A number of readers have asked to see an excerpt from How to Play the Opening in Backgammon, Part 1. I’ve picked the first section of Chapter 3, which discusses positions where you have a choice between making your 5-point or making your 20-point. Enjoy.

3.1 The 5-Point or the 20-Point?

I’ll start off our chapter on the 5-point with a battle of the heavyweights: You roll a number that can make your 5-point or your 20-point, the two most important points on the board. Which one should you choose?

You might think that, with two great points to choose between, you couldn’t go far wrong picking either one. Actually, that’s not true. Depending on the position, either play could be a significant error or even a very large blunder! Let’s look at a few of the factors that should influence your choice.

Am I losing the game? If your opponent has thrown a great shot (like 6-6 or 2-2) and now has a solid edge in the game, making the 20-point is likely to be right. You’re now playing defense, and the 20-point is a great defensive point. If the game is more even, the 5-point goes up in relative value.

How difficult is each point to make? This consideration will normally favor making the 20-point. Suppose, for instance, you start the game with a 4-1 and play 13/9 and 24/23. On your next turn you’ll have only two numbers to make the 20-point (4-3) but a whopping nine numbers to make your 5-point (1-1, 3-3, 4-4, 3-1, 4-1, and 4-3). Given a choice of two good things to do, in backgammon we normally try to do the hardest thing first.

After I make a point, what does my distribution look like? Suppose as before you start the game with a 4-1 and play 13/9 and 24/23. If you next roll a 4-3 and elect to make your 5-point, your resulting distribution isn’t too good. You still have a big stack on your 6-point, your 8-point is stripped, and you don’t have any other builders aiming at your home board. If you had rolled 3-1 or 4-1 instead, you could have unstacked your 6-point while making the 5-point. Looking at your distribution will play a role in selecting which point you want to make.

How’s my communication? If your back checkers are far back (say on your 24-point and 23-point), then they’re far away from the midpoint and the need to make a connecting anchor is greater. If you’ve already split your back checkers to a good point, then connection isn’t as much of an issue and the 5-point rises in value.

Has my opponent escaped a checker? It’s a big deal if your opponent escapes a checker, say with an early 6-5, because it changes the relative value of several important factors. Your opponent now very much wants to release the other back checker, which will achieve his goal of escaping both back men. He also doesn’t want to get hit, which will neutralize what he gained by escaping a man. You want to counter his goals, so here’s what happens:

> Your 20-point now goes down in value. Since you very much want to send a second checker back, you want to arrange your rear checkers to have the best chance of hitting. This means you want them split and far back, which will create some pure double shots if your opponent rolls a really bad number. The best arrangements are the 24 and 23-points, the 24 and 22-points, and the 24 and 21-points. Actually making the 20-point gives you almost no hitting numbers for a long time.

> Your 5-point goes up in value. Since your opponent’s top priority is now to escape his last checker, the extra blocking action that the 5-point creates is valuable. And of course, having a better board is great if you can actually hit a shot.

How many checkers do I have back? If you’ve had a third checker sent back, the 20-point goes up in value. Now you have extra incentive to avoid being blocked in, and an anchor will provide that.

With all these factors in mind, let’s look at a few positions involving a 5-point versus 20-point choice.

White – Pips 161 (-1)

Black – Pips 162 (+1)
Black to Play 4-3

Here’s an easy position where every factor points in the same direction.

Losing the game? White has the early edge with his 4-point, so a defensive point is in order.

Degree of difficulty? The 20-point is harder to make.

Distribution? Using the 4-3 to make the 5-point leaves poor distribution.

Communication? Black’s rear checkers are both far back, so making a connecting point is more important.

Opponent escaped a checker? Not relevant.

Do I have three men back? Also not relevant.

Add it all up, and 24/20 23/20 is absolutely clear and making the 5-point is just a blunder.

White – Pips 161 (-1)

Black – Pips 162 (+1)
Black to Play 4-3

Black’s position is the same as in the previous example, but White has played a 5-1 instead of a 4-2. Let’s see how this modest change affects the decision.

Losing the game? White hasn’t done much yet, so Black’s need for an anchor is low. Strongly favors making the 5-point.

Degree of difficulty? As always, the 20-point is harder to make. But White’s weak position makes this indicator less important.

Distribution? Using the 4-3 to make the 5-point leaves poor distribution.

Communication? Black’s rear checkers are both far back, so making a connecting point is important. But White doesn’t have a position yet, so the need isn’t as great as in Diagram 1.

Opponent escaped a checker? Not relevant.

Do I have three men back? Also not relevant.

