us to not release the anchor until we absolutely have to, that the first player to release their anchor in a mutual holding game is at a disadvantage. And to be sure, Black is at a disadvantage here.

But we also know that outfield control and keeping the checkers connected are crucial elements if you want to play backgammon to win. . Here, with the game close, the edge goes to the side that can successfully make a break for their home.. Once Black buries those two checkers on the 6-point, White will have much better control of the outfield for the duration of the game..

This position reminds me of Kent Goulding’s maxim “If you play to avoid losing, you will inevitably fail.” On the whole , Black’s need for connectivity, flexibility, and outfield control, are much greater than the cost of an immediate shot – with a possible return if White cannot cover.

There is one more interesting point to note with the game in this position: If you look at the equities, most of the plays after clearing the 6-point and White’s return put him right into the window of an efficient double.

The number of rolls that give equity between .530 and .700 are:

21-17: 2 rolls! 5 shakes (hit and cover numbers) leave White playing for a gammon, 66 and 33 give him a double and a big pass, but the other 27 rolls don’t even give him a double. White will get limited value from the cube in this scenario.

5-2 3-2: 9 rolls. 31 lets White play on for a gammon, the other 25 rolls leave a marginal double if at all.

6-5 6-3: 19 rolls! Most of White’s rolls let him get great outfield coverage. The race may be even, but Black will have to leave the first meaningful shot, often a double shot.

I rolled the position out moving the cube to Black’s side – as though White had already doubled. Admittedly this will change the gammon values and White’s later doubling window, but we see that the gap between the plays narrows significantly. . Much of the edge to 21-17 comes from the relative cube inefficiency it gives later.

image004

Admittedly, this analysis has one significant flaw. I looked at equities after White’s next roll. The cube decision will come after White’s roll and Black’s reply. 3 candidate plays times 441 replies was a bit much to analyze. But notice that the difference in the cubeful equity after the rollout between the best and worst of the 3 plays is over 0.300 with White having cube access, and only 0.130 when White has given up the cube.

The key lessons to be learned from this position are :

1) Outfield control means a whole lot in backgammon

2) Occasionally , cube efficiency can mean a lot too