Grant’s Puzzles

Courtesy of Grant Hoffman

#214 – How should White play 51 here?

You were hoping for a better roll but you have to play the role that you were given, not the one you wanted.

You will be forced to leave at least one blot anyway, so why not put one of your opponent’s checkers on the bar with 8/2*:

The problem with this play is even when it works one of your covering numbers, a 6 means that you will have to give up your 8 point to cover, 8/2.

8/2* would have more to recommend it if you had 4 checkers on your 8 point, so that after the hit you still had 3 checkers on your 8 point.

Many times, when you have disengaged, the best move is to simply start to clear your rear most point. Here you could try 15/14 15/10:

You will be hit with any 2 as well as 63, 54, 33 and 53. That is 18 rolls or 50% of the time.

The other disadvantage of this play is that you leave 2 blots. Usually 2 blots are harder to clean up their 1 blot.

If you do have a blot hit, it would be very useful to still have your 15 point to run to with your hit checker.

If you wanted to leave only 1 blot, you could try 13/7:

This leaves only 1 blot, but it perfectly diversifies your opponent’s numbers. They will have 6’s and 5’s to hit on your side of the board and 1’s, 2’s, 3’s and 4’s to make points on their side of the board.

So far, we have determined that it is good to have only 1 blot but we do not want to diversify our opponent’s good numbers.

It would also be good to have another spare on your 8 point to help you build inner board points. 1 spare is okay but 2 spares would be much better.

Consider 13/8 6/5:

You have retained your 15 point, in case you are hit.

The 3’s and 4’s that hit you on your side of the board are also the numbers that Black needs to make their 5 and 4 points – that’s very good duplication.

You have placed a spare on your 8 point.

You have started the 5 point, which you would very much like to have. This is the correct move.

If we move a checker 13/8 and then reconsider the position, now it is correct to hit 8/2*, as you have 3 spares on your 8 point and so can cover with a 6 without giving up your 8 point.

#213 – How should White play 43 here?

You have the better board, and you have a number that hits 10/3*:

Black will hit back with any 3 plus 21 and 11, which is 14 rolls or 39% of the time.

Players in favour of the hit, argue that you want to make moves that allow you to give your opponent a double next turn. The problem here is that you are actually too good to double without Jacoby.

The move with less hits and still a great reward, is to play 13/9 10/7:

This threatens to make a prime next turn or attack Black’s rear most checker, if Black fails to roll a 4.

If Black does roll a 4, they will not only hit the checker but also usually escape their rearmost checker. This is too many good things, so the risk is too much.

After the roll, you will be ahead in the race by 18 pips, so why how about playing 13/9 24/21:

This prepares to escape your last checker, but now black is able to attack your last checker when you advance it to the 4 point. It was safe back on the 24 point, and as their 7 point is not made, you can escape with most 6’s.

Consider 13/9 13/10:

This looks like TMP – Too Many Points, and it is, but now you have only one blot and a good broken prime in front of Black’s rear most checker.

Black will have to be careful and will not want to slot or hit loose on their 1 point, as they risk being hit and put behind this broken prime.

This looks like the ugly play, but sometimes backgammon is not a beauty contest.

This is the correct move.

#212 – How should White play 43 here?

Your winning chances are very low here, even after making the correct move. That is no reason to stop maximising your equity by not choosing the best move.

You must enter bar/21, so you are at the edge of your opponent’s 5 prime.

You are hoping to roll a 6 and jump over Black’s 5 prime or anchor on the 21 point. Both of these plays will preserve your timing.

It may looked like playing 5/2 with the three is automatic:

Next roll, you have to play your 5’s by playing 6/1 unless you roll a 6. Black has no incentive to leave your 4 point. Then you will probably only have a 3 point board.

The big advantage of this play is that it is safe for one roll.

With 11 or 22 you can attack and make a 4 point board.

What about breaking your board now with 6/3?

This creates a 4 point board and prepares to clear your 6 point, which will kill your 5’s. Once you have killed your 5’s, you may be able to keep a 4 point board long enough to escape the checker on your 21 point.

With 21 and 11 you can attack and make a 5 point board. With 22 you can attack and make a 4 point board.

Sometimes, the obvious safe play is not the correct one. Here the bold bar/21 6/3, leaving an immediate shot is the correct play.

#211 – How should White play 53 here?

I was recently reviewing a match between two of my compatriots and the above position occurred, though I have removed the match score.

