Monday, 30 April 2012
Five Positions, Answers.
I hope you read the last post, if you didn't go there now! Where have you been? For the rest of us here are the answers to the quiz. Every position has the same answer. These are all No Double and of course Take. In real play, by strong players they were all doubled and passed, which shows the size of reward a dangerous looking cube can reap. Well done Timothy, the only reader who felt confident enough to have a go at these, shame on the rest of you.
Position One.
Score, 0-0 to 5. Blue on roll. Cube action?
Not a bad double this one, Blue wins about 69% here but doesn't have many market losers and actually gives up 0.063ppg by cubing. However he netted a massive 0.349 blunder when White passed!
Position Two
Blue leads 3-0 to 9. White is on the bar. Cube action.
This one has very similar equity to Position One. Blue is about a 76% favourite to win this and can normally recube and expect a take. At this score though, White's potential to ship a very nasty 8 cube means that Blue should wait and that he gives up 0.085 by doubling. White's pass is a huge 0.315 blunder. Blue should wait a turn and double if White dances, usually losing his market by a bit.
Position Three.
Black leads 2-0 to 7. Cube action?
A double here is only a minute mistake, as with about 74% wins, Black is very close to being in the window. White's huge race lead, the absence of builders in Black's prime and the value of owning the cube when you trail in the match all add up to a very easy take and White's pass cost her 0.228.
Position Four
Score 2-2 to 9. Black has two men on the bar. Cube action?
Black here is a Giant 32 player and couldn't resist doubling here even though he had two men on the bar. That's a blunder but White folded this highly unusual position, costing himself 0.545.
Position Five
Black leads 2-1 to 7. Cube action?
And finally, Black (me!) should wait here and the cube is a very small mistake, only about 0.024. Followers of this blog know that almost good enough is good enough for me and it reaped a fine harvest when White limply folded, a 0.465 blunder.
Passes of this magnitude do happen, even up to championship level, particularly with some gammon threat and particularly when they are recubes, so be brave. Most of us don't like to pump the cube up against weaker opposition, but as they must by definition be even more prone to this sort of bad drop, perhaps we should be just as aggressive with them too.
The Fibsleague play-offs are posted, and BushSucks (Germany) takes on paulc (USA), while Backwoods is paired with runnerup (Germany). These 11 pointers should be good value, so look out for them on Fibs.
David Escoffery's Spring Open rolls on and dlevy (USA) is the first into the money round of 8. David is an expert on the great games writer Edmund Hoyle and you can enjoy his highly specialised blog here.
Tomorrow I want to say some things about splitting the back checkers, how, when and why! Enough for a whole book there, so I'll only be looking at some general points, but if it's an area that worries you, take a look.
Until then, enjoy the game!
Friday, 27 April 2012
Five Position Cube Quiz
Continuing with the theme of useful tools, I keep a collection of positions sorted by type. You might like to do this too if you find it useful. Today I have a little selection of positions that I have saved grouped together, although the connection isn't immediately obvious.
Position One.
Score, 0-0 to 5. Blue on roll. Cube action?
Position Two
Blue leads 3-0 to 9. White is on the bar. Cube action.
Position Three.
Black leads 2-0 to 7. Cube action?
Position Four
Score 2-2 to 9. Black has two men on the bar. Cube action?
Position Five
Black leads 2-1 to 7. Cube action?
All the players in the matches where I saw these are strong, expert or world class level. They didn't play these well, can you do better? If you get them all right you will see what links them.
Oh yes, which style of board do you prefer?
I'll come back to these very soon, so post some answers in the comments please!
Until the next time, enjoy the game!
Tuesday, 24 April 2012
In The Tool Box.
Robert Fontaine made some interesting points in a comment attached to my last post. Broadly speaking, he feels that because we make mistakes in so many different areas of the game, trying to work on them all at once isn't going to get results and that we would be better off concentrating on one area and strengthening our technique there. I can see the sense in this, so this is why as a preliminary I want you to find out what those areas might be. First concentrate on blunders, bad plays that have cost you at least a tenth of a point. Keeping these off the scoresheet will imediately move you into the world class category. Then begin to sort these into categories, grouping similar mistakes together. Categories with very large numbers of members are obviously those that are most going to reward work. How you then tackle these is up to you, but we'll look at some methods in a future post.
However, it is my contention that most mistakes are made for non-technical reasons. Mistakes where we have failed to grasp technique are hard to deal with, but mistakes in preparation, attitude and application are not. What do I mean by this? Here's an example.
