A Maximum Gain in Control With a Minimum of Danger – Paul Magriel

(Another golden oldie from the New York Times of December 7, 1978.)

by Paul Magriel

In the last 5 years, the enormous growth in the popularity of backgammon has resulted in many significant theoretical advances.  Even though the game is thousands of years old, many fundamental concepts have only recently been discovered.  A new generation of talented young players is spearheading this advance.

Foremost among this new breed is 21-year-old Roger Low.  His play combines exceptional analytical ability with a tough competitive spirit.  He alone, among all the world’s best players, seems to have the uncanny capacity to effortlessly remember whole series of games roll by roll and move by move.  This same capacity has helped make him the uncontested top player in the world at blindfold backgammon.

Roger Low and Paul Magriel play blindfoldedin a demonstration match withDenise Hemingway and George Plimpton.  Low is on the left, Magriel at right.

Roger Low and Paul Magriel play blindfolded in a demonstration match with Denise Hemingway and George Plimpton. Low is on the left, Magriel at right.

After attending Cornell University, where he learned to play, he is now on Wall Street training to be  a broker, so that he can divide his time between the backgammon board and the Big Board.

Low1

In the position above, Low showed his ability to visualize all possible plays.  With the roll of 1-1, Black seemingly has little choice because he cannot move the men on the 20-point or 13-point.  The routine play is to hit 24/23* with the first 1, and then break the 16-point and move 16/13, putting another man safely on the midpoint (13-point).

Low discovered a better play, which many players would have overlooked – 24/23*, 16/14, 16/15.  Again, Black hits with his first 1 and then breaks his 16-point, but now he intentionally leaves 2 blots in Red’s outfield.

Low2

By leaving spare men on the 14 and 15-points, Black is able to exert more control over his own outfield.  Specifically, Black gains an extra builder to make his 8-point, and 2 extra builders for his 9-point.  Black and Red are engaged in a 2-way holding game – in which both players have anchors in each other’s home boards.  In such positions, outfield control is often a vital winning factor.

The additional danger incurred by leaving 2 blots is minimal.  Surprisingly, the possibility of being hit is only slightly increased (8 chances out of a possible 36 instead of 7) by this play.  (Note that the duplication principle is at work here.  Red needs 2s and 3s to re-enter, and 2s and 3s to hit.)  Even if Red does re-enter and hit, Black has little to fear because he has security of owning the 20-point and the prospect of return shots at Red’s blot on the 21-point.

(This play hold up today as you can see from the eXtreme Gammon analysis below.
The other candidate play mentioned of 24/23* ,16/13 is second best.)Low3

Bold Building Blocks Escape To Produce a Crucial Victory – Paul Magriel

(This article appeared on May 10, 1979.
Back when Peaches and Herb topped the charts with Reunited, Woody Allen rocked the box office with Manhattan,
and backgammon had a weekly column in the the New York Times!)

by Paul Magriel

The American Stock Exchange Annual Tournament under the direction of Susan Bender was completed recently after several months of elimination rounds.  First place went to 25-year-old Michael Rosenberg, a talented young Scotsman from Glasgow, who took up backgammon seriously just a year ago when he moved to New York City.  A natural games player, he had previously gained international recognition as a bridge expert and member of the British Bridge Team.  The runner-up was Charles Silverman, semi-finalists were Robin Katz and Mel Weiss.

The diagrammed position illustrates a critical situation that arose in the 21-point finals between Rosenberg (Black) and Silverman (Red).  Many of their co-workers on the Amex watched as the lead changed hands several times in this hard fought contest.  Finally, after more than 4 hours and 20 games, the score was tied 19-19.  In the next game, Black built an early lead and doubled.  Red accepted and later the position shown in the diagram was reached.  The outcome of the match now depended on the next few rolls.

Rosenberg

Black has a definite advantage, despite Red’s lead in the race.  Red’s home board has deteriorated and, of greater importance, Red has a man stuck in Black’s home board.  This man sits on the 2-point behind Black’s broken 5-point prime but is able to run out with a 5.  To win the game, Black must contain this last man.

With the roll of 4-1, Black’s immediate concern is to deploy his men in the outfield in order to get the best possible coverage to hit Red if he leaps out.  Black, however, must plan ahead and consider how to permanently prevent Red from escaping – as long as Red is sitting unmolested on the 2-point, he will constantly threated to run out.  One method is to prepare to attack Red and close him out.  To implement this plan, Black can bring a builder into his home board, 11/6 to hit Red later.  Another game plan to prevent Red from escaping permanently is to form a full 6-point prime.  Accordingly, Black might consider playing 14/10, 11/10 in order to keep all his men in the outfield as builders for the bar point (7 point).

After much thought, Rosenberg rejected both these plays.  Instead, he boldly and correctly played 11/7, 8/7 making the bar point, but leaving a blot on the 8-point exposed to a direct 6-shot by Red.  Rather than wait and give Red chances to escape, Black goes directly for the prime, and so forces the issue at once.  If Red fails to roll a 6 immediately, Black will then be a strong favorite (29 combinations out of 36) to cover the 8-point thus ending Red’s chances.  Further, even if Red rolls the 6 and hits Black, Black may still re-enter and hit Red back.  In the actual game, Rosenberg’s play succeeded.  Silverman failed to throw the needed 6.  Rosenberg covered next roll and easily went on to win.

