The Cube That Was Heard Around The World

A few of us silver foxes are old enough to recall, the “shot that was heard around the world” –  Gene Sarazen’s epic double eagle to the 15^th at Augusta in 1935.  Well, now we have the backgammon equivalent:  “the cube that was heard around the world.”

I have gotten wonderful feedback on it from many of the greatest players in history, and it goes right to the very heart about what makes backgammon, and in particular matchplay, such an absorbing, fascinating and challenging paradox.

Initially, I was chided in some quarters by those saying the cube is not as complex as I was making out, but subsequent investigations have blown that theory out the water – in fact the play by young star Ollie Squire has dramatically risen in my estimations, not declined.

The cube is “a play, within a play, within a play”, Shakespeare would have purred:

Not only is it an absolutely supreme command of METs [Match Equity Tables], but it is the ability, nerve and ‘moxie’ to translate that intel into action.  Yes, a fair few of the community are saying:  “gaining 13, losing 11, rewhip.”  But that’s far too simplistic, and the quiz factor has put people on red alert, googling an MET, taking their time, finding the right answer, and then saying, “yeah, it’s a cube.”  But try doing that in a high pressure tournament situation, with the clock ticking, against someone playing off 1, when the judgment is as Times columnist Chris Bray notes, “too close to call.”

Some are seeing the 2% edge as clear, but the different METs all vary by up to 2%!  So you could easily take one of the three figures you need from each table.  For instance, I could argue for days that 3% is a perfectly valid figure for 1a13a.  But I could argue just as long for it being 1%.  KazXG has plunked for 2.

I have played with MET numbers just a tad, by taking them from different tables, and just by doing this, I arrived at 29.0% MWC to cube, and 28.9 not to.  The KazXG goes into detail of 1,000^th of a percent.  Ollie says he’s learned all the outcomes for an 11 point match, but this was 13.  How many in the world, truly know off the top of their head that 9a5a is precisely 72.5?  Not many.  Maybe half a dozen.  And there are two other METs to know here spot-on as well.

Nick’s authentic commentary

Here’s Nick Blasier’s live stream comms on the play, which remember is by the author of the excellent new book, Adjusting to Match Play, on just this sort of thing.  His views are uncorrupted by the quiz factor, and he doesn’t have an MET to hand.

As Seb Wilkinson is pondering his 4 cube the go before  [SW has two on the deuce and one on the ace]:

“And is that ever enough for a cube here?  He wins 5/36 immediately and then he has to calculate how often his opponent misses, which is usually.  So when he isn’t winning close to one-sixths of the time he is winning most of the other 5/6s of that, and his opponent can never double…”

So!  Right there, the 8-cube scenario has completely bypassed Nick, although when Seb cubes and misses, Nick becomes emotionally erect:

“32 is gonna’ miss… and I don’t think he has any sort of recube ideas here… [XG’s cube action then pings up] WOW!!  He’s supposed to recube this!  Ohhh, the match equity calculations on this are brutal.  I wonder if… if Oliver knows to pause and think about this and do some math over the board, that is wild.  I wouldn’t even be thinking of it, because there’s no overage on the 8.  So what XG is telling us is that the 8 points we risk losing to go to Crawford is apparently so much less than the possibility of gaining and being a match favourite, versus being even in the match…

“So those extra points are worth more for him than the 1a13a Crawford lead, which makes sense…  but this is still surprising.  He’s going to be able to pretty simply understand what his winning chances are… usually the way we’d calculate this is risk-over-risk-plus-gain of the actual match equities in each situation.  And this would be pretty deep Match Equity Table memorization or using of Neil’s numbers to get to the perfect numbers to figure this out for Oliver. 

