Backgammon Articles

Basics of Backgammon
by Robert Townsend

"We will bury you"
—Nikita Khrushchev

Part 4:  The Blitz, Flexibility, Duplication and the BRAT
When asked how he planned to take a key objective in the American Civil War, Confederate General Nathan Bedford Forrest is said to have replied:

"Get there first with the most men."

In a blitz, you are trying to keep your opponent on the bar and close him out. Generally, an early double allows you to hit a split enemy checker and make a point or two on your home board. The checker stays out on the bar and the blitz is on. While many are of the opinion that a blitz is a purely dice driven event and an exercise in moving checkers rather than an in depth battle of the wits like a priming game, they sure are fun when you are running one. Fun until you run out of ammunition, your opponent anchors and throws a joker then doubles you out. Or, your opponent anchors and you have not made any preparations to win the game without the blitz.

Social players let the dice dictate their game. Serious backgammon players have a game plan and make their own lucky rolls with flexibility and have a backup plan in case the game changes course. An extension of this concept is applying it to your opponent: If he survives your blitzing attack, how does he plan to win the game and what can you do to dash his hopes? Roll your dice, but before you move a checker run over these three game plans in your head. How do I move to maximize my close out and what can he do to interfere? What is my plan to win if he gets out of this? And how does he hope to win if he survives and how can I disrupt that plan? Then decide where your checkers need to go. Keep in mind, most of your backup plans use your racing advantage, and most of his will use his timing and look to hit and/or trap your back men.

The basic goal of blitzes (from the attacker's viewpoint) is to bring builders to bear on open points, close them, and keep your opponent on the bar until you gammon him. You must prevent him from forming an anchor (especially a high anchor) so hit loose if you must. If you are hit when he re-enters, so be it, just come back in and charge into the fray because in many cases your opponent has not had time to close points on his home board. If not, you may cover the next roll and your position is even stronger.

















A key concept is that the number of rolls that make a point is directly related to the number of builders within direct range of the point. This is the concept of flexibility. Flexibility over all means that you have checkers available to do something you want to do with as many different dice rolls as possible. Duplication is the opposite, you don't want to have to re-enter, cover a blot, make a point and escape a prime with the same 5 for example. The above graphic from Part 1 shows this concept well. The number of checker and the pip count are the same, but one side has excellent flexibility and the other has duplicated his numbers. In the final bear off, which side would you rather be? The same concept extends to bringing builders to bear on a point you need to make.

The formula for non-double rolls that make an empty point is n × (n − 1) where n is the number of available spares within 6 pips of the point in question. To complete the roll count, doubles must be evaluated.



































Example 1

In the opening position, we want to make the 5 point. To do so, we look to our spares within 6 pips of the 5 point (we have one on the 6 and one on the 8). The number of rolls is n × (n − 1) which in this case with 2 spares is 2 × 1 = 2. These two rolls are 3-1 and 1-3. To that we add the doubles 4-4, 3-3 and 1-1 for a total of 5 rolls.



































Example 2

Now we have a spare on 6, 8 and 9. We have 3 × 2 = 6 nondouble rolls 3-1, 4-1, 4-3. Plus our 3 double rolls we now have 9 rolls. Adding only one spare gives us an additional 4 rolls.



































Example 3

Now with 4 spares (6, 8, 9, and 10) we have 12 nondoubles 3-1, 4-1, 5-1, 4-3, 5-3 and 5-4 plus our doubles for 15 rolls.

Each additional spare nearly doubles our point making rolls. Another key point is that stacking checkers on a point does not increase the usable spares. Had we made the 9 point in example 2, we would still have 3 usable spares; our only advantages would be the loss of indirect hitting numbers for blue and a blocking point.

Recall from the first article in this series, the number of rolls that cover a slotted point go up quickly based on the number of usable spares within direct range. An example would be an opening 2-1, playing this 13/11, 6/5 gives you 3 covering numbers (6, 3, 1) for 27 rolls plus 4-2, and 4-4/2-2 for 31 covering numbers against any 4, 2-2, 1-1 and 3-1.