Bob Barker and Drew Carey Agree…

by Gerry Tansey

…you have all overbid.

The Springfield Series starts up on Saturday, October 4, and the Illinois State Championships, an ABT event, happen the following weekend in Peoria.  These are both great events, and you should strongly consider going if you enjoy backgammon tournaments.  I’m writing this article to prepare myself for something both of these events feature: the Calcutta auction (or just Calcutta for short).

For those of you who are unfamiliar, in a Calcutta, the players in the field are auctioned off before the tournament starts, either individually or in lots of 2 or more players.  At the end of the tournament, the proceeds of the auction are paid out to people who bid on the winning players.  Generally, the stronger players cost more than weaker players, but the stronger players also have the best chances of winning.  Typically, players can buy a small percentage of themselves back from the person who bid on them, getting a small percentage of the auction winnings should they do well.

In Peoria last year, Calcutta bidders could either purchase a Giant of backgammon individually, or a two-player team consisting of non-Giants.  The first and highest bidder opted for a two-player team in which I was one of the players.  From my point of view, this was a disaster, because it meant that I would have to pay more money than most people would to buy myself back.  It would be nice if I could lower my Calcutta price this year.  With that in mind, let’s look at this decision I had from a recent online match, which I will present here as a money game problem.

Tansey1

Well, this is a fantastic 44 from the roof.  I entered, made the 4-point on Black’s head, and I didn’t waste too much time unstacking the midpoint with the last 4, playing 13/9.  The trouble with this last 4 is that there is another 4 that is a little better, namely 16/12.  Although this play leaves 3 blots, it is not terribly convenient for Black to hit them after entering from the bar.  Black will need to leave blots himself to hit them in most cases.  My one-blot play gives Black an excellent 6 from the bar to hit and escape a back checker.  Further, 16/12 gives White more builders to make an outfield point, and it begins the process of disengagement of the back checkers while Black is on the bar, a process that needs to begin sooner rather than later.  Yes, 16/12 is probably a bit better than 13/9, although I would have to extend my rollout of the position a bit to be more confident of this fact.

Potential Calcutta bidders should study the following rollout closely.  Notice the massive conceptual misunderstanding I exhibited, not just with my play, but also with my discussion of the position to this point.

1.Rollout1Bar/21 13/9(3)	eq: +0.404 	Player: Opponent:	60.38% (G:16.26% B:0.73%) 39.62% (G:11.53% B:0.44%)	Conf.: ± 0.018 (+0.386...+0.421) - [100.0%] Duration: 20 minutes 06 seconds 2.	Rollout1	Bar/21 13/9(2) 6/2	eq: +0.244 (-0.160) 	Player: Opponent:	56.73% (G:15.83% B:0.74%) 43.27% (G:14.89% B:0.65%)	Conf.: ± 0.020 (+0.224...+0.264) - [0.0%] Duration: 19 minutes 48 seconds 3.	Rollout1	Bar/21 16/12 8/4*(2) 	eq: +0.228 (-0.176) 	Player: Opponent:	55.20% (G:18.28% B:1.11%) 44.80% (G:13.61% B:0.60%)	Conf.: ± 0.019 (+0.209...+0.246) - [0.0%] Duration: 18 minutes 40 seconds 4.	Rollout1	Bar/21 13/9 8/4*(2) 	eq: +0.199 (-0.205) 	Player: Opponent:	54.26% (G:18.95% B:1.18%) 45.74% (G:14.64% B:0.59%)	Conf.: ± 0.018 (+0.181...+0.217) - [0.0%] Duration: 18 minutes 54 seconds   1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

1. Rollout1 Bar/21 13/9(3) eq: +0.404
Player:
Opponent: 60.38% (G:16.26% B:0.73%)
39.62% (G:11.53% B:0.44%) Conf.: ± 0.018 (+0.386…+0.421) – [100.0%]
Duration: 20 minutes 06 seconds
2. Rollout1 Bar/21 13/9(2) 6/2 eq: +0.244 (-0.160)
Player:
Opponent: 56.73% (G:15.83% B:0.74%)
43.27% (G:14.89% B:0.65%) Conf.: ± 0.020 (+0.224…+0.264) – [0.0%]
Duration: 19 minutes 48 seconds
3. Rollout1 Bar/21 16/12 8/4*(2) eq: +0.228 (-0.176)
Player:
Opponent: 55.20% (G:18.28% B:1.11%)
44.80% (G:13.61% B:0.60%) Conf.: ± 0.019 (+0.209…+0.246) – [0.0%]
Duration: 18 minutes 40 seconds
4. Rollout1 Bar/21 13/9 8/4*(2) eq: +0.199 (-0.205)
Player:
Opponent: 54.26% (G:18.95% B:1.18%)
45.74% (G:14.64% B:0.59%) Conf.: ± 0.018 (+0.181…+0.217) – [0.0%]
Duration: 18 minutes 54 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

The right play, by a mile, is Bar/21 13/9(3).  Do not hit.  Do not make an inner-board point.  Just unstack the heavy midpoint and make the 9-point.  I think the important feature in this position is the fact that Black has five checkers back, and three of them are on the 22-point, which is 6 pips away from White’s 9-point.

