Grant’s Puzzles #240 to Present

Courtesy of Grant Hoffman

#248 – How should White play 42 here?

I get very cautious when my opponent has a 4 point board, even if I have an anchor. This may tempt you to make the safe play of 8/6 8/4:

But this leaves Black with the initiative, and the chance to tidy up one or both of their blots.

You need to do something more proactive, so you could consider improving your board with 8/4 6/4:

This would be really good if it wasn’t for the blot on your 8 point. Black will hit with 11 rolls, at the same time moving there rear most checker, which they want to move.

We can seize the initiative by hitting 7/5* 7/3:

Unfortunately, this also leaves a direct shot. If Black misses that shot you will still have to do cover or move that blot on your 5 point. If you cover with a checker from your 8 point, then you will be giving up your 8 point, which is one of your assets here.

To summarise, it is good to take away the initiative but it is dangerous to leave when your opponent has a 4 point board.

Consider 7/5*/1:

When I was learning backgammon, I was taught that moving a third checker to your 1 point was never right. But never is too strong a word, with this play you avoid leaving a direct shot and are only hit with 52 and 43 – 4 rolls or 11% of the time.

You are killing a checker, the third checker on your 1 point is dead and will not be used again until you bear it off. But now Black has some awkward numbers like 62 and 44 which will make Black bury their spare checkers.

You can get away with killing a checker because the game is so well advanced. If the game had a lot longer to go you would not want to move a checker to your one point.

I expect that this move is so horrible to some players that they would not even consider it. Paul Magriel wrote “the biggest mistakes in backgammon are not from choosing the wrong move but failing to even consider the best move”. He was talking about all levels of play.

#247 – How should White play 32 here?

You do have a safe option here, by simply playing 6/1:

But how safe is this? Black has three builders aimed at your blot on Black’s 2 point, and you have just created an inner board blot so Black will be less inhibited about attacking or hitting loose.

Although you can cover the blot you have created with any 1, you have buried a checker so that it cannot be used to make your 4 point.

If you want to improve your position without leaving a direct shot you could play 13/11 13/10:

Although this does not leave a direct shot, you will be hit with 62, 61, 53 and 52 or 8 rolls which is 22% of the time. Your blot on the 23 point will also be hit with 66, 44, 22, 11 and 32 or another 6 rolls which is 17% of the time. If you are hit on any blot, you may not be able to safety the other blots. 13/11 13/10 creates 8 new rolls for Black that hit and leaves 3 blots.

Consider 7/4 6/4:

Now you will be hit with 11 new rolls which is only 3 more than 13/11 13/10. However, you only leave 2 blots and you make a new inner board point. Now if you get into a blot hitting contest, you will have the stronger board. That stronger board will be an asset for the rest of the game, and Black does have some awkward rolls here like 61.

This is the correct move.

#246 – How should White play 22 here?

Any time you roll doubles, it is like you get to play two rolls in a row without your opponent making a move in between.

There is so much you would like to achieve with this roll but you cannot achieve everything.

Consider 24/22 13/11 6/4(2):

You would like to split your back checkers as Black has started to prime you which this move does.

You would like to aim as many builders as possible at your 7 and 5 points, which this moves does.

The problem with this move is that Black has so many rolls that hit one of your two outfield blots or attack your split checker on the 22 point.

If you decided not to split 24/22, then you could focus on offence with 13/11 8/4 6/4:

This is an improvement over the previous move you considered as you do not create another 2 blots in Black’s inner board.

Unfortunately, you still get hit with any 64, 63, 62, 54. Black can make an advanced anchor with 65 and 43. That is 10 rolls or 28% of the time.

The nice thing about this move is you have improved your board, which would help you in a blot hitting contest but there is a better move.

It is really important to split when your opponent is starting to form a prime, so 24/22 8/4 6/4 does that:

Having blots on both sides of the board, does leave you vulnerable to attack. You would like to be able to get a more advanced anchor or jump one checker over Black’s prime, but this still leaves Black too many attacking rolls.

It would be good to have an advanced anchor rather than a point merely slotted.

It is good to be able to improve your board both defensively and offensively so you consider 24/22(2) 6/4(4):

This is an improvement over the previous move, but Black can still fill in their 5 or 4 points which we would like to prevent. If Black does succeed in filling in their 5 and 4 points, Black will be able to attack when you move one of your checkers off your 21 point anchor.

There are so many cases where simply making your 20 point is the most inefficient use of checkers and so is wrong. This is not one of those cases, consider 24/20(2):

This move stops Black from ever being able to priming or attacking your checkers in Black’s home board. You can easily run when you roll 44, 55 or 66, and you will have several rolls to roll one of those doubles.

You will have only one blot and it will only be hit by indirect shots.

If you are not hit, you have plenty of rolls to make your 7, 5 or 4 points, which will improve your position.

