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How Match Score Affects Early Game Play

Mar 13, 2023 | ,

Center cube. Black on move.

Black to play 3-3

(a) in a cash game.

(b) at double match point.

(c) trailing 1-2 in a 5-point match.

(a) Cash game.

As a cash game play, this position has an interesting history. When I started playing serious backgammon in the late 1970s, the game was dominated by a group of aggressive young New Yorkers centered at the legendary Mayfair Club, who emphasized making big plays early on, to set up quick cube turns and gammons. They were bold, ingenious, highly aggressive, and very successful, and most aspiring players followed their lead.

At the time, the old-fashioned play with 3-3 after an opening split to the bar was the obvious 13/7*(2). Why not? It hits a blot, makes a good point, leaves no blots, and unstacks the midpoint. That’s a lot of good things at zero risk. The New Yorkers rejected this play and instead played 13/7* 8/5(2), in accordance with the new (at the time) emphasis on making the 5-point early on no matter what the cost.

When I saw the new play I enthusiastically switched, following my general rule of thumb for beginners: “Ape your betters”. (At least until you know enough to question their judgment.) After a few years, though, I started to have second thoughts. How bad could 13/7*(2) really be? It had a lot to recommend it: good point, no blots, takes a solid initiative. I did some analysis and just couldn’t convince myself there was anything wrong with the play, so I switched and started to play it. I got some hoots of derision, but pretty soon more and more players were switching over, and by the 1990s this simple play was the standard, and the ‘old-fashioned’ 13/7* 8/5(2) looked ‘too loose, too fancy’.

Extreme Gammon rollouts long ago confirmed that 13/7*(2) is in fact best, while 13/7* 8/5(2) is a fairly close runner-up. Also in the mix is 13/7* 6/3(2), also making an inner point, unstacking, and leaving fewer shots and blots. Prior to the bot era, no one would even have considered making the 3-point, although I think most modern players would immediately spot it as a strong alternative.

(b) Double match point.

Double match point is simply any match score where gammons don’t count for either side and the result of this game decides the match. The simplest example occurs when each side is one point from victory. Other match scores can convert into double match point (DMP) pretty easily. For instance, if both players are two away from victory, and someone doubles quickly and the other side takes, then we have a double match point situation by default.

With gammons not counting, strategy in this situation undergoes a few changes. Here’s a quick summary of the major alterations.

1. The best game plans at double match point are (a) escaping your back checkers and winning the race, and (b) building a prime and winning the race. Racing advantages create a lot of wins but not a lot of gammons, which is perfect.

2. Blitzes are a poor choice of game plan unless the dice allow no reasonable alternative; too many gammons, not enough wins.

3. Anchors are less valuable because one of their functions is to prevent being gammoned, which is no longer necessary. The strength of an anchor lies in its ability to transition to a favorable race.

4. Inner board points are still good, but not quite as good. We don’t care about their ability to create gammons but we do care about their ability to create primes.

5. Slotting to build an inner board quickly is mostly wrong.

6. Plays where you run off an anchor to avoid being primed later are commonplace.

7. Escaping the back checkers is even better than usual.

Taking all this into account, it’s not hard to see that 13/7*(2) is even better at DMP than in a cash game. It gains ground in a race while taking no risk of losing ground in the race. The point is useful as well.

(c) Trailing 1-2 in a 5-point match.

Trailing 1-2 to 5, or ‘4-away 3-away’ as it is sometimes called, is a score where gammons matter more than usual for the trailer. If the trailer wins a doubled gammon, he wins the match. If the leader wins a doubled gammon, he still wins the match but some wastage is involved (he doesn’t need the fourth point). As a result, the trailer needs to create positions where he has an elevated chance of winning a gammon, at a reasonable cost. He doesn’t want to go crazy, he just wants to take a little more risk for extra gammon chances.

Both 13/7* 6/3(2) and 13/7* 8/5(2) fit the bill here. They’re the second and third best plays in a cash game, but here the extra inner point creates more gammons at a small cost in raw winning chances. Which of the two is best? A rollout left the two plays in a dead heat. Playing 6/3(2) makes a weaker point, but as compensation it unstacks a big stack and leaves fewer shots.

 

Back Games: When to Redouble

Jan 15, 2023 | ,

Cash game. White owns the cube. White on move.

Should White double? If he does, should Black take, drop, or beaver?

