Back Games, the Myths and the Magic

"Do some articles on back games", is a request that I get more often than any other. It's an odd one in many ways. Back games are rare in modern play, as the first thing we learn about them now is to avoid them if possible! Putting right common mistakes in every day positions pays bigger dividends in the long run. Also, I just don't feel particularly well qualified to talk about a subject that divides players far stronger than me. However, backgames are fascinating, so let's take a look at some  facts and some positions.
What is a backgame? It's a game where one player holds two (or more) points in the opponent's home board and tries to keep them until the bear-in/bear-off stage, in order to disrupt that phase for his opponent, get a shot, hit it and win from there. This player is said to be playing a back game and the opponent is said to be defending against it. In the old days, better players wouldn't mind steering into these, because defending against the back game is very much harder than actually playing one. That ratio of difficulty hasn't changed, but the bots have revealed to us the shocking statistics of how (in)effective the various games are and most importantly how often they get gammoned. Still, the Mad Backgame Geniuses are not completely extinct, although the extent of their success is limited. It's sad in a way, because the games do have a beauty all of their own.
Now I know that as soon as I mention bots, a significant percentage of readers will mutter, "Bots don't understand backgames, so they play them badly". This is not a can of worms I intend to open, because I find discussion of what a bot can and can't do is tedious. Of one thing I am pretty sure though, which is that XG2 plays (and defends) against back games better than 99% of humans! If you disagree, open a thread somewhere else (other blogs are available) and discuss it there please.
There are eight different back games available of which two, the 20pt/24pt and the 20pt/23pt are so weak that they are not playable. The principle strength of back games comes when the two points held are fairly close together, which creates problem rolls for the defender. Points two or three pips apart don't do this. The 21pt/24pt game is also in this category I expect, but is for some reason much rarer and I haven't got any data on that. The 23pt/24pt game is also very weak unless you have enormous timing and the defence against this game is now so well-known and so effective, that getting that timing is almost impossible. I'll try to cover the main points of this game in a later post.
Now you will have seen that I used the T word there, timing. More utter rubbish is talked about timing than almost any other facet of the game, particularly by Mad Backgame Geniuses and I will try to avoid adding my share. Timing means being able to keep your backgame points and the strong prime that you need to win with after a hit, until very late in the game. This doesn't just mean until you first get a shot, it means keeping your position until the second or third opportunity. You can have too much timing and too little and timing is as important, perhaps even more so, for the defender. He should be trying to delay his arrival in the bear-in/bear-off stage if the backgame player is still strong and has lots of timing. The best backgame points appear to be the 22pt/24pt and 22pt/23pt variations. They create the most problems for the defender for sure and we'll look at one of these today.
Here are some positions from a backgame I defended against on GridGammon. The backgame player here has the 23/22pts combo and I have concentrated on the defender's plays.

Position One

Black leads 4-1 to 7 and has 2-1 to play.
Before we discuss the play, we can note that Black has the best anchor and the best board and his only real weakness is the checker on his 4pt, which has no useful function in the foreseeable future and reduces him to 14 playable checkers. White has five checkers back, with the spare ideally placed on the higher of the two points. It's important to note that a backgame doesn't always start at the moment when the two backgame points are made. It's still possible for White to switch out of her backgame and given a good opportunity, she probably should, so Black shouldn't be too adventurous here. The best play is 8/5, not ideal when Black is really looking to prime, but all that he can do for the moment. The more adventurous 13/11, 8/7 is a small error, but close enough to give us a hint of the sort of thing that will be required.
White rolled 3-1 and played 7/3 and then Black has a 6-4 to play.

Position Two

I played 20/10, which I think most of us would play in default of any better plan! It comes out best in the rollout but only by a very thin margin over 20/14, 13/9. Why would that be a good play? When those blots don't get hit, they are in good shape to make Black's 8 or 9pts to extend his prime. When they do Black goes backwards and slows down, improving his timing and thus weakening White's backgame. However, we are now on the cusp of the point at which White finally comits to her backgame, so 20/10 is probably minutely better.
One of the drawbacks to using my own games as examples is that occasionally you get to see a very horrible play. Here's one. I lead 4-1 to 7 remember.