White leads 2-0 to 7 and has the cube. My student Black played 7/4, 7/1, 3/off. Why did he make this play? "I was going for the gammon" he said. Quite right too, obviously a gammon is just what the doctor ordered when you trail and you've cubed, but there is of course more than one way to skin a cat.
Technically speaking, this play carries some risk, blotting next turn on 6-6, 5-5 and 6-4. Is this a risk worth taking in order to get a checker off? Three factors need to be taken into account. First, White has a nice board already, only three points but the best three and it will improve too. It is always going to be a problem for Black if White can hit something. Secondly, we can see that as it stands, White already needs 67 pips to save the gammon, just over 8 rolls, so if Black just makes the safer play of 7/4(2), 6/3(2) and gets down to an 8 roll position himself we can guess that about half of Black's wins will be gammons anyway. Thirdly, we have to consider extended jeopardy, i.e. what happens down the line. Obviously clearing the 6pt now is going to lead to a much safer and faster bear-off later and this is actually the most important of these three factors. Both plays win about the same number of gammons, actually 47, but the safer play now with less extended jeopardy wins a lot more games, 90 against 82 for the match play. If the race to save the gammon was closer or White's board weaker, or both, then Black's play could be right of course, but here it is a big blunder.
That's the technique and this can be learned and it should, but Black is actually a good enough player to avoid this large blunder in the first place, so why did he make it?
First, he was "playing a quick match while I drunk my coffee before I went out for my run". This is a recipe for disaster. There are no "quick" 7 pointers and you can't hope to play well if you think that there are. Moreover, this sort of casual rushed match breeds bad habits like a swamp breeds mosquitoes.
Second, he played it much too fast. He has a tendency, a very common one, to speed up in the bear-in and bear-off phase, almost like a runner approaching the winning post. Really strong players actually slow down in this phase, because with the winning post in sight, they don't want to trip over their shoelaces! A mistake earlier in the game can be put right, but here it can be disastrous.
Thirdly, this is a doublet and all doublets carry an enhanced risk of blundering, so he should have said "Doublet!" and let go of the mouse. Breathe. Think. This one simple tip will save you lots of blunders, believe me.
Lastly, I am willing to bet that he had the radio on and not made any preparation to play at all. Can you imagine Andy Murray going to play or even train without preparation? Of course not, so before you play, check this list.
Have I got time for the match and am I in the right frame of mind to concentrate?
Am I hungry or thirsty?
Do I need a pee?
Is my desk tidy? (yes really).
Radio off? Phone on message?
OK, then sit down to play and give it the same effort that you would if it's a tournament for money and the opponent is Kazaross or Falafel (other opponents are available).
What's interesting about the mistake above is not that this is an especially difficult position technically, but that with proper preparation, attitude and application, it wouldn't have been made in the first place. These are things that we can all put right, without so much as opening a book. Try it, you'll play better overnight.
Of course many of us like to play for fun, without worrying too much about mistakes and improving. That's fine, live as you want to live. You'll get no criticism from me, but let me just say that playing better has two advantages. It wins more, always more fun and more subtly, it makes the game more interesting!
Until the next time, enjoy this wonderful game.
However, it is my contention that most mistakes are made for non-technical reasons. Mistakes where we have failed to grasp technique are hard to deal with, but mistakes in preparation, attitude and application are not. What do I mean by this? Here's an example.
White leads 2-0 to 7 and has the cube. My student Black played 7/4, 7/1, 3/off. Why did he make this play? "I was going for the gammon" he said. Quite right too, obviously a gammon is just what the doctor ordered when you trail and you've cubed, but there is of course more than one way to skin a cat.
Technically speaking, this play carries some risk, blotting next turn on 6-6, 5-5 and 6-4. Is this a risk worth taking in order to get a checker off? Three factors need to be taken into account. First, White has a nice board already, only three points but the best three and it will improve too. It is always going to be a problem for Black if White can hit something. Secondly, we can see that as it stands, White already needs 67 pips to save the gammon, just over 8 rolls, so if Black just makes the safer play of 7/4(2), 6/3(2) and gets down to an 8 roll position himself we can guess that about half of Black's wins will be gammons anyway. Thirdly, we have to consider extended jeopardy, i.e. what happens down the line. Obviously clearing the 6pt now is going to lead to a much safer and faster bear-off later and this is actually the most important of these three factors. Both plays win about the same number of gammons, actually 47, but the safer play now with less extended jeopardy wins a lot more games, 90 against 82 for the match play. If the race to save the gammon was closer or White's board weaker, or both, then Black's play could be right of course, but here it is a big blunder.