 

Positions like this are fairly commonplace when playing back games, and they’re tricky enough to lead many players astray.

White has played a 5-2 back game and has just gotten a double shot. Besides fives and twos, he can also hit with 4-1, so he has a total of 22 hits and 14 misses this turn. In the future of course, White may get even more shots.

Some players, encountering this position for the first time, might reason as follows:

> Wow, I have 22 hits! I’m already the favorite!

> And if I hit, I can easily lose my market!

> And I might get even more shots in the future!

> And I could win a gammon!!

> I double!!!

Anything wrong with this reasoning? Well, just a little bit. Let’s look more closely.

Let’s start by examining what happens when White doubles. True, he then hits 22 times out of 36, a bit more than 60%. But how many of those can he win, once Black owns the cube? Let’s give White a pretty average hitting roll, like 4-2, and see how we think he’s doing.

Position after White hits with 4-2 and plays 20/18*/14.

Although he just got hit, Black still leads by 50 pips in the race, which has to be worth something. In addition, he has some pretty good shots in this position: 6-2, 5-2, 6-1, and 1-1, all of which leave Black in a lot of trouble. Let’s be conservative and say that Black can pull the game out a little less than a quarter of the time from this position. In that case, out of White’s 22 hits, we’ll say he can win about 17 of them, losing the other five.

What about White’s 14 misses? Now he’s in real trouble, trailing by 60-70 pips in the race, with his opponent owning the cube. Black won’t redouble immediately, but he’ll be able to use the cube very effectively in the near future when his position improves a little more. At worst, he’ll at least be able to play the game out to the end. I’ll give White four of these games, but no more.

Overall, White’s chances after doubling look like this:

If he hits, he wins 17 and loses 5.

If he misses, he wins 4 and loses 10.

With the cube on 4, White wins about 21 and loses about 15, for a net of 6 games, worth 4 points each. Total, +24 points.

Now suppose White keeps the cube and rolls. Again he hits 22 and misses 14. But now his 22 hits are very strong. Black needs a great shot immediately or he’ll pass a double, and even if he gets his shot, White can hang around until the end. Let’s make White about a 20 to 2 favorite in these games.

If White misses, he still has plenty of chances in the game. Let’s give him 6 games of these 14, losing the other 8. Now, his chances after not doubling look like this:

If he hits, he wins 20 and loses 2.

If he misses, he wins 6 and loses 8.

With the cube on 2, White wins about 26 and loses about 10, for a net of 16 games, worth 2 points each. His total here is +32 points. So he does substantially better by not doubling.

This is a pretty typical result when you get a double shot in a back game. You’re a big favorite if you hold onto the cube, but just a small favorite if you double. Barring some unusual features, these positions are mostly all no double and take.

 

Prime versus Prime Tactics

Oct 1, 2022 | ,

Cash game. White owns the cube. White on move.

White to play 2-2.

This problem is an example of a somewhat rare breed, a true prime against prime game. Although we talk about priming games a lot, real priming battle don’t arise all that often. Much more common are positions where one side has a prime and the other just a loose connection of points, or games where one side has a prime but the other is conducting a strong attack.

read more…

Blitz or Consolidate?

Aug 1, 2022 | ,

Cash game. Black owns the cube. White on move.

White to play 3-3.

White’s off to a good start in this position. He’s already made a three-point board, whereas Black hasn’t yet made a new point, and White has hit a blot, leaving him 17 pips ahead in the race. Black, meanwhile, is still scrambling to make an anchor. Last turn White offered an aggressive double, and Black quite reasonably took.

Now White throws one of his best shots, 3-3, and has three game plans:

(a) The consolidation play with 14/8 13/10(2), leaving him firmly in control with a nice edge, or

(b) Consolidation plus a little attack with 24/21 14/8 6/3*, or

(c) All-out blitz with either 13/4*/1* or 13/4* 6/3*.

What’s the right idea?

Here’s the general approach for handling these sorts of positions. If your opponent has no structure, and the cube has already been turned (activating gammons), then the blitz dominates any safe game plan. If the blitz fails, White can just drop back into some sort of holding game where he holds a slight edge. If White makes one of the solid plays, he’ll reach those holding games anyway since almost all of Black’s rolls will anchor somewhere. White will be slightly better off if he goes for the holding game right away, because of his racing lead, but the difference is small. But if the blitz succeeds White wins a gammon, and with the cube already turned that’s a quick four points and a huge swing.