Tansey3

Black’s front position is somewhat fragile, and he will need to get those back checkers moving soon to prevent a collapse.  Even if Black can escape a checker or make a second anchor, White’s control of the outfield should allow him to send back any fugitives while continuing to make effective blocking points, both in the outfield and in his own home board.  Visually, the position after the correct play is striking.  White has all of his checkers connected and working together as a team.  Black has a group of five checkers cut off deep in enemy territory, far from the rest of their comrades.

The correct play beats every other play by at least .160 (for some perspective, a blunder is any error of at least .080; a whopper is an error of .100 or more).  XG thinks that making the 9-point is so important that it slightly prefers burying a checker deep with the last 4 to either of the first two plays I discussed.  The play I made over the board earned me a trip to Burger King for a double whopper.

So, Calcutta bidders, remember this play when you start tossing your money around.  For further research on my playing abilities, I encourage you to look at my match with Victor Ashkenazi on Youtube.  You’ll see more of the kind of play I am capable of.

The Hidden Pitfalls Of the Routine Play

by Gerry Tansey

I don’t worry too much about the plays I agonize about over the board.  If I care enough to take a picture of the position, I know I’ll get further feedback on my decision, first from other players, and then, most definitively, from a bot.  Sometimes I’m right or wrong by a lot; sometimes the plays I’m considering are so close that I shouldn’t have cared that much.  But no matter what, I’ll know that there was a backgammon problem that I wasn’t sure how to solve, and I’ll get an answer.

No, what I worry about are the positions I just fly through, thinking there is no thinking required.  My live matches are rarely recorded, so if such a situation arises then, I’ll never know about it.  Fortunately, most of my matches are either played against a bot or online, and when I’m done, XG will let me know about every play it thinks I butchered, whether I was aware of it at the time or not.

The following position came up in an online match.  The score is 6-5 to 7, and we have passed the Crawford game, so the trailer was allowed to use the cube.  Therefore, we are at Double Match Point (DMP).  Whoever wins this game wins the match.  Gammons and future cube actions matter not a whit.  Both players should make plays that maximize their chances to win this game.

Tansey1

In the game, White wasted little time with this play.  He might have uttered a silent curse to himself, but he quickly played 13/2.  Black failed to hit, White rolled 65, and soon the players were shaking hands (virtually, of course).  Nothing to see here, right?

XG took a look at this position and did its best impression of Frank Costanza’s Airing of Grievances:  “I got a lot of problems with you people!”

1.Rollout1	13/8 13/7	eq: +0.137 	Player: Opponent:	56.84% (G:8.52% B:0.12%) 43.16% (G:3.11% B:0.12%)	Conf.: ± 0.002 (+0.135...+0.139) - [100.0%] Duration: 1 minute 48 seconds 2.	Rollout1	13/2	eq: +0.093 (-0.044) 	Player: Opponent:	54.65% (G:8.33% B:0.16%) 45.35% (G:2.39% B:0.05%)	Conf.: ± 0.002 (+0.091...+0.095) - [0.0%] Duration: 1 minute 39 seconds 3.	1-ply	13/7 6/1	eq: -0.340 (-0.476) 	Player: Opponent:	33.02% (G:5.28% B:0.05%) 66.98% (G:30.86% B:1.08%)

1. Rollout1 13/8 13/7 eq: +0.137
Player:
Opponent: 56.84% (G:8.52% B:0.12%)
43.16% (G:3.11% B:0.12%) Conf.: ± 0.002 (+0.135…+0.139) – [100.0%]
Duration: 1 minute 48 seconds
2. Rollout1 13/2 eq: +0.093 (-0.044)
Player:
Opponent: 54.65% (G:8.33% B:0.16%)
45.35% (G:2.39% B:0.05%) Conf.: ± 0.002 (+0.091…+0.095) – [0.0%]
Duration: 1 minute 39 seconds
3. 1-ply 13/7 6/1 eq: -0.340 (-0.476)
Player:
Opponent: 33.02% (G:5.28% B:0.05%)
66.98% (G:30.86% B:1.08%)

XG prefers clearing the midpoint, a play that leaves two blots and twenty shots, to 13/2, which leaves just one blot.  It is not a close decision.  The right play wins the game (and thus the match) over two percent more than the second best play.  What is going on here?

Well, first note that 13/2 is not immediately as safe as one might think.  Let’s count the shots:  Any roll containing a 3 (eleven numbers), 21 and 11 (three more numbers), and 62, 44, and 22 (four more numbers).  That’s eighteen hitters, only two fewer than the 2-blot play.  But still, it is two fewer.  What else is happening?

This is the one

If White gets away with 13/8 13/7, the match is basically over.  All of White’s rolls play safely, and most of them leave at most one point to clear in front of Black’s 20-point blot.  White’s worst roll is 31, which leaves two points to clear (played 8/7, 5/1).

This is the one

Now, if White gets away with 13/2, there is more work to do.  Let’s assume that Black has not rolled 55, 66, or 65, and is thus able to keep roughly the same defensive position (potentially with a made 2-point).  White leaves another shot on the rolls 51, 41, 31, 21, 62, 42, 32, 53, 33, 22, and 11, a total of 19 numbers.  White is an underdog to roll a safe number!  Let’s do some rough arithmetic.  After 13/2, Black will hit initially with 18 numbers.  On the 18 misses, White will leave another shot about half the time, which Black will hit about a third of the time.  18 times (1/2) times (1/3) is 3 more hits, bringing the total number of hits to about 21.  All of a sudden, the 1-blot play looks less safe than the 2-blot play.