That's the technique and this can be learned and it should, but Black is actually a good enough player to avoid this large blunder in the first place, so why did he make it?
First, he was "playing a quick match while I drunk my coffee before I went out for my run". This is a recipe for disaster. There are no "quick" 7 pointers and you can't hope to play well if you think that there are. Moreover, this sort of casual rushed match breeds bad habits like a swamp breeds mosquitoes.
Second, he played it much too fast. He has a tendency, a very common one, to speed up in the bear-in and bear-off phase, almost like a runner approaching the winning post. Really strong players actually slow down in this phase, because with the winning post in sight, they don't want to trip over their shoelaces! A mistake earlier in the game can be put right, but here it can be disastrous.
Thirdly, this is a doublet and all doublets carry an enhanced risk of blundering, so he should have said "Doublet!" and let go of the mouse. Breathe. Think. This one simple tip will save you lots of blunders, believe me.
Lastly, I am willing to bet that he had the radio on and not made any preparation to play at all. Can you imagine Andy Murray going to play or even train without preparation? Of course not, so before you play, check this list.
Have I got time for the match and am I in the right frame of mind to concentrate?
Am I hungry or thirsty?
Do I need a pee?
Is my desk tidy? (yes really).
Radio off? Phone on message?
OK, then sit down to play and give it the same effort that you would if it's a tournament for money and the opponent is Kazaross or Falafel (other opponents are available).
What's interesting about the mistake above is not that this is an especially difficult position technically, but that with proper preparation, attitude and application, it wouldn't have been made in the first place. These are things that we can all put right, without so much as opening a book. Try it, you'll play better overnight.
Of course many of us like to play for fun, without worrying too much about mistakes and improving. That's fine, live as you want to live. You'll get no criticism from me, but let me just say that playing better has two advantages. It wins more, always more fun and more subtly, it makes the game more interesting!
Until the next time, enjoy this wonderful game.
Friday, 20 April 2012
Tools
A long gap between the last post and this I know. I've been away and then doing some work on my own game and then some thinking about what (and who) this blog is for and then some idle procrastination.
All of us ask ourselves the same question, "How can I play better?" Then we log on and play some matches and then we analyse them and look at our mistakes. Then we play some more matches and so on. At least this way we don't get any worse and over a long period it will help us improve, but noticeably, not by much. After the first year or two, it's rare to make much progress. It looks as if this process doesn't work and I think that is because it isn't sufficiently focussed on the repeating mistakes. So, I am trying a new method on my own game and perhaps this would work for you too.
The method works like this. Go through your match, with Gnu or Snowie or ideally XG2, note the big mistakes and focus on those where you haven't understood what you should be doing and why. Ignore those where where you've had a good idea of what you should be doing, seen all the candidates and made an honest but understandable mistake. With the rest, try to put them into a category by type.A quick list might look like this.
Failed to be guided by the pipcount.
Played a doublet too quickly.
Rejected hitting loose on a low point (always a problem for me!).
Missed a cube by failing to use PRAT.
Failed to stay pure in a crunch situation.
Took a gammonish cube without being certain that it was right.
These are just some of my weak points, your list might look completely different.
Once you have your list and it begins to fill up with repeat offences, you need to figure out why you are making these mistakes. Not concentrating enough? Playing when you are tired (or hungry, or thirsty, or intoxicated, or bored, or depressed)? Not really understanding the position? These are just some suggestions, your own list might look completely different.
To recap, you need to know what sort of mistakes you are making regularly, then identify why you made them and then learn how to avoid them.
Here's an example. A student of mine faced this roll. What's your choice?
It's 0-0 to 5. Make your play before you read on.
He played 13/8, 6/3. It looks fairly natural, but it's an auto pilot play, of the type that we all make when we are feeling lazy. It's a particularly bad time to blunder because this game is arriving at the Crunch Point, where the game will be decided one way or the other. Either Black will get home safely or he'll leave a shot and be hit.