As Black acquires more structure, the blitz drops in value. If we alter Black’s position and give him his 5-point (as though he had rolled a 3-1 at some time), then the blitz plays are only slightly superior to the consolidating plays. If we give Black two extra points, say the 5-point and the 3-point, then the blitz plays become pretty big errors and the consolidating plays becomes correct. (There’s very little difference between Play (a) and Play (b) no matter what structure Black has.)

So we’re blitzing. Next question: what’s the right way to blitz?

What makes this problem especially interesting is that White has two distinct ways to blitz: the obvious 13/4*/1* and the obviously riskier 13/4* 6/3*. Problems with two plausible blitzing moves are rare, but we can choose between them by noticing that the double-hit with 13/4*/1* exposes only one blot in the board, and a hit may only allow Black to get an ace-point game later. If White hits on the 3-point and 4-point with two checkers and Black then throws a three or four, he may get a good anchor quickly. The two blitzing plays are close (and far superior to the non-blitzing plays) but the play that exposes only one inside blot is slightly better.

 

 

Improving Your Technique

Jun 1, 2022 | ,

Cash game. Center cube. White on move.

White to play 2-2.

The advent of the bots in the late 1990s enabled players to solve a myriad of small technical plays that recurred frequently but couldn’t really be tackled with hand rollouts or pure reasoning. Hand rollouts were so slow that they really had to be reserved for positions where the solution was unknown but the difference between plays was likely to be large and important. Players ignored what appeared to be small technical stuff, on the theory that solving these problems, even if possible, was most likely a huge waste of energy.

read more…

Creating Mobility

May 15, 2022 | ,

Cash game. Center cube. White on move.

White to play 6-4.

This is a comparatively easy problem if you can properly balance the key features of the position. Let’s step back for a second and look at just what is happening, before we try to evaluate the different choices.

The race: White will trail in the race by 16 pips after he plays his 6-4. Considering that he has five men back to Black’s two, he’s not as far behind as one might think at first glance. Since he’s trailing in the race, however, he wants to maintain a good anchor (to generate some shots) and a good blockade (to contain blots he may hit).

Blockades: White has four good points in front of Black’s anchor. That’s a solid plus for him, if he can maintain it. Black has a motley collection of scattered points, which indicates that he probably won’t be able to build a good block anytime soon, and that he’ll likely have to start leaving shots in the near future.

Weaknesses: For White, what might seem a strength is actually a long-term weakness. He has two great anchors, on the 20-point and the 18-point, but that’s one great anchor too many. The 20-point/18-point combination doesn’t work well together; they tie up 76 pips at a time when maneuvering freely is still key.

Black’s weakness is glaringly obvious; it’s the 2-point, too deep in his board to be useful at this stage. Black might have had good reason to make it in the past, but now he’d be better off if those checkers were back on the 4-point or the 9-point.

Now let’s put all this together and see just what we can do with the 6-4.

8/2 6/2. A bad choice. White burns two of his remaining builders to make a useless point far behind Black’s anchor. Now all his remaining points are stripped and his only convenient rolls next turn are those that can be made entirely with the blot on the 24-point. Take a look at how numbers like 4-1, 3-2, 6-1, 5-2, 4-3, 5-1, and 6-4 play next turn. In complex middle games with action on both sides of the board you need checkers that can move easily, and sometimes you have to take risks to preserve those checkers.

24/18 6/2 and 24/20 8/2. Not as committal as making the 2-point, but half-hearted versions of the same idea. You only have 15 checkers, and you want everyone in play at this stage of the game.

20/10. To those who worship the 5-point, this looks like a shocking idea. White breaks the defensive 5-point before he must. But it’s really a fine move, which solves all White’s problems at once. White doesn’t need both anchors, so he gives one up voluntarily.

Take a look at the position after 20/10 and notice how White has solved most of his problems. He now has five spare checkers, ensuring that he won’t have to concede any valuable points in the near future. He’s got more combinations to make his 5-point or 7-point, as well as more ways to attack if Black should split his back checkers for some reason. Finally, he’s resolved the issue of too many anchors in a neat and efficient fashion.

If you missed this problem, it’s probably because you’re too focused on static features of the position, and not enough on the flow of the game. Try to anticipate how the game is likely to develop over the next couple of rolls, and avoid positions where you have a real shortage of checkers that can move.

 

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