Because Black has 3 gaps in their home board, you might be tempted to make the big play of 18/13 18/15:

If you count the number of rolls that hit you, you will see that any 6, 4, 3 or 1 as well as 22 will hit you. That is 33 rolls or 92% of the time that you will be hit. That number is just too high for this to be the correct move.

You could consider the safe play of 6/1 5/2:

This leaves no blots, but more importantly, Black will have no trouble playing their next roll.

Your position is stripped and most of your rolls will either damage your board or any roll with a 6 apart from 66 will force you to move only one of your checkers from the 18 point.

Put another way, your position is now inflexible and brittle. The safe position is not as safe as it looks, when you look ahead more than one roll.

You will be ahead in the race by 56 pips after the roll, so you would really like to run now, while Black’s board is still relatively weak.

Can you used duplication, to minimise the number of shots that you give Black? Consider 18/10:

You have duplicated 6’s for Black to hit you from the 21 and 13 points and duplicated 1’s for Black to hit you from these 16 and 8 points. This means you will be hit with any 6 or 1 and 54 – 26 rolls or 72% of the time.

As Black has a relatively weak board, you can afford to make this flexible play.

Note that this loses 1.7% less Gammons than 6/1 5/2.

If we give Black a stronger board, by making their 1 point:

Now Black’s board is too strong to play 18/10, now you must play the inflexible and brittle 6/1 5/2.

#210 – How should White play 33 here?

You have the ability to clear your midpoint now with 13/10*(3) 10/7:

There are many issues with this play:

  • You have made your 10 point and the hardest point to clear is 6 pips away from your opponents anchor.
  • You have given Black the chance to make a second anchor in your home board.
  • You have not made your 5 point, and the most dangerous gap is the one immediately in front of your opponents anchor.
  • Some of your 6’s play awkwardly.

If you still want to hit 13/10*/7 8/5(2):

This at least makes your 5 point.

This still gives your opponent the chance to make a second anchor in your home board.

Although hitting is fun, do we really need to hit here? Consider 8/5(2) 6/3(2):

You have made your 5 point, black has no chance of making a second anchor and you have retained a spare checker on your 13 point.

In a holding game, you 1 to have spares as they allow you to handle awkward rolls until you roll the doubles that will clear your midpoint.

All of your 6’s now play safely.

This non-hitting play is the correct move.

#209 – How should White play 61 here?

The big play is 10/9* 10/4:

This is the “go big or go home” play. Unfortunately, after this play you are more likely to be going to the funeral parlour!

Black will hit you with 4’s, 2’s, 31 and 11 – that’s 23 rolls or 64% of the time.

If you really want to hit, then 10/9*/3:

This seems much more reasonable as you will only be hit with 2’s, 11 and 54 – 15 rolls or 42% of the time. If you are hit, and do not immediately hit back, then Black will have a very good chance of picking up your second checker on your 9 point.

Looking at your resulting structure, having 5 checkers on your 3 point looks terrible.

You are also ahead in the race by 25 pips before the roll, so maybe you should just try to get your checkers home safely without hitting, by playing 10/4 3/2:

After this move, you are ahead in the race by 32 pips.

Black will hit you with 20 rolls or 56% of the time. If Black misses, then you will have the stronger board with a fifth point slotted and a direct 6 to cover the slot.

Your board will be dangerous enough that Black will be forced to move the checker on your 9 point.

I find it hard to make passive plays, but you are so far ahead in the race, that this is the correct move.

#208 – How should White play 65 here?

No one likes to leave a blot on a point that your opponent would like to make, especially when they have 3 builders aimed at it.

This makes you consider bar/14:

You have minimised the number of shots by duplicating 2’s but as you will also be hit with 63 and 54, that gives Black 15 hitting numbers.

The alternative is bar/20 13/7:

This leaves you with only 1 blot.

Even though Black would really like to make the 5 point, this is the correct play.

The most important factor here is the fact that after this roll, you will be behind in the race by 13 pips with your opponent on roll. Even if they never hit you, they are the favourite in the race.

If they hit loose on their 5 point, you could return hit.

If they completely miss you, then they will have to tidy up the checker on the 9 point, making your position safer.

To quote Kit Woolsey “when ahead in the race then race, when behind in the race – seek contact”.

#207 – How should White play 31 here?

You really want to stop black from making their 5 point, so you consider bar/24 6/3*:

This confirms to the old adage “when in doubt hit”.

Although this duplicates Blacks 3’s to both hit and cover the blot on their 5 point, it has a significant downside – you are placing a third checker on your 24 point.