There are some shortcuts we are taking, such as ignoring Black’s big numbers that compromise his defensive position, and using one-third for the proportion of Black’s hits in all cases when he gets a second shot.  But over the board, this type of analysis is quite manageable, if one will only recognize that it is necessary and then take the time to do it.

In the online match, it was my opponent who made this mistake, but I’m counting it as my own error, as I am 100% certain I would have done the same thing if faced with the same decision.  I would have thought, “One blot good, two blots bad,” and just made the “safe” play.  Normally it is right to worry much more about the immediate shots you leave rather than what might happen on your next turn.  However, when the shot count for two plays is close, the ease of cleaning up after survival can become the deciding factor.

My Play Would Have Won A Gammon

by Gerry Tansey

That’s what I imagine some armchair quarterback would have said to me if he or she had seen this sequence from a recent sparring session I had with XG.  I was trailing 6-4 in a match to 11, but this game was going swimmingly.  First, I offered a double in the following position:

Tansey1

I’ll talk a little bit about this double at the end of the article.  After XG took the cube, I rolled a suboptimal 53, which I played 13/5.  XG also rolled 53, which was a considerably better roll for the bot.  XG brought one checker to safety and threatened to escape the other, playing 23/18, 16/13.  I was under severe pressure to hit the straggler.

Tansey2

I was under severe pressure to hit the straggler, but I did with a nice 63, bringing down more ammunition with 13/10 13/7*.  I soon filled in the 4-point, and a couple of turns later, I had this 62 to play:

Tansey3

I really didn’t spend too much time on this play.  I ran the back checker, but before clicking on my dice to end my turn, I did think, “Hey, that closes the board too.  Whatever.  We’ll do that later.”

Well, you don’t have to know what “hubris” means to have an inkling of what happened next.  XG rolled 25 from the bar, squirting out to the bar point.  I rolled a 64 (which would have escaped the back man had I closed the board), and had to settle for winning a single game.

In a live tournament match, this kind of sequence can have a negative psychological effect.  The naysayers in your mind may harp on you relentlessly, saying things like, “We just tossed two points down the drain.  What were you afraid of?  His prime had two holes in it.  We could have escaped easily. This is backgammon.  The dice are capricious enough.  We can’t afford to just give points away.”

But remember, the plural of “anecdote” is not “data.”  There will almost always be sequences of rolls that punish the play you made and reward the play you didn’t.  And the fact is that in this case, White does not have much time to escape Black’s blockade if he doesn’t do it now.  Any roll that does not contain a 2 or a 4 (16 numbers) makes no progress, and the board cracks immediately on 65 and 55.  Further, after a number like 52, White still may bust his board before he escapes.  It is easy to see sequences where White fails to escape and thus loses the game.

And in reality, if White uses the 62 to escape, most of the time he can then close Black out later.  Usually Black fans, and most of Black’s entering numbers lead to his being pounded relentlessly.  Yes, 42 and 22 hit, but White often hit back from the roof, and White’s advantage in home board points usually leads to an easy victory, and often a gammon.

A rollout shows that the plays are not close.  Closing the board is a big blunder, losing 6.8% more games, while winning only 1.5% more gammons, than escaping.

1.Rollout1	24/16	eq: +1.380 	Player: Opponent:	90.58% (G:53.78% B:0.10%) 9.42% (G:0.87% B:0.09%)	Conf.: ± 0.005 (+1.375...+1.385) - [100.0%] Duration: 2 minutes 19 seconds 2.	Rollout1	8/2 4/2	eq: +1.231 (-0.149) 	Player: Opponent:	83.83% (G:55.25% B:0.07%) 16.17% (G:1.34% B:0.05%)	Conf.: ± 0.006 (+1.225...+1.237) - [0.0%] Duration: 2 minutes 24 seconds   1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

1. Rollout1 24/16 eq: +1.380
Player:
Opponent: 90.58% (G:53.78% B:0.10%)
9.42% (G:0.87% B:0.09%) Conf.: ± 0.005 (+1.375…+1.385) – [100.0%]
Duration: 2 minutes 19 seconds
2. Rollout1 8/2 4/2 eq: +1.231 (-0.149)
Player:
Opponent: 83.83% (G:55.25% B:0.07%)
16.17% (G:1.34% B:0.05%) Conf.: ± 0.006 (+1.225…+1.237) – [0.0%]
Duration: 2 minutes 24 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

Now, as promised, I’ll discuss the cube mentioned at the start of this article.  Here is a rollout:

Analyzed in RolloutNo double	Double/Take   Player Winning Chances:	61.34% (G:31.93% B:0.50%)	61.46% (G:33.62% B:0.51%)   Opponent Winning Chances:	38.66% (G:9.51% B:0.46%)	38.54% (G:10.01% B:0.53%)   Cubeless Equities	+0.456	+1.016 Cubeful Equities      No double:	+0.610 (-0.234)	±0.012 (+0.598..+0.621)   Double/Take:	+0.844	±0.015 (+0.829..+0.859)      Double/Pass:	+1.000 (+0.156)   Best Cube action: Double / Take Rollout details 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller   Double Decision confidence:	100.0% Take Decision confidence:	100.0% Duration: 11 minutes 35 seconds