From a strategic standpoint we now have priorities:

  1. Make home board points (every point made helps but given a choice start high).
  2. Hit loose if you must to prevent your opponent from getting an anchor.
  3. Put a spare on as many direct range points as you can (especially if they help your backup plan).
  4. If hit and unable to accomplish 1, 2 or 3, run a man around to re-enter the fray.
  5. If your blitz runs out of steam, continue with your backup plan and interfere with his game plan.

If all goes well, we continue to a closeout and a gammon. But what happens if we are stopped? Say our opponent makes a high anchor on our 5 point—the blitz is now over and he is playing a holding game and we are bearing in. Now is when our prior planning comes into play—how are we still going to win and what is his new game plan?

Recall from our earlier discussion in Part 1, winning in backgammon comes from strategy—what is our game plan and what is his. We make moves and decisions based on what is good for our plan and bad for his. If we are ahead in the race, we win by racing/avoiding being hit, if behind we win by blocking/recirculation. What are our options? Have a look at this position:

Until now, most of our evaluations have dealt with races. Clearly there are other considerations in contact positions. Paul Lamford popularized an organized way to evaluate these positions—PRAT. This stands for Position, Race, and Threats. Let's go over the elements, recalling that we are talking relative advantage to your opponent. An overwhelming advantage is just that, it carries far more weight than a relative one when it comes to cube decisions. This is not all inclusive, but gets you thinking correctly.

Position

  • Inner board points.
  • Outer board points.
  • Primes in place.
  • Back men escaped.
  • Anchors.

Race

  • Pretty self explanatory. Do a pip count, half crossover count or eyeball it.
  • Timing and how does it affect the current game plans.

Threats

  • Blots to be hit.
  • Points to be made.
  • Primes to extend.
  • Anchors to be forced off.
  • Blots to be exposed in the bear in.

There are three general rules of thumb when we compare these three considerations to our position and our opponents.

  1. If we have relative advantage in 2, it is a double/take. If we lead in all 3 it is a double/pass.
  2. An overwhelming advantage in any strongly skews the results to double/pass.
  3. With an overwhelming advantage, consider playing on to gammon.
Consider this position:



































Position • 3 red vs 1 white inner board, 5 point made by red.
• Red has split back men guarding red's inner board and spares on 6, 8, 9, and 13.
• White is static, pretty much stacked in the opening position and on the bar but has some builders aimed at the bar and 5 point.
Advantage: 
Red.
Race • Red has 24 half crossovers and 150 pips (rolled a 3-3 and 4-1 for 17).
• White has 30 half crossovers and 165 pips (rolled 3-2 and hit on the 22).
Advantage: 
Red.
Threats • Red has three builders in direct range of his open 4 point.
• There is an enemy blot on the 15 that is under indirect attack and the enemy blot on 1 can be hit to start that point.
• White must re-enter and may anchor on the 1 point or hit our builder with a 2-6 or come in on the 2 or 4 (and possibly get covered by the blot on 1).
• Double shot on a reentering blot on 4 that can't escape or be covered.
• White can re-enter then hit our back men on the 23 or 24.
Advantage: 
Toss up leaning toward red. Gammon chances for red still good.

So what does this tell us so far?

He hopes to re-enter and anchor, maybe even on our 4 point with a 4-3 or on the 2 point with a 2-1, then work on his prime and trap our back men or even if the dice gods smile, launch his own blitz (we don't do anything special after he re-enters then he rolls a 4-4 and puts us on the bar). Our priority is to make the four point and/or hit the blot and slot the point. Nailing the blot on 15 with 6-3 or 5-3 would get a back man out and put the blot on the roof.

If he anchors on the 4, then we go to Plan B—convert the blots on 8 and 9 to landing points from the spares on the midpoint, then get the back men out to safety and convert to more of a racing game, being mindful of how we will get home past his midpoint and 4-point holding game. Since timing would be the key to his game, we might consider bypassing a hit so he can't recirculate a checker (let him bury it instead) and force him off his holding point.