I have a saying “three checkers on your 24 point is the kiss of death” it is a bit dramatic but it shows how much I hate having a third checker on my 24 point. The more inner board points your opponent has, the worse it is as you have less numbers that split off the 24 point.

This means that the 3 has to be played bar/22:

You have only to decide how to play the 1.

You could just consider playing bar/21:

This duplicates Blacks 1’s to hit and to cover their 5 point. The danger here though is that Black has 12 checkers in the attack zone and will attack you.

You could stay further back and play either 11/10:

Or 8/7:

Both of these moves, do little to improve your position, and are just moves that seem okay but do nothing special.

You need to step back and firstly think about Paul Magriel Safe Versus Bold Criteria. You have 3 checkers back while Black has only 1 checker back. Therefore, you should be more inclined to make a bold play.

You would like to either attack or prime Black’s rear most checker and either game plan will be enhanced by your making your 5 point. Simply slotting 6/5 is the direct way to improve your board. You are risking very little as you are already behind in the race with 2 extra checkers back compared to your opponent.

You are helped by the fact that this duplicates 2’s to hit on both sides of the board, but that is more a bonus rather than the prime factor here.

This is the correct move.

#206 – How should White play 52 here?

After the roll, you will be ahead in the race by 13 pips, which may tempt you to run 24/22 8/3:

The problem is that Black has 10 checkers in the attack zone, and your checker is now on a point that Black will fight for, hitting loose if necessary. You have an inner board blot on your 3 point, which will make Black more willing to hit loose – if they are hit they may get a shot at your checker on your 3 point.

The other issue is that all your outfield points are stripped without any spares.

If you had fully escaped the checker on your 24 point, and were just committed to getting your outfield checkers past Blacks anchor, then this move would go up in value. With a checker back on the 24 point, you could get into an exchange of hits and even if you make your 1 point, you would have many gaps in your board. This type of Swiss cheese board, is not very threatening.

You could try to make a better board by playing 8/3 6/4:

This leaves you with a stripped out of board with no spares.

While the 3 point is better point to make than the 1 point, you would rather make your points in order.

In summary:

  • You want to avoid stripping your outfield points.
  • You would like to create spares in front of Black’s anchor.
  • You would like to make your board in order
  • You want to keep your checker on the 24 point where it is.

Consider 10/8 10/5:

You could choose to keep the checker on your 24 point and the spare on your 8 point by playing 6/1 6/4:

You now have 2 spares (on your 8 point) in front of Black’s anchor, a more flexible position, a better point slotted and you can cover that slotted point without breaking your 8 point.

It looks like you are giving up the 10 point, but you will need to clear it soon anyway, and this move creates a much more dynamic position.

#205 – How should White play 62 here?

After the roll you will be ahead in the race by 12 pips, so you may consider running 23/15:

It is said that “Fortune favours the brave”, while this may be true, sometimes being brave will just get you slaughtered. Black will hit you here with any 5, any 1 and a lot of combinations of 2’s, 3’s and 4’s.

Your highest priority here is to play 23/21, which makes your 21 point anchor and enables both checkers to jump over Black’s prime with direct numbers.

The real question is how do you play the 6?

You might think that as you now have an advanced anchor and have more checkers back compared to Black, that you should make the bold play of 8/2*:

The problem with this play is that you are hit with any 2, plus 11 and 54. That is 14 rolls or 39% of the time.

Instead consider the quiet play of 9/3:

This looks terrible, as you have created a stack on your 3 point. However, Black only escapes by rolling a 5. If she does not escape then you will have pointing numbers and 13 checkers in the zone.

Even if Black does roll a 5, you are ahead in the race by 12 pips before the roll and you still have an advanced anchor. You will continue to build your board, and there will be racing and potentially hitting chances to come.

I find it hard to make passive plays, but there are times when you have to be able to make them.

#204 – How should White play 21 here?

Black has a solid 5 prime here. Unfortunately, you have a checker trapped behind it.

It may look tempting to safety the blot on your 15 point with bar/24 15/13:

Black will have some rolls that do not safety the blot on the 20 point, but no roll that forces them to leave another blot.

You also could benefit from having an anchor.

Consider bar/23 6/5*:

Black stays on the bar with 4 rolls – 66, 44 and 64.

Black is forced to leave another blot if they roll 62.

If Black hits you, you now have the chance to make an anchor.

This move may look flashy and aggressive, but it wins 10% more games and 3% more Gammons.