The best play by a lot is 13/10, 6/1. A highly skilled player with a very advanced positional sense might get this right by thinking, "It can't be right to pile a sixth checker on the 3pt. I may very well want to hit something in the bear in, so I'd better slot the ace and then one of the spares on the 3pt will at least have something useful to do." A more pragmatic player or even the same player might think, "I'll make the safest play for next turn, it's usually a good guide." Then he'll read the numbers. This just means looking at all his next rolls after each of the candidate plays (there are only two) and seeing which of them leaves a shot. Did you do this before choosing your play. If you didn't, go to the back of the class! Do it now and you will quickly see that 13/8, 6/3 has 14 blotting numbers next generating a total of 234 hits, while 13/10, 6/1 has only 9 which generate 126 shots. One of these, 5-5, you'll leave voluntary double shots although you could play safe but with much greater extended jeopardy.
So here is a bearing-in error, made by failing to read the numbers. How often do you read the numbers? If the answer is never, then it's time to learn and the only way to do that is to practise, by looking through your matches for bear-in positions and counting them up. Do it with pencil and paper at first, then graduate to doing it in your head. Do it until it is easy and then do it in matches until it becomes second nature to always do it. It's going to swing a lot of losses into the win column. Note that in most cases (and particularly here) you'll need to multiply the shot numbers with the number of shots that they leave to get the definitive answer.
News. Fibsleague season 56 ends on the 27th of April. Master A is still very open with a lot of matches undecided and a lot of players in with a chance of catching current leader BluNick (Italy) who has 8-3 with a match to play. Master B is however decided, with Backwoods (Finland) and BushSucks (Germany) through to the play-offs yet again, so congratulations to these perennial strong men. At the other end, jackdaddy and blotsalot (both USA) are relegated with magic_one, DeaDice (both USA) and Gammonrider (Germany) battling to avoid joining them in Gold next session. This is a very good time to register for the league and enjoy regular tough matches in a well run league, for which we have to thank Franck del Rio, better known as Tomawaky, who is now in his eleventh year as director. Take a bow Franck!
Tomorrow we'll look at another blunder and how it might have been avoided. Until then, enjoy the game!
All of us ask ourselves the same question, "How can I play better?" Then we log on and play some matches and then we analyse them and look at our mistakes. Then we play some more matches and so on. At least this way we don't get any worse and over a long period it will help us improve, but noticeably, not by much. After the first year or two, it's rare to make much progress. It looks as if this process doesn't work and I think that is because it isn't sufficiently focussed on the repeating mistakes. So, I am trying a new method on my own game and perhaps this would work for you too.
The method works like this. Go through your match, with Gnu or Snowie or ideally XG2, note the big mistakes and focus on those where you haven't understood what you should be doing and why. Ignore those where where you've had a good idea of what you should be doing, seen all the candidates and made an honest but understandable mistake. With the rest, try to put them into a category by type.A quick list might look like this.
Failed to be guided by the pipcount.
Played a doublet too quickly.
Rejected hitting loose on a low point (always a problem for me!).
Missed a cube by failing to use PRAT.
Failed to stay pure in a crunch situation.
Took a gammonish cube without being certain that it was right.
These are just some of my weak points, your list might look completely different.
Once you have your list and it begins to fill up with repeat offences, you need to figure out why you are making these mistakes. Not concentrating enough? Playing when you are tired (or hungry, or thirsty, or intoxicated, or bored, or depressed)? Not really understanding the position? These are just some suggestions, your own list might look completely different.
To recap, you need to know what sort of mistakes you are making regularly, then identify why you made them and then learn how to avoid them.
Here's an example. A student of mine faced this roll. What's your choice?
It's 0-0 to 5. Make your play before you read on.
He played 13/8, 6/3. It looks fairly natural, but it's an auto pilot play, of the type that we all make when we are feeling lazy. It's a particularly bad time to blunder because this game is arriving at the Crunch Point, where the game will be decided one way or the other. Either Black will get home safely or he'll leave a shot and be hit.
The best play by a lot is 13/10, 6/1. A highly skilled player with a very advanced positional sense might get this right by thinking, "It can't be right to pile a sixth checker on the 3pt. I may very well want to hit something in the bear in, so I'd better slot the ace and then one of the spares on the 3pt will at least have something useful to do." A more pragmatic player or even the same player might think, "I'll make the safest play for next turn, it's usually a good guide." Then he'll read the numbers. This just means looking at all his next rolls after each of the candidate plays (there are only two) and seeing which of them leaves a shot. Did you do this before choosing your play. If you didn't, go to the back of the class! Do it now and you will quickly see that 13/8, 6/3 has 14 blotting numbers next generating a total of 234 hits, while 13/10, 6/1 has only 9 which generate 126 shots. One of these, 5-5, you'll leave voluntary double shots although you could play safe but with much greater extended jeopardy.
