Opening Rolls

 Average advantage of winning opening roll

 From: Chuck Bower Address: bower@bigbang.astro.indiana.edu Date: 22 October 1998 Subject: Re: Who goes first in Matches Forum: rec.games.backgammon Google: 70oddo\$113\$1@flotsam.uits.indiana.edu

```Laury Chizlett  <laury@trpdata.demon.co.uk> wrote:

> ... What is the edge gained by going first? ie the
> equity of a player, after winning the opening throw - whatever this
> throw is, but before moving. Is it just the arithmetic mean of all the
> equities of the best plays of the 15 possible opening throws? Is this a
> question!?

I will answer you questions in REVERSE order.  Yes, this is a question.
(In fact, it is a GOOD quesiton.)  Yes, it is the weighted mean.
("Weighting" is needed if you include doublets since a specified doublet
happens half as often as a specified singlet.  But if you don't allow
doublets, then there are 15 singlets, all of which are equally likely, so
you just add up their worth and divide by 15.)

Now, back to the question you REALLY wanted the answer for:  how much
of an edge does the opening roller have.  In cubeless equity units (no
cube, but gammons count twice and backgammons thrice) it is worth 0.038.
Playing that form of BG (no cube, but counting gammons...) the opening
roller wins 51.2% of all games.

These numbers come from Jellyfish rollouts of REPLIES to opening rolls.
I have chosen only results where JF is forced to make the correct reply to
the correct opening where "correct" means JF rollouts give the highest
equity result to that play.  The standard deviations on the above numbers
are about 0.001 on the cubeless equity and 0.02% on the winning chances.
(These are only statistical uncertainties.  They don't account for the fact
that JF level-6 may be misplaying one side more than the other.)

I have not done such an extensive study of games where doublets are
allowed by the opening roller, since this is not the form of backgammon
that I play.  However, I just did a quick (432 trial) JFv3.0 level-6
cubeless rollout and the results (with standard deviations in parentheses)
was that opening roller has a 0.071(0.015) edge in equity and wins 52.5%
(0.6%) of all games.  From this it looks like, if doublets are allowed, the
edge to the opening roller is doubled.  (Pun?)  Since doublets occur only
1/6 as often as singlets, you can see that they are considerably more
valuable at this VERY EARLY stage of the game (which qualitatively should
not come as much of a surprise).

While visiting some Greek friends last summer I was told that in their
coffee-bar games, for a series of games the winner of the previous game is
(further) rewarded by being allowed to roll first.  You could also let the
loser of the previous game roll first, if you so desired.  (This would be
similar to basketball, and many other sports where the opponent of the side

The bottom line is that custom or tradition tends to dominate the
rules.  As long as both sides are playing under the same rules (and here I
include the assumption that both sides are AWARE of what rules they are
using) then there is no intrinsic advantage to one person or the other.

It is unlikely that anyone is going to convince US tournament players
(or online server players) to alter the current rules even this much
(i.e. alternate opening roller).  But lest anyone think we "Westerners"
are particularly hard-headed, how likely would it be that you could walk
into a Greek (or Armenian or Arabic or....) backgammon gathering spot and
convince them to change their rules?

Chuck
bower@bigbang.astro.indiana.edu
c_ray on FIBS
```

### Opening Rolls

At different match scores  (Louis Nardy Pillards, July 2002)
Average advantage of winning opening roll  (Chuck Bower, Oct 1998)
Choosing a strategy  (Daniel Murphy, June 2001)
Early game rule of thumb  (Rich Munitz, Feb 2009)
Factors to consider  (Kit Woolsey, July 1994)
How computers play  (Kit Woolsey, Mar 1995)
Magriel's Chapter 5  (Hayden Alfano+, May 2006)
Mloner vs Jellyfish  (Kit Woolsey, Dec 1995)
Nactating a whole game  (Nack Ballard+, Jan 2011)
Nactation  (Jim Stutz+, June 2010)
Nactation overview  (Nack Ballard, Oct 2009)
Nactation--Why use it?  (leobueno+, Jan 2011)
Opening 1's: Split or slot?  (Douglas Zare, Dec 2003)
Opening 21: Rollout  (Stick, Mar 2006)
Opening 21: Split or slot?  (Dick Adams+, Dec 2003)
Opening 32: Rollout  (Stick, Feb 2006)
Opening 43: In GOL online match  (Raccoon+, Feb 2004)
Opening 43: Pros and cons  (Stick+, Jan 2006)
Opening 43: Which split is better?  (Peter Backgren+, Aug 2000)
Opening 43: Which split is better?  (Michael J. Zehr+, Mar 1996)
Opening 51: Rollout  (Stick, Feb 2006)
Opening 52: Merits of splitting  (Peter Bell, Apr 1995)
Opening 53: Magriel's recommendation  (George Parker+, July 1997)
Opening 53: Split to 21?  (Alex Zamanian, Aug 2000)
Opening 53: Why make the three point?  (Kit Woolsey+, Feb 1996)
Opening 6's: Slot the bar point?  (Chuck Bower+, Feb 2000)
Opening 6's: Slot the bar point?  (David Montgomery, June 1995)
Opening 62: Could running be best?  (Gary Wong, Sept 1997)
Opening 62: Split, run, or slot?  (Chuck Bower, May 1997)
Opening 63: Middle Eastern split?  (Mark+, Apr 2002)
Opening 63: Slot the four point?  (Dennis Cartwright+, Mar 2002)
Opening 64: Make the two point?  (William Hill+, Jan 1998)
Opening 64: Make the two point?  (Darse Billings, Feb 1995)
Opening 64: Rollout  (Peter Grotrian, Jan 2006)
Opening 64: Split to 20?  (Peter Bell, June 1995)
Opening 64: Three choices  (Brian Sheppard, July 1997)
Opening 65: Becker on lover's leap  (Jeffrey Spiegler+, Aug 1991)
Opening 65: Computer rankings  (Chuck Bower, Jan 1997)
Opening rolls ranked  (Arthur+, Apr 2005)
Rollouts of opening 21 and replies  (Alexander Nitschke, Oct 1997)
Rollouts of openings  (Tom Keith+, Jan 2006)
Rollouts: Expert Backgammon  (Tom Fahland, Aug 1994)
Rollouts: Jellyfish 3.0  (Midas+, Sept 1997)
Rollouts: Jellyfish 3.0 level 6  (Chuck Bower, Feb 1999)
Rollouts: Snowie 4.1  (Rene Cerutti, Apr 2004)
Slotting the four point  (Joe Loria+, Oct 1999)
Snowie's openers and replies  (rcerutti, Feb 1999)
Splitting versus building  (Dave Slayton+, Aug 2000)
Splitting versus slotting  (Daniel Murphy, Apr 2001)
Splitting versus slotting  (Daniel Murphy, Sept 1997)
Trice's rankings  (Marty Storer, Feb 1992)