“Ummm, I don’t have access to all that information to do the calculation over the board, and I would be probably going off gut feel here, right?  And if I had this idea; if I’d seen this before, that the difference between our upside is much bigger than the difference between our downside, then I might think about cubing it.  But this is a really impressive one.  I need to flag this one and do a video on it I think, I like this quite a bit.  And yeah, I’m so impressed with Oliver to be pausing to think about this one…

“I will be pretty surprised if he finds this… or if any player finds this.  I’m not sure who would know this… maybe someone like Neil Kazaross, or Mochy?  But this is a surprise to me.  But I get the impression that Oliver is pausing because he’s seen something like this before, and has the idea that the recube could be that effective.  That’s er, wow, that’s impressive stuff…”

Ollie cubes.

“And he’s gonna’ send it back!!  Wow, really great find.  That’s amazing.  Let’s see if he can get rewarded for it.  The 56 takes two off!  Really impressive stuff, how exciting is that?!”

Ollie’s clock went from:  10:30 to 7:53 for the play, for a 2:37 conflab.  He started the match with 16:30, but obviously time well spent, although just 7:53 left and more than half the match to go showed that he couldn’t really afford to think much more.

 

The confusion of 0-8; and ‘Opponent is everything’

Some people are cubing any opponent here, and I think this the heart of the matter.  Ollie was off 2 here and Seb Wilkinson off 1.  But, if you’re off 2 and your opponent is off 10, how can you give them this gilt-edged 8-point passport to the match?  That’s where the MET of 14% of 0-8 to 13 comes in.  It’s loads higher than 14% if your opponent is weaker.

What is the MWC of a 2pr vs 10 going into a 13 point match?  62%?  Yes, at least.  Probably a fair bit higher.  PR matters, this much we know, and why so many of us train and study so hard.

Let’s take my last 50 matches on Galaxy when my PR was 4+ superior to my opponent:

9-3       7-0       0-11     9-6       9-4       0-11     9-0       11-9     9-0       9-0       6-7       11-9

11-0     11-4     0-3       7-2       6-7       0-5       2-5       7-5       7-0       7-2       0-9       6-11

7-4       7-0       7-1       5-11     11-6     5-4       9-0       7-4       5-0       11-5     0-13     0-11

8-9       0-11     13-0     0-7       7-4       11-0     9-4       1-13     7-11     11-5     13-0     7-13

13-7     9-4

So as you can see, there is plenty of mayhem and loss there, but the win rate is 32/50 of 64%.

So my question is are we cubing this play against someone with a PR differential of +4; and what is the chances of winning when 0-8?  8-4 is going to be a about 80% win chances vs the weaker player – up 16% then on 4-4.  What about the loss?

We know that we’re at 64% at 0-0, and we know we’re 0% at 0-13.  That’s 4.92% per point, which means we can comfortably arrive at the 0-8 scoreline against a player we’re around 4 pr better than:  4.92×5:  24.6%.  This is more than a fighting chance, and a whole lot more palatable than 4.92% which is 0-12.

What we deduce is against an even opponent, and so many of the community have pointed out, is that we gain 23, but only lose 12 by cubing.

But against a weaker opponent of around a 4 differential, we gain 16, but lose 20.  It’s a hugely different scenario.

Doing it the more complicated way, with MWC assuming 64% wins at level score we find that cubing this play to a weaker player gives:

 

Cube win:                    38.9x.8            =          31.12

Cube loss:                   61.1x.0492      =          3

Cube MWC                  31.12+3           =          34.1

No cube win:               38.9x.64          =          24.9

No cube loss:              61.1x.24          =          14.7

No Cube MWC            24.9+14.7        =          39.6

 

And there you have it!  Cubing this play vs a weaker opponent of +4, gives 34.1% MWC, but NOT cubing brings 39.6%, for a massive 5.5% “Whopper with cheese” [with apologies to Paul Magriel.]

 

38 Beasts of the Backgammon Jungle have their say

Right!  Enough from me, let’s see what the giants of the community are saying about this marvellous piece of BG wizardry from the young Squire.

