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Let me give you some examples

Posted By: Stick
Date: Friday, 13 January 2017, at 3:55 p.m.

In Response To: Let me give you some examples (Tenland)

Let's walk through these one at a time using cluster counting.





White is Player 2

score: 6
pip: 144
7 point match
pip: 189
score: 1

Blue is Player 1
XGID=--B--BBaBa--cBa--bbe---ABB:1:-1:1:51:1:6:0:7:10
Blue to play 51

eXtreme Gammon Version: 2.10

The first thing I'll point out is I kind of hate using examples where we don't need to know the count like ever. When will we need to know the pip count with two on the bar and 3 other men back?? Using real life examples where we would need to know the count is more practical because we practice something we're likely to use again. Anyway, any exercise is better than no exercise at all.

I'll start with Blue.

I'd group the back men all together and see them quickly as 125-4 or 121. On the bar is 25 pips so I imagine them all on the bar and subtract the pips forward they are.

Now to the outer board. You should either have this memorized (preference) or you can do it the old fashioned way or some sort of mental shift way I suppose. Generally with cluster counting you shouldn't use more than 4 steps, 3 if possible. These steps are often:

  • Checkers in opponent's home board + 18pt)
  • Checkers in your outer board (1 or 2 steps depending)
  • Your inner board

So either you know it's 42 by rote or you could do it all sloppy 13x2 + 8x2 or you could mentally shift around the 10pt. When you mental shift using cluster counting you try to focus on the 5pt, 10pt, 15pt, and 20pt when possible. (or how I used the '25pt' in the first step) This is because it's much easier to add, multiply, etc... fives and tens than it is all the other randoms.

If I were to mentally shift this outfield around the 10pt here is what I am envisioning.





White is Player 2

score: 6
pip: 0
7 point match
pip: 42
score: 1

Blue is Player 1
XGID=----------BB--------------:1:-1:1:51:1:6:0:7:10
Blue to play 51

eXtreme Gammon Version: 2.10

Now I do 10x4+2= 42. The math in this post while typed out is a much longer process than the automatic math your brain will do once you start doing this type of counting.

Now for the inner board I just see that it's 22 and 4 or 26. We have 121 + 42 + 26 or 189.

For the opponent it is much easier. You should know both of these formations separately as 30 pips.





White is Player 2

score: 6
pip: 30
7 point match
pip: 0
score: 1

Blue is Player 1
XGID=-----------------bb-------:1:-1:1:51:1:6:0:7:10
Blue to play 51

eXtreme Gammon Version: 2.10
White is Player 2

score: 6
pip: 30
7 point match
pip: 0
score: 1

Blue is Player 1
XGID=-------------------e------:1:-1:1:51:1:6:0:7:10
Blue to play 51

eXtreme Gammon Version: 2.10

Since we know that automatically it's easy to see our side of the board is 71. I also know from reference that 3 on the midpoint is 39 and that 9 + 1 add together nicely so in one glance I would see 110. Now all I have to do is add the two remaining checkers which are 34 (or 17x2 pushing them together to the same point) and get 144.





White is Player 1

score: 3
pip: 114
7 point match
pip: 127
score: 6

Blue is Player 2
XGID=--bCBBBAC---aa---c-d-AbAb-:1:-1:-1:66:3:6:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

Again, why on earth do we need to know the pip count? I never stop complaining.

For the previous problem I ignored the dice roll but obviously we would just subtract six from the final tally of the player on roll. In these next two examples if we want to know after the roll it's a little more muddled because of the hitting that is involved. Anyway, to the on roll player which is once again Blue

The back checkers are 46. The outer board is 49. I see 49, there's practically no math involved. Any two checkers across from each other is 25 pips or two points across from each other is 50 pips.





White is Player 1

score: 3
pip: 0
7 point match
pip: 25
score: 6

Blue is Player 2
XGID=------------AA------------:1:1:1:66:6:3:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

25 pips. And if they were both made points obviously 50 pips.

I have no neat trick that actually saves any time for the inner board but the math is very basic esp. since we're left with a nice 24+6+2 or 32. So 46+49+32.

Now for the opponent. First, the two men back we work around the 20pt. Basically with men back in the opponent's board you use the 20 point to multiply by the number of checkers back then you add the extra pips it takes to get to those checkers from the 20pt. Here is what you should be picturing with two men back:





White is Player 1

score: 3
pip: 40
7 point match
pip: 0
score: 6

Blue is Player 2
XGID=-----b--------------------:1:1:1:66:6:3:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

Now for every pip removed from the 20pt you simply add. You could imagine what you have to roll to make the 20pt, a [31] for example, and know you're 4 pips more than 40. This process will quickly become automatic after you've done it a few times. You'll look at a position like this and you'll see 44, no work needed.

There's only 1 more step for our side of the board. I again mental shift and see this:





White is Player 1

score: 3
pip: 70
7 point match
pip: 0
score: 6

Blue is Player 2
XGID=-----------------bbbbcb---:1:1:1:66:6:3:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

I've shifted one pip forward to make a six prime and one pip backward to keep the count the same. Now you can figure out a prime of any length by adding the front point (the 3pt here) and the rear point (the 8pt here) and multiplying it by the length of the prime. So we would have 3+8 = 11x6 = 66. Then we add the extra checker that was sitting atop the 4pt and we have 70. 70+44=114

The nice part about cluster counting is there may be more than one way to do it and you learn as you go constantly adding more reference positions and fiddling with more efficient ways to do it. It's like a puzzle within' a game. For example for the opp's side of the board I could have done his outfield as a reference position (the made 7pt and 8pt = 30 pips as I showed you above) and simply added 1 giving us 31.

Now the inner board trick we need to work with is knowing how many pips a closed board is. Damn useful. I work around that so often.





White is Player 1

score: 3
pip: 42
7 point match
pip: 0
score: 6

Blue is Player 2
XGID=-------------------bbbbbb-:1:1:1:66:6:3:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

So a closed board is 42 pips. What we are looking at is this:





White is Player 1

score: 3
pip: 39
7 point match
pip: 0
score: 6

Blue is Player 2
XGID=-------------------bbbc---:1:1:1:66:6:3:0:7:10
Blue to play 66

eXtreme Gammon Version: 2.10

Ask yourself, how many pips are we missing from having a closed board? We are missing 6 pips, the made two point and the made one point. Next question, how many extra pips do we have? That guy on our 3 point would be considered the extra pips because it's more than two checkers on a point. So we are missing 6 and we have 3. So overall from our closed board reference position we are missing 3 pips, must mean our inner board is 39 pips.

You could then add 39 + 31 (70) and once again the back checkers being 44 to get 114.

Unfortunately it takes about a gazillion times longer to type this out then to actually do it or explain it orally and I don't have time for the last problem. I have a backgammon lesson to give. Just remember that it is so, so, so much easier than it looks or maybe even reads. Here is the link to a good intro course for Cluster Counting but you can go so much farther and faster than that.

Cluster Counting

Stick

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