Our game plan is to continue the blitz. We have the lead, the builders and the position to make additional points. He has no anchor and has one on the bar. Our hopes to close him out and get a gammon are reasonable so we hang onto the cube for now. 324 trials with gnu show our winning chances to be 81% with 58.1% gammon wins and 4.7% gammon losses. We do clearly have a double and he has a drop, but rather than take one point we play on for two.

So we roll (4-2), he rolls well (2-2), and here we are:



































This illustrates one of the problems with the blitz: lack of ammunition for follow through. If he survives this attack, he is setting up to close his 20 and 18 points to prime our back checkers. We too have the makings of a prime if we cannot press the attack. So our goal is to make the 20 point to disrupt his plan and at least slot our own 7 point to bring a builder up and set ourselves up for a priming game. If we slot the 7 and he rolls a 6 and hits us, we re-enter a two point board and hit him back on our bar point from the 13 or the 9.

Position • 4 inner vs 2.
• 4 point partial prime for red, 3 point interrupted prime for white.
• Still no anchor for white.
• Blocking point slotted for white on 17 with spares on the midpoint.
• Red inner board points stripped and one builder on 9.
• Back men for red getting into danger.
Advantage: 
Red.
Race • Red with 23 half crossovers, 144 pips.
• White with 27 half crossovers, 155 pips.
Advantage: 
Red.
Threats • White pointing on the blot on 23.
• White able to point on 20.
• Red able to point on 18 and extend prime to 5 points.
• Red threatens to make the 22 or 20 point.
• Red is running out of ammo.
Advantage: 
Still to red.

Let's see the evaluation per gnu:

324 trials with gnu show our winning chances to be 72.3% with 47% gammon wins and 8.3% gammon losses. Still a double with excellent gammon potential; we will play on.

We are clearly running out of steam.

We roll well this time with a 3-2 and white responds with 4-2.



































On this move three events occurred, white failed to anchor on the 2 but moved an extra builder for the 7 point to the 11 and we stepped up to the 20 and slotted a point we need to interrupt our opponents' potential prime.

Position • Red has 4 vs 2 inner board points.
• Red has a 4 point prime with two back men trapped, white has a broken 3 point prime but we have slotted his bar point.
• Red has split back men.
• White has stripped his mid-point.
Advantage: 
Red.
Race • Red has 19 half crossovers and 138 pips.
• White has 24 half crossovers and 144 pips.
Advantage: 
Red by 6 pips.
Threats • Red is poised to make the 20 point or his own bar.
• Red has a triple shot if white escapes a checker from the 1 or 2 point.
• Red's back men are moving and have slotted a high anchor.
• White still has no anchor, but is pointing on his 20 and bar points.
Advantage: 
Both are threatening to improve their position this move.

Gnu shows our winning chances to be 66.9% with 32.6% gammon wins and 9.6% gammon losses. Again, no-double/take but we play on.

Finally a slotting play. Red rolls 5-4.



































Position • Red: 4 point board; white with 2 points.
• White is on the bar.
Advantage: 
Red.
Race • 25 half crossovers, 146 pips for white.
• 17 half crossovers, 129 pips for red.
Advantage: 
Red.
Threats • Red covers the blot on 2 for a 5 point boat with white on the wall.
• White re-enters and hits blot on 2.
• White stays out another turn and red significantly improves my making the 2, bar or 20 point.
• Red indirectly hits blots on 14, escaping a man and putting a second man up.
Advantage: 
Red.

Gnu shows our winning chances to be 78.8% with 50.7% gammon wins and 6.0% gammon losses. Now we are too good and going for the gammon.

Overall, we did not have much to work with other than an initial double during this blitz. There were not many builders in place and we had two men deep and under threat. But we had a solid winning back up plan—a prime in front of his back men. We understood what his game plan and goals were and moved to prevent them, and we brought spares into the attack that were useful in forming a prime as well. By emphasizing these other game plans in a weak blitz, we learn to continue to appreciate them even when everything goes our way. Spare checkers are plenty and the dice gods are smiling on us.