Position Three

Black on roll. Cube action? For money I would say that this is a thin but reasonable double. White does have two very strong points but it isn't at all clear that she is going to be able to time this. She can take quite easily though, because of the two Black spares on the 5 and 4pts that are more or less out of play, so Black can't realistically hope to make any more prime points. At this match score, doubling is a huge blunder. White can redouble on almost any pretext, pushing Black into overage, killing his gammons, killing the cube and activating White's gammons as match winners. This is an X-rated blunder, not to be shown to children and those of a nervous disposition. Note too that White's play is going to be a lot easier than Black's, usually true for backgame players, so she will probably get closer to the theoretical equity than Black.
 White took and then I rolled 5-4.

Position Four

How would you tackle this one? While you are thinking about that, I'll go and get on with some other stuff, so come back tomorrow and we'll see what happened next.
Until then,  enjoy the game!

The Major Split, Right Or Wrong?

Two interesting comments on my last post. In the first Boop commented that it should be possible to program the bot to assess the opponent's playing strength on what it observes in the match and adjust it's cube action accordingly. I expect that this is possible, although my knowledge of computer programming is on the level of an amoeba, but whether it is desirable or not is another matter. At present, when a bot analyses a position, it makes an objective assessment based on the assumption that its opponent is a player of equal strength. If you make it play according to the strength of its opponent, then those who want to learn from the bots will see it making plays that may be optimal to deal with a beginner opponent, but not actually the best play otherwise. In my view it's better to let the bots do what they do and make our own adjustments based on a known bench mark.
David Levy also raises the point that I failed to mention market losers. If your opponent opens with a 3-1 he argues, it is correct to double but equally correct to refrain from doubling. This is absolutely true. If you are strong enough to recognise when you have any market losers (one sequence is enough), then I agree that not doubling may be right. If you are not confident whether or not you have any market losers or even what a market loser is, then turn the cube and concentrate on the game! You cannot make a mistake on your first turn, but you can on your second and subsequent turns. If you don't know exactly what you are doing, why risk it?
This post was written in reponse to several fibsters who queried why a bot would want to double on the first turn in a 2 point match. David is probably in the top 1% of players in the world. You can see why he thought it inadequate!

I have an American student who is a model of how to study. Here is an example and here is the position.
Position A
 

Black trails 4-away, 3-away and has 6-3 to play. He chose 24/18, 8/5 which is a blunder, costing about 0.11ppg. The best play is clear, 13/10, 11/5 and I commented (with hindsight),  "The 18pt is a bad place to be hit when the 5pt is slotted. Note too that the match play, as well as leaving three blots, rather leaves the checker on the 11pt with nothing useful to do at the moment, whereas the XG play leaves active builders on the 10 and 8pts, very useful."
All very well and true as far as it goes, but then Ace Student reminded me of a position from a previous match. Here it is.
Position B