We’ll start with the non-cubers, in alphabetical order:

 

Not Cubing [15]

Roohollah Amiri Andy

 I won’t recube to 8, and if my opponent gives me this cube I will take it easily.

Josephin Bichler

So I would probably not have found it, but since you ask, I suspect it is a double.

Super impressive.  The logic is easy, but applying it correctly is definitely not, and I suppose he didn’t know the exact numbers but knew enough to get close.  You always have to be willing to look like a fool.  Nothing really smart ever happens by trying to avoid it!

Karsten Bredahl

No redouble.  Numbers are from memory from Neil’s Numbers so there is another source for errors.

And XG says I am wrong.

Redoubling when the other guy is the fish is plain and simple a blunder.  The 80 you pay for missing the cube will be a great investment over several more games.

Tobias Hellwag

Of course in a match I first look at the score. If this is a redouble then I don’t understand the score. Over the board I wouldn’t be tempted to double.

Pia Jeppesen

I would not double.🙂

Sander Lylloff

Well 22 numbers miss.  If I lose, my opponent goes to Crawford, which is bad. So I can’t see any way I would ever double.

[And when apprised:]

Funny that doubling is better.  To tell you the truth, even if I knew the answer, I would still not double it.🤪

Carter Mattig

Jeez. Yeah, I wouldn’t have found the double. Was it one?

I think I’m just grateful for a shot at winning that. I may find that in a dream.

Michy

Score 8-0 is not the end of the world. I would not double.

Wow, I’m surprised that this is a double!!!

Mochy

Over the board I would do the math then adjust based on my opponent’s skill level.

If I have to decide by my gut feeling I wouldn’t double.  You are less than 40 %

But the fact that everybody got excited means it was a small double ?  Now I use Quiz Factor 🙂

Haha, so I was wrong, but at least I knew it was close to cube.  Nice position.

Jason Pack

I redouble if the checker on the 5 is on the 4, but not this.

Frank Talbot

I roll pretty quickly here as I am an underdog to get off in one roll, my opponent needs all the points, and I feel my opponent can make a lot of cube errors going forward, due to the fact the cube action is very complicated nursing a big lead.

Now, let’s crunch the numbers.

After some dozen lines of intricate maths, Frank revised his verdict:  “Note to self – Do the math!!!”

Chris Trencher

I think it’s [the cube] bad.  I view 13a5a as a long but doable road.  The most difficult point for the leader are always the last few… why make it easy?

James Vogl

OTB I probably wouldn’t. If I knew match score equities it wouldn’t be hard to calculate doesn’t seem very complex to me.  Just a one roll position, 14 good 22 bad. So it’s simple maths if know equities. I don’t as don’t play tournaments.  I mean instinctively I like to ship a high cube when stuck in a match but with just 14 numbers I probably wouldn’t have found it.

Akiko Yazawa

My first impression is no redouble. If black has 2 and 5, maybe redouble. But I need more time for think about this score…

 

Too close to call, uncommitted, or only Cubing certain opponents [17]

Simon Barget

I don’t think Oliver knows match equities at these scores off by heart.

I think I would have either not stopped at all or if I had done would have seen it was a re cube.  But its hard to say with the quiz factor element.

Art Benjamin

To double I need 11.5/34.5 = 1/3 = 12/36. Since Black wins 14/36 then Black should redouble (and of course White should take).

I tend to do what the numbers tell me to do. But I may have not done so against a much less skillful opponent.

Chris Bray

My apologies, I thought the match was to 11.  I have redone the numbers and in a match to 13 it too close to call and then, yes, the opponent does matter.

Ray Fogerlund

Okay so it is close… Just the kinda thing you don’t want OTB because it takes a long time to figure out. When I was playing MCG, he is number 1 on Galaxy, so I had a license to be bold.

