Backgammon Problems: Back Games

Back Games: Redoubling and Taking

Feb 1, 2023 | Backgammon Problems: Back Games

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

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

In our last problem we looked at a back game where the back game player got a double shot, but still couldn’t double until he actually hit the shot.

While that’s a generally good rule for many normal back game positions, it’s not always the case. When playing a massive back game, stay alert for positions where your opponent’s game has deteriorated so much that you can double much earlier.

Back Games: When to Redouble

Jan 15, 2023 | Backgammon Problems: Back Games, Uncategorized

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.

A Back Game with Questionable Timing

Dec 15, 2022 | Backgammon Problems: Back Games

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

White to play 4-3.

This isn’t a particularly hard position when presented as a problem. The right play is 8/5 13/9, keeping both back points, slotting the 5-point, and playing 13/9 so as to create two cover numbers for the 5-point.

Over the board, with no one hinting that this is actually an interesting position, it’s fairly easy to make a small mistake. I’d expect to see a lot of players move either 13/9 13/10, a slight error because it doesn’t start the 5-point, or 8/4 8/5, another slight error because the builder on the 4-point is somewhat misplaced and White has fewer cover numbers for the 5-point than he should.

Leaving a blot on the midpoint after 13/9 8/5 is not especially costly because for the most part Black doesn’t want to hit it. Let’s take a quick look at how Black should play his aces after White plays 13/9 8/5.

Black needs to notice these features of the position:

> If he can play safe and not hit, he should do so. Not hitting leaves White’s timing in jeopardy, while hitting improves White’s timing somewhat and may give White a shot at Black’s blot on his ace-point. Right now White trails by 65 pips in the race, which is enough to give him some reasonable winning chances, but not enough to say that he has a well-timed back game. One extra checker back, especially if White could dance for a turn, would make a big difference.

> Playing safe is essential for Black, so if he can only play safe by hitting, he will do so. Black very much doesn’t want to get hit right now, because White’s board is already strong enough to cause real trouble.

> If Black can’t play safe, hitting wins more gammons, and may decrease the count of hit and cover numbers.

So with 6-1, 5-1, and 4-1, the best plays are 13/6, 13/7, and 13/8, all without hitting.

With 3-1, Black can only play safe by hitting, so the right play is 13/12* 4/1.

With 2-1, Black can’t be safe no matter how he plays, so he should hit. Hitting substantially increases his gammon chances compared to the non-hit play (13/11/10), while his losing chances are close after both plays.

As a last point, note that White shouldn’t consider playing 23/16 with his 4-3. While it’s true that his back game/holding game isn’t ideal, it’s the only game he has. Playing 23/16 breaks much of the contact and leaves him 58 pips behind in a game that will mostly become a 5-point holding game, an essentially hopeless situation. If White really wanted to break one of his anchors, the better choice is to keep the back anchor and play 20/13.

Handling a Proto-Back Game

Sep 15, 2022 | Backgammon Problems: Back Games

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

White to play 2-2.

First, let’s try to orient ourselves. White looked like he might get stuck in some sort of miserable ace-point game, but has just thrown a fantastic shot, 2-2, which is so good it actually lets him pursue a few different options. In backgammon, it’s good technique to try to list all the reasonable plays before you start analyzing the merits of any one play. With that goal in mind, let’s see what we can find for candidate plays.

Playing Against a Busted Back Game

Aug 15, 2022 | Backgammon Problems: Back Games

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

White to play 4-3.

Something a little different this time. Identify the worst of these three plays:

(a) 11/7 5/2

(b) 11/4

A couple of Proto-Backgame Positions

May 1, 2022 | Backgammon Problems: Back Games

Cash game. Center cube. White on move.

Position (A): White to play 2-1.

Position (B): White to play 6-5.

We’ve talked a little in previous posts about proto-backgames, those transitional positions that lie between ‘normal’ backgammon and true backgames. Here are our first couple of examples of proto-backgame positions, so let’s pause for a bit and discuss just what each side is trying to do.