 Now it's 5-away, 5-away and Black has to play 6-2 from the bar. Here he played bar/23, 13/7, a play which I critiqued as follows.
"I view this type of position with your forces in the role of defenders in a castle. Your play has your forces staying within the walls and declining contact in the hope that things will get better later. Sometimes they do, but more often those checkers get primed and you get doubled out in a roll or two. The XG play forces contact now with a bold sally out through the main gate, in the hopes of exchanging hits and/or making the high anchor that will keep you in the game. As so often, this bold approach pays."
You can see the problem here. In the first position, it's very wrong to make the major split, but here it's very wrong not to do so. He asked, "Why in one case it is correct to split to the 18pt and in another it is not?
The reason 'bad place to be hit when 5pt is slotted' can be applied in both cases."
I expect you want to know why too!
The bar is a bad place to be hit in both positions. The point is that in Position A it isn't a risk worth taking. Black only has two men back and he can play all of the roll very productively on his side of the board, making the 5pt and putting his checkers in excellent shape to build a prime. Also, White's back checkers haven't moved. In (pos B) it is still a bad place to be hit, but now it is a risk worth taking, one that is almost forced on Black. He starts on the bar with three men back, whereas White has partially escaped one man. On his own side of the board Black hasn't yet made a point inboard and his checkers are very awkwardly placed to build a prime. All this means that staying back with three checkers deep in White's board is not feasible and Black has to fight for life now or face being doubled out in a turn or two. Either way he is a clear underdog, but definitely worse off if he doesn't split to the bar.
In position A there just aren't these imperatives to split. Both sides have two men back and Black has a small race lead. He is a small favourite in the game. A nice quiet play is fine.
Splitting to the opponent's bar, whether the 5pt is slotted or not, always has dangers. We just have to weigh risk against gain and treat each occasion on its merits, because there are no hard and fast rules and there can't be in a game where the position of all 30 checkers has a bearing. We do have a tendency to just focus on the point in question, White's bar point in this case and to look at the extra hit and cover numbers, but every piece has a part to play. If you haven't looked at all 30 checkers, you run the risk of making a big mistake.
We can't learn backgammon by learning moves, we have to learn to think about the game while it unfolds. This is a paraphrase of something that Emanuel Lasker said about chess and if anybody knows the original quote, send it to me please!
Until the next time, enjoy the game!

The Great Two Point Match Mystery

I'm going to write all that I know about two point matches, but first, let me direct you to the comment on my last post from Timothy Chow. Timothy adds considerably to my theme and also alerts us to an unusual play of 6-5 in this position.



The "automatic" play here is 24/13, adding an awkward sixth checker to the midpoint and making no positional gain in a race where we trail by 6 pips. However the best play for match or money is the more adventurous 13/7, 13/8, unstacking the midpoint, putting two more checkers into the zone and bidding for a prime. A story goes with this, as I actually found this one for myself several years ago and eagerly looked for a chance to play it. I have seen it exactly twice since, once when I was at GammonSave where it is a small mistake and boring old 24/13 is a bit better and once at DMP where it doesn't matter much what you play!

Anyway, on to Two Point Matches and cube action. A fibster writes, "In a Seven Point match against a bot, we got to 5-5 and the bot doubled immediately and then rolled 5 doublets! Suspicious eh?" Well no actually.
At this score, it is technically correct to double at the first legal opportunity. Even if your opponent starts with a 3-1 which leaves you as a clear underdog, you should turn the cube, so obviously it is correct in every situation. Your opponent will always have a correct take.
To understand this, we need to understand why we don't double this early at other scores. It's because owning the cube has value and the longer the game has until the end, the more value it has. Once you have the cube, you only need to become a strong favourite (about 82%, less with some gammon chances) and you can cash the game. Your opponent by contrast has to get all the way to 100% to get his points. Owning the cube effectively shortens the ladder that you need to climb for victory. At 2-away, 2-away, owning the cube has no value whatsoever, so you can double anything where you have the advantage. "Aha", I hear you cry, "but if my opponent starts by making his 5pt, I am an underdog, so why double?" Because even if you roll your worst, probably 2-1, he should double next turn and you will still have a trivially easy take. This game is going to be played for two points whatever, so it may as well be you who doubles!
There is however one key word in all the above and that is "technically". Technically assumes equal players and correct cube action on following turns. In real life, a strong player playing a much weaker opponent may well leave the cube in the middle, in the hope that by doubling later he may get an incorrect take or pass from his weaker opponent and/or be able to play on for an undoubled gammon. To do this you need to be strong enough to be very confident that you will assess the cube correctly later and you need a considerable skill advantage over your opponent. If everything in this post is old hat for you and your opponent is about 250 rating points weaker than you, waiting to double might be your best option. If you are any other sort of player and/or your opponent is stronger than you, cube immediately.
So, was the GBot correct to double at this score? One weakness that Bots have is that they are not capable of assessing their opponent's playing strength and adjusting their cube action accordingly.  The GBot assumed that it's opponent was equally strong and on his turn would make the best play. A real life player of that ability would probably have played on and gained by doing so.
I write this in the hope that it will be understood and all the players who don't auto double on the first turn will begin to do so and thus win a little more often and thus have more fun, but they won't! There is a huge resistance to making a play that means that the match will end this game. That inertia is hard to overcome, so I guarantee that some of you will read this, even understand and agree with it and still when it comes down to it, not do it the next time they are at 2-away, 2-away! It's your life, live as you want to live!
Until the next time, enjoy the game!