You will only be playing with one blot, and you do not have to worry about being attacked or primed after this play.

Sometimes slow and steady is correct.

#245 – How should White play 62 here?

You have a safe play available here, 13/5:

To quote Malcolm Davis “that play hurts my eyes”. The problem with this play is that you have TMP – Too Many Points. You have 7 points and only one spare checker. The issue with TMP positions, is you have very little choice how to play future moves, and will usually have to do leave a blot within the next couple of rolls. And in the next couple of rolls, Black’s board will improve.

You have a window of opportunity to make a move that will improve your position while Black still has an inner board blot and you have the better board.

Consider 14/8 10/8:

Now you have 3 spare checkers, your two blots and the third checker on your 13 point.

Black can hit you with 2’s and 3’s, but notice the duplication. 2’s and 3’s are the rolls that cover Black’s blot on her 4 point. This makes it less likely that she will be able to hit and cover that blot.

If Black gives up either their 18 or 12 point anchor, you will have returned shots from the bar, maybe at their inner board blot if they have not covered it, and probably some blots in their outfield.

Here you have the stronger board, and you have an advanced anchor so you will never be closed out. Add to that their inner board blot and the duplication that you create, then now is the time to take a risk and make your position more flexible for the future.

#244 – How should White play 62 here?

If you wanted to minimise blots here you would simply play 16/8:

This leaves only one blot and the minimum number of shots for Black to hit it.

But what are you trying to achieve here? After the roll you will be behind in the race by 26 pips, so racing is not your best game plan.

What does your opponent want to achieve here? Being ahead in the race by 26 pips before the roll they would love to bring all their checkers home, starting with their rear most checkers. They want to leave their 18 point anchor, and one of the best ways to do this is by hitting as part of that leaving process.

16/8 allows Black to do that with any 1.

You could try to make it harder for Black to get there checkers home by making your 14 point with 20/14 16/14:

Although this will make it harder for Black to bring all their checkers home, they have enough spare checkers to play behind your anchor while they wait for the doubles that they need.

You need to think how you intend to win this game. One of your primary game plans is what Julius High calls the ambush. The idea is simple, you retain an anchor, while building a board and waiting to get a shot. What is the best way to ambush here?

Consider 20/14 13/11:

Let’s consider White’s position. White has the stronger board, White has an advanced anchor, White has more checkers back and Black has an inner board blot. These up all four criteria for Magriel’s Safe Versus Bold criteria. These criteria say that you should make a bold play here. While these criteria are excellent, they do not tell you which bold play to make.

After 20/14 13/11, how keen will Black be to hit any blots? Especially if they have to give up either there 18 or 13 points. If they do this without covering the blot on their 1 point, then you will have an immediate return shot from the bar.

If they do give up either their 18 or 12 points, you have a good chance of hitting in the outfield. And even if you cannot do that immediately, they will have to tidy up all clear blots that they generate, which they may not be able to do.

This is the alternative that leads the most blots, but it is clearly the correct move.

#243 – How should White play 64 here?

This comes from a recent tournament I was playing in, and my opponent had a 64 to play here.

When your opponent makes their 2 point, they are giving up priming as a game plan. This was noted by Paul Magriel in his 1976 book “Backgammon”. Making a prime from your 8 point through to your 2 point would require 14 out of your 15 checkers – which is very hard to do.

So Black should be focusing on attacking and racing. For Black to attack, they would ideally like to fill in the missing points in their board.

One option is you could try to prime your opponent by playing 13/7 13/9:

Black would like to focus on attacking and racing, so this move lets Black do exactly that. Any 6 will let Black hit and at the same time escape. You will also lose a large amount of pips slotting your 7 point as your checker will go back a long way when hit.

This move really plays into your opponent’s game plan, so you must look for alternatives.

Running 24/14 was the move that my opponent played over the board.

After the roll you will only be ahead in the race by 4 pips. This means that your opponent will be behind in the race by 4 pips and on roll. As the average roll is 8 pips, being on roll and behind 4 pips means that the race is even.

It is always good to race when you are reasonably ahead in the race, but here you are not. You are risking being hit with any 2, and when missed, you will only be even in the race. It is just not worth it.

Consider 24/18 13/9:

This must leave more shots than the previous move, but if Black hits you with a 1, they are sacrificing their 8 point and will be leaving you many return shots. Even if your opponent hits you from their 13 point, if they do not safety the hitting checker, then you will have many return shots.

If Black misses you, then you have a good chance to anchor on your 18 point. If you make that anchor, all you have to do is wait until you roll doubles to bring your rear most checkers closer to home.

If you make the 18 point, Black cannot blitz you or prime you. Those two major gameplans are out the window for Black. Making the 18 point is of such major benefit, it is worth the risk to get it.

Normally I hate giving my opponent good 6’s but here, this is the best of the alternatives and the move that my opponent should have made.