So here is a bearing-in error, made by failing to read the numbers. How often do you read the numbers? If the answer is never, then it's time to learn and the only way to do that is to practise, by looking through your matches for bear-in positions and counting them up. Do it with pencil and paper at first, then graduate to doing it in your head. Do it until it is easy and then do it in matches until it becomes second nature to always do it. It's going to swing a lot of losses into the win column. Note that in most cases (and particularly here) you'll need to multiply the shot numbers with the number of shots that they leave to get the definitive answer.
News. Fibsleague season 56 ends on the 27th of April. Master A is still very open with a lot of matches undecided and a lot of players in with a chance of catching current leader BluNick (Italy) who has 8-3 with a match to play. Master B is however decided, with Backwoods (Finland) and BushSucks (Germany) through to the play-offs yet again, so congratulations to these perennial strong men. At the other end, jackdaddy and blotsalot (both USA) are relegated with magic_one, DeaDice (both USA) and Gammonrider (Germany) battling to avoid joining them in Gold next session. This is a very good time to register for the league and enjoy regular tough matches in a well run league, for which we have to thank Franck del Rio, better known as Tomawaky, who is now in his eleventh year as director. Take a bow Franck!
Tomorrow we'll look at another blunder and how it might have been avoided. Until then, enjoy the game!
Tuesday, 3 April 2012
News, Blunders and Answers
So, the answers to my April Fool's Day Quiz. Five positions and no, it's not a joke, I really did blunder all of these in a single match. Nothing like public confession for keeping you on the straight and narrow in the future. Here they are again.
Position One
Score 0-0 to 7
If you were too lazy to do the pipcount, you'll struggle with this one. Black trails by a pip (82-81) after the roll, so mandatory to continue to block sixes. I had no excuse as pipcount was on when I played it, so this has to go down in the "Sloppy and Careless work, see me" column. The best play is the simple 7/5, 4/1 but the imaginative 7/5, 6/3 isn't far behind. The 3pt could yet be very useful and White won't be hitting unless she can roll 1-1 or 1-6. Yes, hitting with 1-5 is wrong.
Position Two
Score Black leads 4-1 to 7
By far the toughest position in this quiz, the rollout is quite clear and Black must play 18/9! 9/4, 7/3, which is what I played is too feeble. If White is going to escape with a five or six, Black must simultaneously slow himself down by allowing the hit. Plays like 18/13, 18/14 also do this, but five blots is a bit too loose, boosting White's wins and gammons by significant amounts. Positions like this lie well beyond my powers of analysis, but it is a very instructive position to practise. Play from here, try some different plays, analyse, get a feel for it. At least you don't have to worry about the cube play. Hard to see Black ever turning it here.
Position Three
Later the same game.
We've had a careless blunder, inexcusable and a very tough play blunder so far. Here I made a "Too clever by half" blunder, opting for bar/21, 3/1*. My thinking was that if I could knock White off the ace point and make it later, it would make the bearin and bearoff much safer. This is true as far as it goes, but I can always take that risk later if I have to. Now is not the time, as two men back could be very dangerous. Big blunder, good old bar/19 is correct.
Position Four
Black leads 6-1 crawford.
I played 10/5, 8/5, another blunder like the last, imaginative but too much risk for the gain. It may have been sparked by the "I've seen something like this recently where it was right" syndrome, to which I am particularly prone. I don't mind that too much actually, as it often pays off, but be wary of relying on it. Use it as an option if you really can't choose something better.
13/10, 13/8 is quite a decent play but a very small error. Black needs to hit something and you can choose between hitting one or two! 10/7*/2* and 13/8, 10/7* are neck and neck in the rollout. I am always very reluctant to start speculative attacks in cubeless games where I can't win a gammon, but here it works just a little better than the quiet play.
Position Five
Black leads 6-3 to 7, post crawford.
Lastly, one from the "Too ambitious" school of blunder. I played 12/11, 7/4*, but the quiet 12/8 is better in the circumstances. My play wins the most games for me, but White's deadly gammons jump from about 20 to 29, so clearly I shouldn't be risking that. Sometimes backgammon is just about cutting your losses and living to fight another day.