Analyzed in Rollout No double Double/Take
Player Winning Chances: 61.34% (G:31.93% B:0.50%) 61.46% (G:33.62% B:0.51%)
Opponent Winning Chances: 38.66% (G:9.51% B:0.46%) 38.54% (G:10.01% B:0.53%)
Cubeless Equities +0.456 +1.016
Cubeful Equities
No double: +0.610 (-0.234) ±0.012 (+0.598..+0.621)
Double/Take: +0.844 ±0.015 (+0.829..+0.859)
Double/Pass: +1.000 (+0.156)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 11 minutes 35 seconds

It’s a huge double and a big take.  White has a modest racing lead, a better board, and threats to hit Black’s blots.  Any hit-fan sequence is a huge market loss.  Black certainly has enough chances to take, though.  Sometimes White fails to hit Black, sometimes White hits the 9-point checker and Black anchors, sometimes White hits loose with a 6 and Black hits back.  Black is doing fine in all these sequences.

The score matters a little bit here.  At the score, Black will have to wait a long time before he can give a correct redouble, and if the position is gammonish, that redouble may never be right.  As a result, White should be a bit more eager to use the cube at the score, as Black’s redoubling potential is severely limited.  That being said, for money the correct decisions are the same, and they’re still not close.

Analyzed in RolloutNo double	Double/Take   Player Winning Chances:	61.49% (G:31.03% B:0.55%)	61.72% (G:32.44% B:0.52%)   Opponent Winning Chances:	38.51% (G:8.93% B:0.44%)	38.28% (G:9.55% B:0.49%)   Cubeless Equities	+0.452	+0.927 Cubeful Equities No double:	+0.514 (-0.121)	±0.010 (+0.504..+0.523) Double/Take:	+0.635	±0.016 (+0.619..+0.651) Double/Pass:	+1.000 (+0.365)   Best Cube action: Double / Take Rollout details 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller   Double Decision confidence:	100.0% Take Decision confidence:	100.0% Duration: 9 minutes 16 seconds

Analyzed in Rollout No double Double/Take
Player Winning Chances: 61.49% (G:31.03% B:0.55%) 61.72% (G:32.44% B:0.52%)
Opponent Winning Chances: 38.51% (G:8.93% B:0.44%) 38.28% (G:9.55% B:0.49%)
Cubeless Equities +0.452 +0.927
Cubeful Equities
No double: +0.514 (-0.121) ±0.010 (+0.504..+0.523)
Double/Take: +0.635 ±0.016 (+0.619..+0.651)
Double/Pass: +1.000 (+0.365)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 9 minutes 16 seconds

The double goes from “huge” to merely “big,” while the take goes from “big” to “monster.”  A lot can happen in the next couple of rolls, and often one side is not going to be very happy.  This volatility is the heart and soul of backgammon.  Relish it.

And by the way, I do realize that I just showed you a game where I did everything right.  It does happen every once in a while.  I promise I’ll show you a screw-up next time.

“To see what is in front of one’s nose needs a constant struggle.” – George Orwell

by Gerry Tansey

(Quick note-I’ve made the positions as large as I can, but if you would like to see it a bit bigger, click on the picture and it will open in a separate window.)

I have a feeling that a lot of my posts are going to arise because someone screwed up while playing backgammon.  Alas, the “someone” in question will usually be me.  Here is a position that arose during an online match the other night.  I was White, and while I was leading the match to 7 by the score of 5 to 1, I was white-knuckling it in this position while holding a 2-cube.  I had to play a 65.

65-1

You can skip this next paragraph if you are not interested in a little mathematical discussion.  The score matters here, but not as much as many may think.  Of course, I can’t use the cube or win a gammon.  But shouldn’t I be super-cautious to avoid losing a gammon?  Well, not really.  Losing a single game gives me roughly a 67% chance to win the match, while losing a gammon puts me at 50%, a difference of 17% match-winning chances.  But if I win the game, I win the match, so the difference in match equity between winning the game and losing a single game is 100% – 67%, or 33%.  Thus the gammon price, in this case the ratio 17/33, is almost exactly the value of 0.5 that it is for money.  In more plain English, I should be willing to make a play that trades 5% more wins for 10% extra gammon losses, just like in a money game.

Now, how do I play this 65?  Well, first I have to decide what to do with the 6.  We’ve all heard the expression “Sixes don’t grow on trees.”  (If you haven’t, you have now).  And indeed, it is often right to take some risks to get one’s checkers free from a blockade, particularly if the forward position will collapse otherwise.  The trouble is that after the play 24/13, Black has 13 shots, after which he wins many gammons.  This is simply too many, considering that the game is not won even after a miss.

So I covered, playing 11/5, 7/2, leaving just 61 and 62 as hitters from the bar, while hoping to extricate my straggler later.  But I didn’t even consider the best play, and when that happens, I usually make a big blunder.  This occasion is no exception.

