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Playing the Opening Move, Part 2: The Split or Build Rolls Playing the Opening Move, Part 2: The Split or Build Rolls

04-25-2009 , 04:54 PM
Last time we looked at the general goals that guide play in the very early game. Now we’ll start to look at particular opening rolls and see how best to play them.

Note that there are only 15 possible opening rolls. The rules require each player to throw a die to start the game, and the player throwing the higher number moves first, using his die and his opponent’s die as his roll. So if I throw a 6 and you throw a 2, I move first and my roll is a 6-2. (Some players use a non-standard variation where the winner of the opening roll-off then rolls again, and uses that number as his opening roll. This variation allows doubles to come into play, but it’s not part of the standard rules and no tournament would permit this.)

Keep the starting position in mind as we divide the 15 opening rolls into four groups, based on common characteristics:

The forced rolls: 3-1, 4-2, 5-3, 6-1, and 6-5. (5 rolls)

The build-or-split rolls: 5-4, 5-2, 4-3, and 3-2. (4 rolls)

The run-or-split rolls: 6-4, 6-3, and 6-2. (3 rolls)

The slot-or-split rolls: 2-1, 4-1, and 5-1. (3 rolls)


Playing the Forced Rolls

We called these rolls “forced” because one way of playing them dominates all the others. Here are the right plays with each of these rolls:

With 3-1, make the 5-point with 8/5 6/5. (This is the best opening roll, making the strongest inner-board point.)

With 4-2, make the 4-point with 8/4 6/4. (This is considered the second-best opening roll, just a shade better than 6-1.)

With 6-1, make the 7-point (also called the “bar point”) with 13/7 8/7.

With 5-3, make the 3-point with 8/3 6/3.

With 6-5, run a back checker to the midpoint with 24/13.

Four of these rolls actually make a blocking point. While the fifth, 6-5, completely escapes a back checker. These are big accomplishments from the opening position, which is why the rolls aren’t played any other way.

You may wonder why 6-1 isn’t considered the “best” opening roll. Many beginners like it because it makes three points in a row, which looks like a strong blocking formation. The problem with 6-1 is that, while it makes a blocking point, it doesn’t make an inner-board point. The 3-1 roll, which is better, makes both a blocking point and an inner-board point, and closing inner-board points helps keep your opponent on the bar when hits occur.


Playing the Build-or-Split Rolls

There are four rolls in the “build-or-split” category. These are named because the main choices for each roll are either bringing two builders down from the midpoint or bringing down one builder while splitting the back men. Let’s look at each roll in turn.

54: the building play is 13/8 13/9, and the splitting play is 13/8 24/20.



Diagram 2. Position after 13/8 13/9.



Diagram 3. Position after 13/8 24/20.

Both these plays have merit. The common part of each play is 13/8, using the five to bring down a builder and unstack the midpoint. Playing 13/9 with the four adds another useful builder while creating a huge number of rolls that now make one of the key blocking points (the 5-point, 4-point, and bar-point). Playing 24/20, on the other hand, starts the crucial 20-point anchor, while guarding White’s outfield and preventing White from conveniently bringing down builders of his own.

What’s the right play? Master opinion considers the two plays very close, but most top players prefer splitting with 24/20 in money games or matches where the score is close. The 20-point is very important, and splitting is the most direct way to fight for it. Of course, Black’s 5-point is also crucial, but 13/9 only creates a few more rolls that directly make the 5-point.

One note: if you’re trailing towards the end of a match, so that winning a gammon gains a lot and losing a gammon is not so costly, then 13/9 is clearly right. The extra builder restrains White from splitting his back men (because you have more ways to attack) and more gammons result when your opponent isn’t able to make an advanced anchor quickly.


52: the building play is 13/8 13/11, and the splitting play is 13/8 24/22.



Diagram 4. Position after 13/8 13/11.



Diagram 5. Position after 13/8 24/22.

The situation here is obviously similar to the previous play; 13/11 adds a builder, while 24/22 splits to a potential anchor point.

In this case, master opinion heavily favors the split play. While the 22-point is apparently only a modest improvement over the 24-point, it’s enough to reduce the gammon danger significantly when Black makes it. In addition, the split back men give plenty of extra coverage over White’s outer board.

Playing 13/11, on the other hand, doesn’t add a lot of new building numbers to Black’s arsenal. He gains 4-1, 6-4, and 6-3 to make new blocking points. That’s not nearly as big a gain as after 13/9 with a four.