#203 – How should White play 41 here?

Black has 11 checkers in the zone, and has made their Barpoint. They have started to prime you, and look like they will be extending that prime over the next few rolls.

Because they are priming you, you need to enter on the 21 point with the 4. If you do not advance now, Black will usually make another inner board point and it will be more dangerous, to advance later.

Then you have to decide how best to use the 1.

The 21 point is a great anchor, but you could try for the 20 point anchor by advancing 21/20:

Unfortunately, Black now has 4 builders aimed at their 5 point, the point they most want to make next. This is just too risky.

You could try playing 24/23:

However, all this does is give your opponent another checker to attack or point on.

You could try playing 11/10, which minimises shots and by moving to the 10 point, you have more point making combinations, especially rolls that make the 4 point.

This is a good play but as someone once said, ‘good is the enemy of best’.

Consider 6/5:

6/5 the splot play. A Splot is a combination of splitting and slotting. In his book called “Backgammon”, Paul Magriel warned against slotting while your back checkers are split. His rationale was that if your opponent missed the slotted checker, they could attack your split checkers making it hard for you to cover the slotted checker. This is a very good advice, but the danger in backgammon is applying good advice to situations that are the exception.

For a splot play to be correct, you usually need to be duplicating a number and have a reasonable number of covers.

Here you duplicate 4’s to hit on both sides of the board and have a reasonable number of covers.

I always like to give myself good 6’s and here 6/5 does that.

#202 – How should White play 52 here?

Sometimes backgammon is looking ahead to what will happen, choosing the right game plan and playing according to the right thing. However, other times like in the end game, it is tactical – which means you just have to go through all the numbers.

You can use themes to help you, so I thought it would be good to go over the above position.

If you play 8/3 6/4:

You now have 8 rolls that leave a shot – 66, 55, 44, 22, 65 and 64.

Another indicator that this is not the correct move is the fact that the top 2 points, the 6 and the 5 points have an odd number of checkers on them. You really want to avoid leaving an odd number of checkers on the top 2 points.

Now consider 8/6 5/off:

The fact that the 5 point is stripped of any spares might put you off this play, but it should not.

You have an even number of checkers on the top two points.

You only leave a shot with 65, 54 and 53 – that is 6 rolls.

If I had the time to count the rolls, then I would. If I were under severe time pressure, I would just play to the theme and try to keep the top two points with an even number of checkers on them.

#201 – How should White play 53 here?

This position is from a match where one of the top giants in the world made the wrong play. This should give you hope that even the best make mistakes.

You could consider 15/10 13/10:

This does make another point, which is 6 pips away from your 4 point, so does give you good 6’s if Black splits to your 4 point. Unfortunately, you already have good 6’s, as they moved checkers from your opponent’s outfield, into your outfield.

Black will gladly attack, especially in their inner board, as they would like to close you out. They would give up their midpoint to achieve a closeout if necessary. Then they would merely have to extradite their 2 rear most checkers to win.

This does leave 4 blots so maybe you want to anchor in your outfield with 21/16 23/20:

This is still a racing move when you will be behind in the race by 34 pips after the roll.

This only leaves 3 blots, but again although there is some duplication of 3’s, Black will willingly attack here – especially in their inner board.

The anonymous giant played 23/18 21/18:

This gets rid of your blots in Blacks board and creates a great anchor. However, if this becomes a blot-hitting contest, Black has a better board than you do.

In all of the above moves, because Black has made their 1 point and to a lesser extent their 3 point, Black will not be priming but is playing in attacking game. Whatever you do, you will be leaving blots that your opponent will attack. One of the easiest ways to counter in attacking game is to make a prime.

Here the priming move is 13/8 11/8:

There is some duplication of numbers, as 4’s hit for your opponent in 3 places and 3’s are useful to hit and to split 24/21. This duplication is a nice bonus but not the primary reason.

Some players are sceptical about the value of the 4 prime, but it increases in effectiveness the more checkers your opponent has behind it and when your opponent is far ahead in the race.

You still leave 4 blots with this play, but now if you are hit, you will gain more timing as you will fall further behind in the race.

In addition, any hit from the bar by you will just make their situation worse as you put another checker behind your 4 prime.

#200 – How should White play 43 here?

When you are forced to leave a shot, some players advise you to leave the minimum number of shots. This is great advice but it is not always the most important factor.

Over the board, 13/6 was the move selected.

You will be hit with any 5 or 1 and 66. That is 23 shots. The good news is that you will still have an anchor, and the player very much wanted to retain his anchor.