The trouble with my play is that have to deal with my 18-point anchor sooner, rather than later.  If I don’t roll a 6 immediately, I will have to break the anchor, potentially in a disastrous fashion.  Even if I do get a quick 6, it is extremely unlikely that Black will stay on the bar long enough for me to break contact and bring all of my checkers around.  I am likely going to have to break that anchor at an inconvenient time.  Also, breaking the 7-point to bury a checker is just generally an awful idea.  I should start the process of disengaging now while Black is on the bar by playing 18/13, 11/5.  Although this play leaves 3 blots, there are only 5 immediate hitting numbers for Black.  If Black misses, I could escape my back checker, make the midpoint, or bring down builders for the 6-point, depending on what I roll.  But mainly I’m breaking the 18-point (which I will have to do eventually anyway) on my own terms, when it is relatively safe to do so.  The plays are not close.  Each play is about .150 better than the next best play.

1.Rollout118/13 11/5	eq: -0.212 	Player: Opponent:	48.25% (G:5.05% B:0.02%) 51.75% (G:15.20% B:0.75%)	Conf.: ± 0.004 (-0.216...-0.209) - [100.0%] Duration: 1 minute 37 seconds 2.	Rollout1	11/5 7/2	eq: -0.361 (-0.149) 	Player: Opponent:	41.55% (G:4.52% B:0.01%) 58.45% (G:16.85% B:0.69%)	Conf.: ± 0.004 (-0.366...-0.357) - [0.0%] Duration: 1 minute 40 seconds 3.	Rollout1	24/13	eq: -0.514 (-0.302) 	Player: Opponent:	41.56% (G:3.82% B:0.01%) 58.44% (G:30.32% B:1.20%)	Conf.: ± 0.004 (-0.518...-0.510) - [0.0%] Duration: 1 minute 49 seconds   1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller eXtreme Gammon Version: 2.10, MET: Kazaross XG2

1. Rollout1 18/13 11/5 eq: -0.212
Player:
Opponent: 48.25% (G:5.05% B:0.02%)
51.75% (G:15.20% B:0.75%) Conf.: ± 0.004 (-0.216…-0.209) – [100.0%]
Duration: 1 minute 37 seconds
2. Rollout1 11/5 7/2 eq: -0.361 (-0.149)
Player:
Opponent: 41.55% (G:4.52% B:0.01%)
58.45% (G:16.85% B:0.69%) Conf.: ± 0.004 (-0.366…-0.357) – [0.0%]
Duration: 1 minute 40 seconds
3. Rollout1 24/13 eq: -0.514 (-0.302)
Player:
Opponent: 41.56% (G:3.82% B:0.01%)
58.44% (G:30.32% B:1.20%) Conf.: ± 0.004 (-0.518…-0.510) – [0.0%]
Duration: 1 minute 49 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.10, MET: Kazaross XG2

I guess I should be glad that I merely played a whopper with cheese rather than a triple whopper.  But I was so concerned about choosing between play A and play B that I didn’t grasp the whole position.  I never even thought about play C, which looks superficially risky, but, as the rollout shows, loses the fewest gammons of all the plays.  It also wins a ton more games.

I Told You That Story So I Could Tell You This One

by Gerry Tansey

In my last post, I went through the proper cube actions for a 2-roll position versus a 2-checker position in the bearoff.  I’d like to use a little bit of what we learned to examine a position that could occur one roll earlier.  What is the proper cube action for money in the following position?  What about at 2-2 in a 5-point match?

Tansey1.png

In a money game, if White redoubles to 4 and Black takes, White will immediately hate his life upon rolling 21, since he must then pass Black’s redouble to 8.  Unpleasant but takeable recubes also arise when White rolls 31 and 11.  Rolls of 32 and 41 lead to the fun scenario in my last article, usually ending with a 16-cube in play.  But White shouldn’t be too afraid of these rolls, since Black’s redouble is just barely correct in that case.

On the plus side, White wins immediately with three rolls: 44, 55, and 66.  Further, White wins barring Black’s rolling a set on 65, 64, 54, and 33, or seven additional rolls.  We must also consider the five numbers 63, 53, and 22 to be really good numbers for White, as they lose the market by a mile provided Black does not roll doubles.  White is usually pretty happy with 43, 52, and 62 as well.

For the rest of White’s numbers, he is indifferent about whether or not he doubled, provided that Black does not roll a set.  That is because he would be redoubling – and Black would be taking – after these sequences anyway.  For instance, if White holds onto the cube and rolls 42, and Black fails to roll a doublet, then White would redouble and Black would take.  The end result is usually going to be the same in these cases regardless of whether White redoubled before his first roll or not.

A better player than me might be able to calculate all of this precisely over the board.  But what I would glean from this examination of the numbers is that a lot more could go right for White than go wrong, and so I would redouble as White.  Hopefully you can see that Black has a trivial take in this position.  Black wins immediately on 2 of White’s numbers, and practically speaking we can count the 31 and 11 rolls as 3 wins for Black, since he gets to give such a nice recube in these variations.  It is not hard to find 4 more wins for Black out of White’s remaining 28 non-winning rolls to give him the requisite 9 wins out of 36 for a take.  Here is what XG has to say

Analyzed in XG Roller++No redouble	Redouble/Take   Player Winning Chances:	64.66% (G:0.00% B:0.00%)	64.66% (G:0.00% B:0.00%)   Opponent Winning Chances:	35.34% (G:0.00% B:0.00%)	35.34% (G:0.00% B:0.00%)   Cubeless Equities	+0.293	+0.586 Cubeful Equities No redouble:	+0.399 (-0.072)	 Redouble/Take:	+0.470	 Redouble/Pass:	+1.000 (+0.530)   Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 64.66% (G:0.00% B:0.00%) 64.66% (G:0.00% B:0.00%)
Opponent Winning Chances: 35.34% (G:0.00% B:0.00%) 35.34% (G:0.00% B:0.00%)
Cubeless Equities +0.293 +0.586
Cubeful Equities
No redouble: +0.399 (-0.072)
Redouble/Take: +0.470
Redouble/Pass: +1.000 (+0.530)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10

It is indeed a sizable double and a monster take for money.  Now, what if this is a 5-point match and the score is 2-2?  How does this change things?