Thanks to Julia, Clem and boop for having a crack at these. You can see their ideas in the comments to the previous post. Join them next time, the more the merrier.
Lots of action already in the Spring Open, particularly for sita (Matthias Krings) and yes (Thomas Brizendine) who are off to a flyer with wins that take them into the third round. You can follow this tournament direct on http://www.escoffery.com/main.txt .
We'll have some more dorbelblundas to look at tomorrow or thereabouts, so I look forward to seeing you again. Bring peanuts. Until then, enjoy the game!
Sunday, 1 April 2012
News and Blunders.
As of today, those who base their plays on XG2 rollouts will be looking with interest at new results showing that making the 5pt may not be the best opening 3-1 after all. At GammonGo the wide-open 6/5. 6/3 is almost certainly better, many more gammons and a chance to go into a deep backgame if hit. I look forward to trying it out, so let me know how you get on with it.
The Fibs Spring Open is under way with an entry of 105 players, generating a prize pool of $4, 725.
There are 13 previous winners in the field so it should be a tough tournament to win. This tournament offers a rare Fibs chance to see Kit Woolsey in action, still one of the strongest players in the world.
In the real world, Easter is always the time for the Nordic Open and as usual a very strong field will be on its way to Denmark. It's not too late to book in, http://www.nordicopen.dk/ has all the details.
A lot of the players from the Nordic will then head off to Velden in Austria for backgammon by the lake on the following weekend. This too will be well run and offer a good deal to players of all standards, so go to http://www.wbf.net/ for details. Even if you don't think of yourself as a strong player, you'll find a division suitable for you at either of these venues and you'll make new friends and have a great time for sure.
Robert Fontaine recently made the point that it is very difficult to improve one's standard of play, even with a lot of study and work. I know how he feels! There's no doubt though that concentrating on the blunders, the really big mistakes is the way to go. A blunder costs you more than a tenth of a point, so keeping these off your scorecard will make you an overnight expert. Here are some of mine, without comment, so take a look at these and let's see if you would make the same mistakes. I'm playing a 7 pointer with The_Blade, a very strong Israeli player.
Position
0-0 to 7, White has the cube, Black to play 3-2.
Position Two
Black leads 4-1 and has the cube and has to play 5-4.
Position Three
Same game, Black leads 4-1 to 7, holds the cube, is on the bar and has a 4-2 to play.
Position Four
Now it's Crawford, Black leads 6-1 and has to play a 5-3.
Position Five
Lastly, post-crawford, Black lead 6-3, has the cube and has a 3-1 to play.
How hard are these? I got them all badly wrong, so let's see if you can do better. Until then, enjoy the game!
The Fibs Spring Open is under way with an entry of 105 players, generating a prize pool of $4, 725.
There are 13 previous winners in the field so it should be a tough tournament to win. This tournament offers a rare Fibs chance to see Kit Woolsey in action, still one of the strongest players in the world.
In the real world, Easter is always the time for the Nordic Open and as usual a very strong field will be on its way to Denmark. It's not too late to book in, http://www.nordicopen.dk/ has all the details.
A lot of the players from the Nordic will then head off to Velden in Austria for backgammon by the lake on the following weekend. This too will be well run and offer a good deal to players of all standards, so go to http://www.wbf.net/ for details. Even if you don't think of yourself as a strong player, you'll find a division suitable for you at either of these venues and you'll make new friends and have a great time for sure.
Robert Fontaine recently made the point that it is very difficult to improve one's standard of play, even with a lot of study and work. I know how he feels! There's no doubt though that concentrating on the blunders, the really big mistakes is the way to go. A blunder costs you more than a tenth of a point, so keeping these off your scorecard will make you an overnight expert. Here are some of mine, without comment, so take a look at these and let's see if you would make the same mistakes. I'm playing a 7 pointer with The_Blade, a very strong Israeli player.
Position
0-0 to 7, White has the cube, Black to play 3-2.
Position Two
Black leads 4-1 and has the cube and has to play 5-4.
Position Three
Same game, Black leads 4-1 to 7, holds the cube, is on the bar and has a 4-2 to play.
Position Four
Now it's Crawford, Black leads 6-1 and has to play a 5-3.
Position Five
Lastly, post-crawford, Black lead 6-3, has the cube and has a 3-1 to play.
How hard are these? I got them all badly wrong, so let's see if you can do better. Until then, enjoy the game!
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