Playing 4-3 and 3-2.

Now let’s look at the 4-3 roll. It can be played as a pure building roll, with 13/9 and 13/10. Take a look.



Diagram 6: Position after Black plays 13/9 13/10.

This is a bold variation, exposing two blots in the outfield, but creating a myriad of point-making opportunities in return. White has a total of eleven rolls that hit one of the blots (4-4, 3-3, 2-2, 6-3, 5-4, 6-2, and 5-3). That’s almost one-third of White’s possible rolls. However, if White doesn’t hit, every legal roll by Black will make at least one blocking point next turn! It’s a high-risk, high-reward way of playing 4-3.

The play has one more upside: if White doesn’t hit, he’ll be constrained from splitting his back men at all, since Black now has more attacking checkers in what we call “the zone”. By the zone, I mean the area between the 6-point and the 11-point, where builders are poised to attack and/or make inner-board points. The more builders your opponent has in this area, the less you want to split your back men.

If instead you want to build-and-split with 4-3, there are actually two ways of doing so: 13/9 24/21 or 13/10 24/20. Here’s what the two plays look like.



Diagram 7. Position after Black plays 13/9 24/21.



Diagram 8. Position after Black plays 13/10 24/20.

While the two plays may look similar, most top players have a preference for 13/9 24/21. There are several reasons:

• A builder on the 10-point is less useful than a builder on the 9-point. After playing 13/10, notice that some of your good point-making numbers are duplicated. (Duplication just means that a roll does multiple good things. That’s bad, because you can only use one of those good things at a time.) A roll of 3-1 can now make either the 5-point or the bar-point, while a roll of 5-3 makes both the 3-point and the 5-point. This doesn’t occur after 13/9, where every roll now makes a unique point, and hence you’re getting more work out of your checker formation.

• Splitting to the 21-point is less costly if your opponent points on you. If you split to the 20-point with 24/20, and your opponent then rolls 3-1, pointing on you, he’s both put you on the bar and made the best point in his inner board. But if you split to the 21-point and he rolls 4-2, pointing on you, he’s only made his second-best point. You still have a chance to come in and make the 20-point later, with a good game. So by splitting to the 21-point, the downside when your opponent rolls well is less.

• Splitting to the 21-point gives your opponent more difficult problems. Most players know that if your opponent splits to your 5-point (his 20-point) with a four, you’re suppose to hit him there and fight for the 5-point. Not as many players understand that the same rule applies if he splits to your 4-point (his 21-point). With rolls like 2-1, 6-3, and 5-4, you still need to hit and fight for the 4-point, to prevent your opponent from making a good anchor. Since many, if not most, players will play passively in that case, splitting to the 21-point and taking advantage of those errors becomes especially good.

So of the two build-and-split plays, 13/9 24/21 is slightly preferable. But there’s yet a fourth way to play 4-3! You can make what’s called the “Middle Eastern split”, moving both back checkers with 24/20 24/21.



Diagram 9. Position after Black plays 24/20 24/21.

The term “Middle Eastern split” comes from the fact that this way of playing (moving both back checkers on almost all opening rolls) is popular in Middle Eastern countries like Turkey, Greece, Lebanon, and Egypt, where the game is played by millions in cafes and coffeehouses, the doubling cube isn’t used, triple games aren’t scored, and the game is played mostly as a straight racing game. The play isn’t terrible, and in a few match situations it’s actually best. (If you don’t need a gammon and your opponent does.) Still, it’s never become popular. The right antidote is to hit both checkers if you can and play for attack.

So what’s the “best” 4-3 play? Playing two men down with 13/9 13/10 is my top choice, producing difficult positions with extra tension. An excellent runner-up choice is 13/9 24/21, which tends to produce positions that are easier to play, with fewer gammons for either side.


The 3-2 roll presents much the same problems as 4-3. The two main ways of playing the number are the building play with 13/10 13/11, and the splitting play with 24/21 13/11. Here’s what the board looks like after each play.



Diagram 10. Position after Black plays 13/10 13/11.



Diagram 11. Position after Black plays 13/11 24/21.

The building play here is a little less risky than after 4-3. White can only hit with seven numbers (6-3, 6-4, 5-4, and 3-3), so Black is less likely to be on the bar. On the downside, Black has slightly fewer numbers to make points.

The splitting play is also low-risk, since the new builder on the 11-point is very safe, only in jeopardy to a 6-4 from White.