Splitting

One of the hardest problems that we face in the early part of the game is when and how to split our back checkers. For a variety of reasons we do have to get them moving. They are vulnerable to being primed where they are and while they are static back on the ace point, our opponents can bring down builders from the midpoint without much danger. Once you have split them, your chances of improving your anchor get better and your coverage of the outfield doubles. The downside of splitting is that you are vulnerable to being attacked, but as you can't win the game without moving them, they do have to get off the ace at some point. It's my belief that for most of us, the time to split is on the first roll, when the danger of being attacked is at its lowest and our opponent is keen to bring down builders to make points. Generally speaking, the computer rollouts support this tactic at level scores and the balance tips even more in favour of splitting when you lead, less so when you trail.
Splitting does have one major benefit for most of us though, which is that in my view, it leads to games that are slightly easier to play where we will make fewer mistakes. The more skilful players, experts and above, like to make the more complex plays, slotting their 5pt aggressively and bringing down builders rather than splitting. For them, this is a good tactic, making the game harder to play so that they have more chance of outplaying their opponent. For the very great majority who will never reach this level and don't particularly aspire to do so, the split play will pay dividends.

It's the Crawford game and Black trails 0-4. White is the stronger player of the two. Black chose 13/10, 13/11. This is, according to the rollouts a minute mistake, 0.004ppg less than optimal so just about as unimportant as it can be. However he should split, partly because it's minutely better, but mostly because it makes the game easier to play. There's no cube in this game, so the back checkers have to move to win the point and the decision of when and how to split them is only going to get harder as the game goes on. 24/21, 13/11 is the usual split with this roll but 24/22, 13/10 is almost as good with the same equity as the two-down play. Worth a try on novelty value!
On his second turn, Black already had a tough choice.

He chose 11/9, 10/9, a 0.060 error. He can either make the 9pt without splitting, or he can make the 10pt and split. As the 10 and the 9pts are roughly equal in value, it's clear that he should make the 10pt and split.
The next turn, the play gets harder still, after White has rolled 5-5, played 13/3(2).

Black played this 24/21, 13/11, on the face of it an entirely reasonable play, looking to make progress on both sides of the board. This is another error though, about 0.068 this time and he should play 13/10, 6/4. Not many people will find this play OTB. As a rule, we are all (often wrongly) hesitant to slot after the opening roll and it's actually quite rare to slot the 4pt with the 5pt empty and it's also rare to want to slot when our opponent has a better board. What makes it right here? The secret lies in the stacks that both players have on their 6pts. These need to be developed and soon and for White it is even more urgent than for Black, as she has no other active builders. Doublets aside, she isn't going to have much chance of converting her stack into a prime, so she will welcome the chance to attack on her 4pt. Splitting also turns her 5-5 on the next turn from a disaster into an excellent roll and the huge swing on this one roll is quite important. Black's stack also has to be developed and the 6/4 slot is a nice way to do it, giving him good sixes next turn too. This play is more attractive here than usual, as Black can't lose a gammon, but it still looks right even at normal scores.
One useful tool for me is the use of mental flags, highlighting features of the board that are important on the next turn. I like to put a flag on stacks. The flag on my own stacks says "Unstack me now". The flag on my opponent's stack says, "Danger of falling checkers, keep clear". Try this one yourself, it's often a useful tool, steering us in the direction of a correct play.

So to recap, split early. It only gets harder later!

Until the next post, enjoy the game!