Much depends on the player factor. If playing someone better… Do you want to win this game only to be tied? Not me! One wants to strike a blow psychologically and tactically. If we are weaker then we must activate the bozo factor in our opponent… “I don’t wanna lose to this Bozo”. So you might get a pass from an expert if it is close, at any rate he can’t make a mistake if you don’t put the question to him. So, if I calculate OTB that it is at least close to a redouble, then send it and let him think about it. Meanwhile I will be thinking where I want to have lunch if it doesn’t work out, lol. Must have a contingency plan, you know?

So I would redouble an equal opponent and they have to be really weak to wait.

I just guessed at 0-8/13 equity don’t know why I was so far off on the other side.  [Some of Ray’s METs were quite a bit out.] Its a risky business.  I guess because it is a longer match I gave too much equity per point, so I learned a little for future reference too.  But it goes to show that one can guesstimate and still end up in the right vicinity… It’s not an exact science OTB.

Jorgen Granstedt

I’m used to making these calculations so would have got it right I think.  If I needed more than 2.5 mins I would do so.  I had a difficult match cube decision in a league game last week and took 7 min to decide.  So much equity can be won/lost so well worth spending time on these decisions.

I would probably double if opponent played 4 or better.  You have some players who care too much about their own PR.

Geoff Hall

I did watch this match on catchup and thought that Oliver made an excellent play. When I stopped and worked out the numbers I was pleased that I came out with 29% as the redouble point, although it took me about 4/5 mins and that was sitting at home rather than the pressure of playing over the board.

I honestly don’t know if I would have found the redouble under the circumstances. It’s possible but I still commend Oliver for finding it.

To be honest I’m not sure how long it would have taken me to calculate over the board as I use Janowski’s formula rather than Neil’s numbers.

Then there’s the added part of how sure I would be that I didn’t make an error – also bear in mind that I have a degree in mathematics and would have found this really challenging. I was very impressed by Oliver’s play even though I ‘may’ have got there myself.

It’s actually a position that, unless you stop and realise how low your doubling window actually is, you can easily just roll the dice.

Raj Jansari

Amazing.

Neil Kazaross

While clear for one GM to cube another, it is also clear to not cube vs someone who normally plays a few PR worse than you do.

Roberto Litzenberger

The biggest fallacy in the question is “try not to spend more than 2.5 minutes”… It is a key 8 cube. You are supposed to spend AT LEAST 4 minutes on this. These positions are easy to conquer if you spend the time. The person has 8 minutes on their clock. So that means there is all the time in the world. The biggest mistake one can make is to think that they need to rush. End game is fun and one is meant to spend time BECAUSE one knows they can NAIL it if they do spend time. So it is time well spent. Clear Double… more than obvious take.

Any player at my level or above.  Any even slight screwed MET would show this as a no double for a stronger player.. even a 2 PR difference prob…

I don’t really go by PR difference but by levels.  Slight above.. slightly below etc

There is proof that METS are off for unequal players… this is measured also by players that want to hedge but not willing to hedge straight up… that is a practical application of unequal METS.  Lowering volatility is key against weaker players

Juergen Orlowski

I guess you need about 1/3 in order to give 22 bad numbers? So 14 good numbers which is more than 1/3.  so I would ship it over.🙂 Nice challenge.  I guess you are playing most of the time against weaker players.  In this case I would probably keep the 4-cube.

Kimon Papachristopoulos

Easy to miss because the 8 cube is a rare animal. It is known that high cubes require underdog doubles if only they can lose the market. Not sure if I would double over the board. Hard to calculate correctly under pressure.

Lawrence Powell

I am pretty quick on these things and get a risk of something like 12-13% and gain of 23%.  Thus 14 wins so around 40% clear double even allowing for some inaccuracy.  If really no time I might well have chickened out.

Against Seb for sure I cube, and against much weaker for sure not.

Marc Olsen

We can probably swing an underdog cube here.  But we are rather big underdogs…

You probably wouldn’t against a bad player.