Well, Black’s take is still trivial, since his take point is 25 percent at the score, and he has over a 35 percent chance to win this game.  However, White should be even more willing to redouble in this scenario than for money.  Remember that White is a favorite in a highly volatile position.  Often times this turn will be White’s last chance to use the cube he owns.  For money, the main deterring factor for White’s recube is Black’s ability to shove it back down White’s throat on a poor roll.  But in this match scenario, White is giving Black a dead cube when he redoubles.  White’s recube is all ice cream and no spinach, and failing to ship the cube would be a massive blunder for White.

Analyzed in 4-plyNo redouble	Redouble/Take   Player Winning Chances:	64.66% (G:0.00% B:0.00%)	64.66% (G:0.00% B:0.00%)   Opponent Winning Chances:	35.34% (G:0.00% B:0.00%)	35.34% (G:0.00% B:0.00%)   Cubeless Equities	+0.293	+0.585 Cubeful Equities No redouble:	+0.398 (-0.186)	 Redouble/Take:	+0.585	 Redouble/Pass:	+1.000 (+0.415)   Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Analyzed in 4-ply No redouble Redouble/Take
Player Winning Chances: 64.66% (G:0.00% B:0.00%) 64.66% (G:0.00% B:0.00%)
Opponent Winning Chances: 35.34% (G:0.00% B:0.00%) 35.34% (G:0.00% B:0.00%)
Cubeless Equities +0.293 +0.585
Cubeful Equities
No redouble: +0.398 (-0.186)
Redouble/Take: +0.585
Redouble/Pass: +1.000 (+0.415)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10, MET: Kazaross XG2

The above scenario actually arose in the first match I ever played against one of the Giants of backgammon.  The Giant was White, and he failed to redouble me after a long think.  He was probably relieved when he rolled 31, but after I failed to roll a set, he was able to bear off his checkers.  And then I won the next two games to win the match.  This was the only major mistake the Giant made in our match, but it cost him dearly (Unfortunately, I still played a bit worse than he did).  This position taught me that the Giants are human, and beatable.  If you find yourself playing a Giant, just fight as best as you can.  Sometimes they will give you a gift.

 

This Article Is Brought To You By The Numbers 324 & 1296

by Gerry Tansey

Imagine this bearoff scenario.  You own a 2-cube in a money game and have a 2-roll position (3 checkers on the ace-point, for instance).  Your opponent has two checkers left somewhere in his home board.  Under what conditions should you redouble?  Under what conditions should your opponent pass a redouble?

Let’s answer the second question first.  Your opponent must pass a redouble if his winning chances are less than 25%.  Your opponent’s winning requires a parlay:  you must fail to roll doubles, and he must then bear off both of his checkers.  You fail to roll doubles with probability 30/36, and your opponent bears off with probability x/36, where x is the number of rolls that bear off.  So your opponent’s chance of winning is the product of these two fractions, or 30x/1296.

The denominator of this fraction is a good one to know: 1296.  An even better number to know is 324, which is 25% of 1296.  So if 30x is less than 324, your opponent should pass.  If your opponent has 10 rolls that bear off, then 30x = 300, which is less than 324, so your opponent should pass.  With 11 good rolls, 30x = 330, which is bigger than 324, so your opponent has a take.

What does a pass look like?  Here’s one example.

Analyzed in 4-ply Player Winning Chances:   76.85% (G:0.00% B:0.00%) Opponent Winning Chances: 23.15% (G:0.00% B:0.00%) Cubeless Equities: No Double=+0.537, Double=+1.074 Cubeful Equities:        No redouble:     +0.537 (-0.463)        Redouble/Take:   +1.074 (+0.074)        Redouble/Pass:   +1.000 Best Cube action: Redouble / Pass eXtreme Gammon Version: 2.10

Analyzed in 4-ply
Player Winning Chances: 76.85% (G:0.00% B:0.00%)
Opponent Winning Chances: 23.15% (G:0.00% B:0.00%)
Cubeless Equities: No Double=+0.537, Double=+1.074
Cubeful Equities:
No redouble: +0.537 (-0.463)
Redouble/Take: +1.074 (+0.074)
Redouble/Pass: +1.000
Best Cube action: Redouble / Pass
eXtreme Gammon Version: 2.10

With checkers on the 5 and the 4 point, the rolls 65, 64, 54, 33, 44, 55, and 66 bear off, which is 10 numbers out of 36, so your opponent must pass.  But if we improve the position by one pip, by placing both checkers on the 4-point, your opponent now has one additional roll that bears off, namely 22.  This 11th number gives your opponent a close take.  (A much better one-pip improvement is to place the checkers on the 5- and 3-points, which gives your opponent 14 winning rolls).