#242 – How should White play 64 here?

After the roll you will be ahead in the race by 39 pips, which means even if your opponent rolls 66 you will still be ahead in the race by 15 pips which is a significant amount.

Because of this race lead it is tempting to play 10/6 8/2:

This leaves no blots so your opponent cannot hit you. But the advantages end there.

If you roll a 6 or 5 next roll, you will be forced to run off your 18 point and leave a blot unless you roll 66 or 55. Black will have the checker on your 9 point, giving them shots and control of the outfield.

Control of the outfield is important, and you do not just want to give it up.

You consider 10/6 18/12:

This gives you four builders aimed at your 3 point and two builders aimed at your 7 point. Although this is good, you leave two blots which can be hit with any 3 as well as 21, 11, 61 and 52. That is 18 shots or 50% of the time your opponent will hit you. This is just too much.

Although it is good to keep an outfield presence and put pressure on Blacks blot on your 9 point, this leaves too many shots.

Consider 18/8:

This only gives you three builders for your 3 point rather than for in the previous position, but it makes your 8 point and you are only hit by any 1 as well as 63. That is 13 rolls or five rolls fewer than the previous move. Being hit 14% less is significant.

Making your 8 point is significant here, as is leaving fewer shots for Black. This is the correct move.

#241 – How should White play 42 here?

As several rolls are similar, we will narrow it down to two moves representing the two different approaches to this position: 19/13 or 13/7. Take your pick.

You want to win here, and even without knowing the Pipcount, you realise you are too far behind in the race to win if you disengage.

You would like to hit one of Black’s checkers, but have to decide how much risk to take to increase your chances of hitting that shot.

If you make this play you will get a double shot at a Black blot if Black rolls 64, 61, 54 or 51 – 8 rolls or 22% of the time. That sounds great, but before you pick up the dice you need to weigh the downside.

You do not need to consider rolls that move from being good rolls to great rolls like 22 and 11 which now put a White checker on the bar. These were great rolls whether or not Black put White on the bar as their position become so much easier to bring home.

Black will pick and pass or hit your White checker on the 19 point then move the hitting checker to safety with 52, 54, 32 and 21 – also 8 rolls or 22% of the time.

You may think that this balances out with the rolls that give you extra shots, but playing 13/7 means you lose an extra 8% of Gammons. And it is the gammon loss that makes this the incorrect move. If this was DMP ( or Double Match Point) 13/7 would be the correct move because gammon wins or gammon losses are simply irrelevant. As one Grand Master joked “at DMP make the move that loses the most Gammons”. Although this was said in jest, there is a lot of truth in this comment.

You notice that 52 which was used to pick and pass when there was still a White checker on the 19 point, now leaves us a single shot.

The take away from this is that you need to get a significant number of extra shots to justify the extra gammon losses or it needs to be DMP.

You are giving up 2% extra wins to avoid losing 8% extra Gammons.

Sometimes you have to give in and move on to the next game.

When you look at 13/9:

Consider the altered position:

Now after playing 13/7, you will get a double shot when Black rolls 65, 62, 61, 54, 52 and 51 – 12 rolls or 33% time and only be picked and passed with 53, 43 and 31 – 6 rolls or 17% of the time.

Now winning an extra 5% of the time makes up for the 9% extra Gammons you loose.

#240 – How should White play 32 here?

I have always thought of these types of positions as Scrambling Positions. I have used that term since I first read it in Kit Woolsey’s  great book “New Ideas in Backgammon”.

The idea is that White is scrambling to get his remaining checkers home, while Black is trying to contain him by either building a prime or putting him on the bar.

You need to ask yourself whether you should move closer to home by playing 17/14 3/1:

The idea behind this play, is that if you are missed it should be easier to get home and if you get into a blot hitting contest, your board is as strong as your opponent’s.

The first issue is the only numbers that Blackness you with our 44, 43 and 31. That is only five rolls or 14% of the time.

Then you have 10 rolls 55, 33, 22, 11, 42, 31 and 21 which leaves Black at least a double shot.

Although keeping your board as strong as possible, if the only way to do that is to advance into so many shots, then you need to weaken your board and stay further back.

Consider 5/2 3/1:

This is much better as you will be missed with 66, 11, 64, 61, 43, 42, 31 and 21. That’s 14 rolls or 39% of the time.

You should ask yourself what good is the blot on your 5 point? I can see no benefit from having that there but if it gets hit, say after you hit one of your opponent’s checkers, then you will be trying to scramble 2 checkers around the board. That is much harder to do than merely scrambling one checker around the board.

This leads us to the best move of 5/2 5/3:

You leave the same number of shots, but never have to worry about getting a second checker hit.

I have to think long and hard before I consider leaving another blot that could be picked up by my opponent in scrambling positions.