Chris Rogers

Very nice spot by Oliver

Joseph Russell

Great problem, btw, and I doubt many would find the recube.

I think you recube anyone that you are within 3 or so PR of, as the error to not recube is pretty large. I am not sure how big the PR difference must be, 4, 5, 6, 7 to make it wrong.

Wil Snellings

Quick, crude math…90 seconds… came up with 4% better MWC by recubing

When I corrected him:

That’s fairly off… I play no matches between October and April every year, since working… need to recheck ME tables, which I do come late April.😉

My PR is basically 3.0, tad less when in rhythm, but who cares… knowing the answer, I wouldn’t ship against anyone other than a 3.5 or lower opponent.

I also feel that on average I pick up a little extra against many opponents the longer a match drags on… psychologically, emotionally… especially in important matches.

Zdenek Zizka

Not really MET needed, just knowing the idea of the score and understanding why I feel everything depends on the opponent.  Anywhere there is a 4/8 cube in a match, it sure matters who the opponent is.😀

 

Cubing Anyone [6]

Aref Alipour

These redoubles aren’t too difficult to find if the player understands the equities. Doubling window always opens when underdog trailing in matches. It even opens quicker when a small % of gammons come into equation. I’d have shipped this against anyone. There’s not much room for adjustment. If I were Seb, I wouldn’t have shipped the 4 cube knowing Oliver struggles most of the time with his time management. He should have dragged his feet and extend the match time imo.

8-0 down against anyone is very difficult to recover. 🙂

Radu Ciortan

Think it’s redouble take because of score.  On board its difficult but probably I will do.

I have different strategy depends by tournament or by opponent.  Here probably does not matter.

Petko Kostadinov

Redouble / Take. I would not spend more than 2 seconds on this decision as Black or White. Thank you for asking, Will!

I did not calculate MWC at this score. I felt that the cube action was clear. I would still redouble against a weaker opponent.

I do not adjust my cube action against weaker players anymore. I just play my game, and whatever happens happens.

Bill Robertie

If you play a lot of long matches, you’ve seen this play (doubling as an underdog when you’re trailing and there’s a big cube involved) many many times. You should run through the math in your head to make sure it’s correct. But if your clock is running and you don’t have time to check the calculation, you just double. Since you’ll be down 8-0 anyway if you lose, you’re not risking much.

I’m more eager to redouble if the opposition is weak because there’s an added bonus — they may pass.

Jonah Seewald

I know this is a cube as underdog from reference.  I cube anyone here.

The crazy thing if you move the checker on the 5 to the 6 its barely a mistake to double. And same if you have them on the 4 and 3 point

The key here to find these is to realize the possibility of a hyper-aggro cube happens when the score deficit is significant and the cube is bloated.

For sure you have to be able to realize the conditions are there, otherwise you roll on thinking of it at normal scores that it can’t be considered a recube.

Phil Simborg

I think you have to cube this against anyone. For one thing, a weaker player might make a cube error if you give the cube… he cannot if you don’t cube.

I agree this is fascinating. One reason I am playing my opponent less is because I teach people 2-3 hours a day not to do that… first you must focus on learning what is right, and then when you are really sure of what is right, you can start changing your game. I’m not quite there yet myself!

 

In summary

What can we make of all that?!  It’s a breath-takingly varied contribution from many greats of the game, and it’s all here:  skill, psychology, safe vs bold, top maths, data retention and decades of hard graft study has gone into those replies.   The six “cubing any oppos” are all top players or legendary figures – far be it from me to say they’re wrong.  But it is my dream to get flung a snowman at 38% from a BG great.  A more valuable paperweight I never did see… and even Coco the Clown on acid would be tripping the light fantastique to pass this.

Anyway, for sure I’ve learned a lot during this investigation, and I think it’ll be a very long while before I see a more brilliant intuitive, dynamic and incisive piece of backgammon.  Congratulations indeed to [as his cyber handle goes]: “Squire O’Shakes”.