There’s also a Middle Eastern variation for this roll as well: Black can play 24/21 24/22, but this is very rarely seen in tournaments.

What’s best? I normally play 13/10 13/11, just because it leads to more complicated play. If I were protecting a lead in a match, I’d switch to 24/21 13/11 to get an anchor, but even there it’s a close call.
Playing the Opening Move, Part 2: The Split or Build Rolls Quote
04-25-2009 , 05:29 PM
I see several places of "match score is close" or "I have good lead in a match", "so I play the alternative move".

Isn't BG like poker that we shouldn't concern about the score/profit/loss? Of course we vary our play based on read of opponent, but we don't vary our play based on score, right?

This would make sense in a (post-) Crawford game (like folding AA preflop in a tournament), but before that, why do we change our play if it is has the best EV?
Playing the Opening Move, Part 2: The Split or Build Rolls Quote
04-25-2009 , 10:18 PM
Quote:
Originally Posted by httassadar
I see several places of "match score is close" or "I have good lead in a match", "so I play the alternative move".

Isn't BG like poker that we shouldn't concern about the score/profit/loss? Of course we vary our play based on read of opponent, but we don't vary our play based on score, right?

This would make sense in a (post-) Crawford game (like folding AA preflop in a tournament), but before that, why do we change our play if it is has the best EV?
EV isn't a constant in match play; it will vary depending on the score. It won't vary by huge amounts, but it will vary enough to alter the preferred order of two otherwise close plays.
Playing the Opening Move, Part 2: The Split or Build Rolls Quote
04-26-2009 , 10:31 AM
ht,
Here a slightly more lengthy answer to your question. Check out this page, and scroll down to "G11 Match Equity Table." What this tells you is your chances of winning the match from various scores. So, suppose you were beating me 4-0 in a match to 7; this would be 3-away/7-away, and according to the table your chances of winning are .765.
Now, notice how these change based on various outcomes:

You win 1 point: 2-away/7-away, .844, gaining .079
You win 2 points: 1-away/7-away, .909, gaining .144
You win 4 points: win match, gaining .235
I win 1 point: 3-away/6-away, .714, losing .051
I win 2 points: 3-away/5-away, .650, losing .115
I win 4 points: 3-away/3-away, .500, losing .265

Single points are worth less to me since I have further to go, but multiple points may be worth more to me (since you can only use 3 points of a doubled gammon, but I could use all 4). Suppose we reach some point in this game where I have doubled you; in a normal money game your EV would be roughly 2*p(you win normal) + 4*p(you win gammon)-2*p(I win normal)-4*p(I win gammon). In this match situation though, it's .144*p(you win normal) + .235*p(you win gammon) -.115*p(I win normal) - .265*p(I win gammon). So, I would prefer to make aggressive plays that lead to more gammons for both sides, and you would prefer to do the opposite.
Playing the Opening Move, Part 2: The Split or Build Rolls Quote
04-27-2009 , 12:32 PM
Here's a concrete example which is probably clearer.

Suppose you're playing a 7-point match, you trail 5-6, and it's the Crawford game, so no doubling this game. You roll a 6-4 to open the game.

A Snowie rollout shows the following cubeless probabilities for an opening 6-4 roll:

Play -------You win -------You win ----You win
--------------------------a gammon --a single game

24/14 -------51% ----------13%--------38%

24/18 13/9 --50% ----------14% -------36%

8/2 6/2 ------49% ----------16% -------33%

Clearly if we win a gammon this game, we win the match. If we just win a single game, we get to 6-6 and now we have to win yet another game to win the match.

If we play 8/2 6/2, we win the match 16% of the time this game, and another 1/2 of 33% = 16.5% in the next game. Total match-winning probablilty = 16% + 16.5% = 32.5%.

Do the same calculation for the other two plays and we get 32.0% match winning chances. So 8/2 6/2 is the better play with a 6-4 when trailing 5-6 at Crawford.

Now suppose we play 8/2 6/2 and go on to win just a single game. We set up the pieces for the final, double match point game, where only winning counts (no extra points for gammons) and we again win the opening roll with a 6-4. What do we play now?

Clearly we only care about raw winning chances, and from our table it's clear that 24/14, with 51% winning chances, is now the right play.

Q.E.D.
Playing the Opening Move, Part 2: The Split or Build Rolls Quote
04-28-2009 , 07:11 PM
Thanks for the clear explanation, Gammoner and Robertie.
Playing the Opening Move, Part 2: The Split or Build Rolls Quote

      
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