Another approach is to play 13/10 13/9:

Now you will be hit with any 1 or 2, as well as 62 and 63. That is 24 shots.

The problem with both of the above moves is that they abandon your midpoint. Even if you are missed, you have isolated your rear most checkers. Retaining your midpoint here, when you are ahead in the race, is very important.

Let us go back and examine the assumption that you should keep our 21 point anchor. If you played 21/14:

You have kept your midpoint, and your blot on the 14 point will be attacked, as will your inner board blots, so why would you do this?

If your opponent hits you loose in their inner board, you will have returned shots and you have a stronger board than your opponent.

Next notice that Black with 6’s and 2’s hits your 14 point blot. Your blot on your 21 point is hit with 6’s, 4’s in 2’s. Notice the duplication of 6’s and 2’s. Your blot on your 23 point is hit with 6’s and 4’s; again, there is duplication of 6’s.

Duplicating your opponent’s good rolls is very important. Getting direct return shots from the bar is also very important. In this position both of these factors make abandoning our anchor with 21/14 the correct move.

The fact that you have a stronger board than your opponent is very important.

#199 – How should White play 54 here?

You have the better board, more checkers back and an advanced anchor. These factors should be pointing you towards making a bold play. They are some of the more important factors of Paul Magriel’s safe versus bold criteria.

Your 4 point would be a nice point to have, so you might consider slotting it 13/4:

This is a bold play but you have stripped your midpoint and left your 6 point stacked.

Black will hit you with any 3, as well as 61. That is 13 shots or 36% of the time. You also leave 2 blots.

If you are missed and Black does not escape, you still might not cover the blot next roll.

This looks like too much risk for too little return.

You would like to Unstack your 6 point, and you have the stronger board so why not attack with 6/1* 13/9:

You will be hit with any 1, as well as 62, 54 and 44. That is 16 rolls or 44% of the time – this is just too many rolls. You also leave 3 blots.

The only awkward hitting roll that Black has is 41. Can you find a move that gives Black more awkward hitting rolls?

Consider 13/8 6/2:

This only leaves 11 hitting rolls, 1 blot and it unstacks your 6 point. As an added bonus, your 8 point is made. Your 8 point may not seem important, but it gives you 2 checkers in the zone that can be used to cover the blot on your 2 point and aid in any future attack.

When you look at Blacks hitting rolls, you will notice that 61, 41 and 31 are very awkward for Black. Would Black actually hit with 61, 41 and 31?

Black should not even hit with 61, but should instead make their 5 point with 11/5 6/5. This unstacks there 6 point and gets rid of the gap in front of Whites anchor.

Black should still hit with 41, but the best move 24/23* 6/2, leaves a direct return shot from the bar. The advantage of 6/2 is that it unstacks Blacks 6 point.

Black should not even hit with 31, but should instead make their 5 point with 8/5 6/5. This unstacks there 6 point and gets rid of the gap in front of Whites anchor.

So in the original position, instead of being hit with 11 rolls, we should only correctly be hit with 7 rolls after the correct 13/8 6/2.

When you are considering how many rolls your opponent will hit with, ask yourself is it correct for my opponent to hit here?

#198 – How should White play 21 here?

If you want to play 24/21:

You should ask yourself what you are trying to achieve with 24/21. This is the racing play when you are behind in the race. You will be behind in the race by 11 pips after the roll.

You will have also moved to the point that Black most wants to make, when he has 3 builders aimed at it.

This play is just too dangerous.

Moving 24/23 13/11:

This moves to a less desirable point for Black to make, but just because it is less desirable to make does not mean that Black does not want it. There is a saying “all points are equal in the blitz”, meaning when Black is attacking they will take any point that they can get, especially if it puts us on the bar at the same time.

This is too dangerous and you need to leave your checker on the 24 point alone.

You want to keep your board intact so any move that breaks your 4 point should be discarded.

When leaving a shot, most players just think about the number of shots they leave their opponent. This can be the most important consideration but sometimes it is more important to leave the blot in front of a point that they would rather not give up. Especially if you will have returned shots from the bar if they hit you from an anchor.

The correct move here is 13/11 8/7:

If Black hits you with any roll other than 22, you will have returned shots from the bar. Particularly you will have returned 6’s from the bar.

If Black misses you, you will have a good chance of making your 7 point.

You have also duplicated 2’s to hit on both sides of the board.

This is the correct move as it forces your opponent to give up an asset they would rather not give up.