A final word on cube action in the blitz. If you can gammon your opponent, charge on for the gammon rather than let him away with one point. If you are running out of steam, your cube decisions should be to double your opponent out or you should double him in based on your plan B game plan and his plan B game plan.

Finally, remember a bit of human psychology. If your opponent survives your attempt to crush him with a blitz, he may begin to feel a bit invincible and over estimate his chances. Play on this with the cube; you may get some extra points from a bad take. An advanced psychological tactic might be to deliberately leave just enough hope to encourage a back take.

Consider yourself white in this position a few rolls after the last:



































White has survived the blitz and anchored, reduced his gammon risk to 29% and is threatening to make his 5 point on our head or his bar point, we even have 5 blots scattered around. Kinda looks juicy for white. Can white take a cube? Hint: What happens if red pops out a 4?


At the start of the article we talked about the concept of blitzes being exercises in moving checkers. So let's move some checkers: Some wisdom of Paul Lamford.

Question 1: New point or hit loose?















Red to play 4-2.















Red to play 5-4.

Assume all 15 checkers are on the board for both sides, but have no effect on the checker play in question, and in both white has a man on the bar. In the first situation the choice is between making the 4 point and putting another man on the bar against a 3 point board by hitting loose. In the second, the choice is between making the 2 point or hitting loose on the 5.

To answer the question, we need to remember the game plan. We are blitzing; our opponent is hoping to defeat the blitz by anchoring, preferably with a high anchor. If we fail to hit, white may anchor on the 2 point or the 5 point. We can still win against a deuce-point game with a prime or racing lead. If he makes the 5 point, we cannot prime him and he has much higher winning chances.

So when faced with the choice, if our opponent has a blot slotting a high anchor, we hit it. If he slots a low anchor, we make the point. If he has slotted the 3 point, considerations elsewhere on the board will make our decision.

Question 2: Inner board shift to hit, or use the roll elsewhere?












Red to play 3-3.

Here the consideration depends on what is going on elsewhere in the board. The goal of the blitz is to hit and close out. Because of this, an inner board shift to hit is generally preferred—we don't weaken our board and we put him on the wall. The exception to this concept is when we want to force our opponent to play his rolls, for example if he has primed our back man or his home board is collapsing. In the former situation we want the prime to open- so we bring builders to continue the blitz or convert to a race or prime of our own. In the later, we want to reduce his winning chances if he does hit a blot so we again bring builders or convert our game plan.

Question 3: Do we risk slotting or play it safe with our builders?

Slotting our 5 point or better yet hitting loose and putting a man on the wall is very tempting. But the considerations of Bold vs Safe still apply, although we are willing to stretch them a bit. Slotting, according to Lamford, is not justified against an opponent's closed board and exceedingly difficult to justify against a 5 point board. Slotting, especially with good coverage next turn, is palatable against a 3 point or less board. 4 point boards can go either way depending on the follow up.

Question 4: We survived the blitz and anchored, how long do we stay?

The answer to this depends in part on whether gammons count and our racing chances if we convert from a holding game to an all out race. If gammons do not count and our racing chances are poor, we stay a bit longer and try to hit a shot if it is our only chance to win the game (i.e. in a single game or at match point for our opponent). If not, we need to look at crossovers. How many do we need to get home? Our anchor represents 6 crossovers, once our opponent is down to 8 checkers, we had best be moving, especially if gammons count. Depending on the awkwardness of our opponents' bear in and/or our chances of getting a shot off the bar we may consider running with one checker and leaving one back for a roll if the win is essential for us and the gammon risk is not fatally high. Otherwise, live to fight another day.

More on this question in our next article, "Holding Games and the Magic of the Number 324."

Happy Journey.

Article © 2007 by Robert Townsend.

Bob Townsend is the director of the Northern Michigan Backgammon Club.
You can contact him at DrRTownsend@msn.com.

 

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