White hasn’t made progress in improving his front position, so Black’s immediate need for an anchor is much less. But note that one new feature of the position has appeared: White’s back checkers are split, so making an inner point has risen in value for Black. (The stronger Black’s board becomes, the more dangerous it becomes to have split back men vulnerable to attack.) In addition, White’s split men pose more danger to Black’s builder on his 9-point, so cleaning up the blot while making the 5-point is a big plus.

Put all those factors together and making the 5-point becomes correct by a modest margin.

White – Pips 156 (-6)

Black – Pips 162 (+6)
Black to Play 4-3

Again we’ve kept Black’s position the same, but we’ve given White a 6-5, letting him run a checker to the midpoint. Now what should Black do with his 4-3?

Some of the features we’ve discussed so far would lean toward making the 20-point. It’s the harder point to make, it helps connect the back checkers to the rest of Black’s army, and it leaves the front checkers a little better distributed. As in the last diagram, however, the rear checkers aren’t under any pressure, so making the 20-point isn’t especially vital right now.

But now a new positional factor enters the equation: White has escaped a back checker. White’s running play hasn’t created any new builders, so as long as Black keeps good coverage of White’s inner and outer boards, White may find himself reduced to stacking up checkers or leaving some unwanted shots. But if Black plays 24/20 23/20, the pressure is off and White can dump checkers in his inner board while waiting to release his lone back checker. That’s a powerful incentive for Black to leave his rear checkers alone for now, and hence 9/5 8/5 is the best play by a small margin.

White – Pips 159 (+1)

Black – Pips 158 (-1)
Black to Play 3-1

Here’s a slightly different riff on the 5-point versus 20-point idea. Black split with an opening 5-4, after which White rolled a 5-3 and made his 3-point. (A small but extremely common error; as we saw in Chapter 2, 13/5* is better.) Now Black rolls a 3-1 and can make either point. What’s right?

This position fools many players who feel that, having already split, they now have more of an investment in the 20-point. As a result, they quickly cover their blot with 24/20. But if we run through our list of key factors, we might see the position a little differently.

Strength of position? White has made his 3-point, strengthening his inner board and making the value of an anchor go up a bit. But his 8-point is stripped, so some of his hitting numbers involve breaking that point. The net favors making the 20-point by a bit.

Difficulty of making the point? There’s been a big swing here. With the 20-point slotted it’s now much easier to make than in our first few examples. The 5-point is now a much harder point to make, so a strong edge to 8/5 6/5.

Distribution? Not even close. Making the 5-point unstacks two loaded points.

Communication? Splitting to the 20-point has greatly relieved Black’s communication problems. Now he has lots of rolls that make either the 20-point or the 18-point, or run the front checker to safety. Since the need for communication has gone down, the value of making the 20-point has gone down.

Put all the factors together and making the 5-point is clearly right, while making the 20-point is an outright blunder. It’s a counter-intuitive result – just splitting to the 20-point relieved so many of Black’s problems that the value of actually making the point has gone down.

White – Pips 156 (-4)

Black – Pips 160 (+4)
Black to Play 3-1

We’ve changed the previous problem, giving White a running 6-5 instead of a point-making number. All the reasoning in Diagram 4 still applies, and in addition White’s escaped checker makes the 5-point more valuable while the 20-point is less so. Again 8/5 6/5 is the best play. What’s worth noting about the position is that the two plays are now closer in value than in Diagram 4. Since White has escaped a man, the 5-point is only blocking one checker rather than two, so it does a bit less work.

White – Pips 143 (-15)

Black – Pips 158 (+15)
Black to Play 3-1

Here we’ve changed the position again, this time giving White a 6-6 instead of a 6-5. Now Black’s checker on the 20-point is in much more danger; White has 10 pointing numbers instead of the five in Diagram 5. At the same time, White’s rear checkers have escaped, so while making the 5-point gives Black a good distribution, it no longer blocks anything. The result is a huge swing in the evaluation, with making the 20-point now correct and making the 5-point is a blunder.

White – Pips 157 (-3)

Black – Pips 160 (+3)
Black to Play 4-1

Here the opening sequence was a 4-3 for Black followed by a 6-4 for White. Although Black hasn’t split to the 20-point, the fact that he has split to a potentially advanced anchor has once again lessened his need to actually make the anchor. All other factors favor making the 5-point: his distribution will be better, his communication is already good, his back men aren’t under any special pressure, and White has (mostly) escaped a checker. The right play is 9/5 6/5.

White – Pips 161 (-9)

Black – Pips 170 (+9)
Black to Play 4-3

Here’s a final position from a little later in the opening. Now most factors favor making the 20-point: White’s builder on his 7-point makes the threat of a block more real; Black’s rear checkers are far back and isolated; finally, Black has three men back rather than two, so he has a greater need for an anchor. On the other side of the board, making the 5-point leaves Black poorly distributed, with a stripped 8-point and a stacked 6-point. Making the 20-point is now the better play.