Analyzed in 4-ply Player Winning Chances:   74.54% (G:0.00% B:0.00%) Opponent Winning Chances: 25.46% (G:0.00% B:0.00%) Cubeless Equities: No Double=+0.491, Double=+0.981 Cubeful Equities:        No redouble:     +0.491 (-0.491)        Redouble/Take:   +0.981        Redouble/Pass:   +1.000 (+0.019) Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10

Analyzed in 4-ply
Player Winning Chances: 74.54% (G:0.00% B:0.00%)
Opponent Winning Chances: 25.46% (G:0.00% B:0.00%)
Cubeless Equities: No Double=+0.491, Double=+0.981
Cubeful Equities:
No redouble: +0.491 (-0.491)
Redouble/Take: +0.981
Redouble/Pass: +1.000 (+0.019)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10

Now, when can you redouble your opponent?  You should definitely redouble your opponent if your opponent is not a favorite to bear off when you fail to roll doubles.  You are a favorite in a last-roll position, and your opponent cannot profitably redouble you back.

But what if your opponent is only a very tiny favorite to bear off when you do not roll doubles?  You gain from a redouble when you roll a set, but your opponent will redouble to 8 when you don’t roll a set, which is most of the time!  Can your gains possibly outweigh your losses?  Well take a look at this:

Analyzed in 4-ply Player Winning Chances:   56.02% (G:0.00% B:0.00%) Opponent Winning Chances: 43.98% (G:0.00% B:0.00%) Cubeless Equities: No Double=+0.120, Double=+0.241 Cubeful Equities:        No redouble:     +0.120 (-0.028)        Redouble/Take:   +0.148        Redouble/Pass:   +1.000 (+0.852) Best Cube action: Redouble / Take eXtreme Gammon Version: 2.10

Analyzed in 4-ply
Player Winning Chances: 56.02% (G:0.00% B:0.00%)
Opponent Winning Chances: 43.98% (G:0.00% B:0.00%)
Cubeless Equities: No Double=+0.120, Double=+0.241
Cubeful Equities:
No redouble: +0.120 (-0.028)
Redouble/Take: +0.148
Redouble/Pass: +1.000 (+0.852)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10

You have a small redouble in this position, even though your opponent has 19 rolls to bear off.  Most of the games will end up with your holding an 8-cube as a small underdog after you fail to roll doubles.  We won’t go through the math in detail here, but it turns out that the gain you get from redoubling before rolling your 6 immediate winning numbers just barely outweighs the fact that most of the time you will be playing as a 19-to-17 dog holding an 8-cube.  Of course, I’ve heard examples of opponents beavering the redouble to 4 here, which is a *huge* mistake.  Just comfort yourself with that knowledge the 44% of the time you are paying your opponent 16 points!

 

 

The Dictionary – Part One

by Jana Bohrer

Back Game
Noun The Wonderland one wanders into after rolling an opening 4-1 creatively played by splitting and slotting the 5 “as an experiment to see how it turns out”.  Followed by an opponent’s 4-3 hitting twice. Then fanning, coming in, getting hit again somewhere else, and repeating this sequence until one achieves a number of men in the opponent’s board for a “well-timed” game.  At some point during which, one takes the cube because:
1.  One is a masochist whose hobbies include watching Nickolodeon marathons of Gilligan’s Island and patronizing a holistic dentist who believes betel leaves are an anestheticgilligan
2.  One is off one’s meds
(See also:  Backgammoned and Creative)

Backgammon(ed)
1.  Verb Losing 3x the amount of the cube.  Frequently occurring in a 5 way chouette in which one is holding 4 sixteen cubes in the box. This often results voluntary homelessness, as one is too frightened reveal that one has lost a significant amount of the household grocery money and all of the little tyke’s college fund;  (See also: Back Game, Chouette)

bilbo
2.  Noun The game on the back of the checkers board variously known as:
a. Jacoby’s Bane
b.  The One Game
c.  The Game of Power
d.  The Precious

Builder
Noun  A checker you anticipate  using to build a useful point.  It should be noted that Builders must be used sparingly and while still in earliest stage of their development.   If the metamorphosis of a builder is not interrupted;  or if a hive of Builders is allowed to form; the Builders transform into Blots.  These Blots will in time emerge from their chrysalises as Gammons.
(See also:  Blot, Gammoned, Creative)

gammon

Chouette
Noun A type of backgammon game which allows more than two players.  Side effects include, but are not limited to:
1.  Superiority Complex – “Every other player in this chouette is a creative idiot.”
2.  Inferiority Complex – “I should say something about leaving 5 blots, but I’m losing, and they’ve been playing so many more years than I have.  He keeps saying they’re builders…”
3. Rage Complex – “Well, if he hadn’t refused to hit twice when I told him too, I wouldn’t have had to hit him with the baffle box.”
4. Sleeping in the Car Complex – “I told you.   I checked out of the room already and now we don’t have the money to check back in.  The car’s perfectly comfortable, just imagine you’re shorter.”
(See also: Creative, Builder, Gammoned, Backgammoned, Back Game)

Chouette is derived from the French for “Train”.t2

Creative
tut
Adjective  Term used by experienced players to describe various plays made by less experienced players.  Most commonly used by one’s spouse/significant other, as in it’s first known written usage found on the wall of King Tut’s tomb which depicts Queen Ankhesenamun saying:
(See also:  Sarcasm)