Things to Remember – Handy Rules and Guides

One of the things that I am struggling with is remembering all of the rules of thumbs, guidelines, etc. that I am coming across as I attempt to improve my game. So I decided to create a post that will expand as I collect more information, and hopefully find that it is helpful to me and others. Some of the items have been discussed in other places, but this is sort of a “cheat sheet” for trying to keep things in a handy reference. (And yes, I know, I am not posting much here as I seem to always be behind on my backgammon study)

Safe/Bold Criteria

Trice discusses this and I think I dealt with it in an earlier post, It is a guide for deciding whether to play safe or take more risk to gain a positional advantage.

The follow description of safe/bold criteria is taken from http://www.bkgm.com/articles/Townsend/BasicsOfBackgammon1.html

Here are some additional criteria for bold vs. safe play and how to interpret them:

1. Home board points. Relative strength in home board points allows for more aggressive play.
2. Anchors. One anchor vs. none allows for more aggressive play, this extends to:
   • Multiple anchors vs. single anchor.
   • A higher anchor vs. a lower anchor.
3. Blots in your home board discourage aggressive play (if you hit, they may hit you as they re-enter). Conversely enemy blots in his home board invite an exchange of hits.
4. More back men allow for more aggressive play, while counterintuitive, this is based on sound logic:
   • More than one man back can combine to form an anchor.
   • A single man back can only escape or be attacked.
   • A hit with only one man back may critically reduce your racing lead.

Other factors to be evaluated include outer board blocking points (especially points that block the escape of an enemy back man with 5’s or 6’s), blots exposed (the side with more exposed blots will wish to clean them up rather than expose more in many cases), and racing lead (lead discourages bold play).

The Last Two Checkers

Trice gives a chart of the number of the rolls that bears off one or two checkers at the end of game. Trice discourages memorization of the chart and supports learning to calculate the rolls. I find that – at least in online play—taking the time to calculate the rolls is a bit of an issue and my memory is not what it used to be.  While you have to know the number of rolls for doubling decisions there is a handy rule for determining how to place you checkers when playing. This will usually be where you have born off the 13th checker with half the roll and then must decided how to play the other half of the roll, for example if the have checkers on the 5 and 3 with a 1 to play should you move a checker from the 5 to the 4 or from the 3 to the 2.  To determine the best play use 3, 2, 4, 1, 5, 0 as a guide to determine how far apart to place you checkers, 3 apart being the best if possible, followed by 2 apart and so on. [Note: In a comment on this article Timothy Chow points out that an easier way to remember this is to place your two checkers as close to 2.7 pips apart as possible.]

So in the above example moving 3/2 is better than moving 5/4 because it places the checkers 3 apart rather than 1 apart.

For a nice chart of 1 and 2 checker positions and rolls to bear off see http://www.bkgm.com/articles/Koca/CuringYourShortBearoffBlues.html.

N-Roll Positions

N-Roll positions where the number of rolls to bear off without a double can be readily determined. This would be situations where there are checkers only the ace and deuce point, N being the number of checkers on the points divided by 2 and rounded up. For N roll positions the player on roll has the following chances of winning the game (rounded, cubeless):

2 – 86%

3 – 79%

4 – 75%

5 – 72%

Some positions that are not true N-roll positions will be very close, for example if you have 1 checker on the 3pt, 2 on the 2 pt, and 3 on the ace point you do not have a true N-roll position, but unless you roll 2-1 three times in a roll it is not going to matter.

Race Formulas

When there is not longer contact there are a variety of formulas that can be used as a guide to determine if you should double. None is perfect, but most are better than just guess. The two I use are:

Walter Trice’s Method which he discusses in Boot Camp:  I have rearranged it some to make it more formulaic, but this is the same logic:

If leaders pip count is > 62 Trice Number= leader count/10 + 1 round up

If leaders pip count < 62 Trice Number = (leader count-5)/7 round down

Count Difference = Trailer Count – Leader Count

If Count Difference < Trice Number  — Take

If Count Difference +3 > Trice Number – Double

If Count Difference + 2 > Trice Number – Redouble

Trice applies this formula to low wastage positions. In positions with higher wastage Trice applies the above to an adjusted pip count. In Boot Camp he uses the Ward count to make adjustments to pip counts but applies the decision criteria above.

Keith Count – Is the adjusted pip count method I use. The Keith Count works as follows:

Start with the raw pip count

add 2 for each checker more than 1 on the ace point

add 1 for each checker more than 1 on the 2 point

add 1 for each checker more than 3 on the 3 point

add 1 for each gap on the 4, 5 and 6

For player on roll add 1/7 of pip count (round down)

Once the above is calculated for each side

Keith Number = Adjusted Count for Player on Roll – Adjusted count for opponent

If Keith Number < 4 double

If Keith Number < 3 Redouble

If Keith Number > 2 Take

For an excellent discussion of the Keith Count as well as other formulas and race theory in general see http://www.bkgm.com/articles/CubeHandlingInRaces/

Bearing Off with Opponent on Bar But With Checkers Off

This type of position arises from a backgame, ace point game, or similar situation. You managed to hit your opponent and send them to the bar after they started bearing off. Now you are bearing off with the opponent on the bar and need to decided whether to bear off two checkers leaving a blot in your home board or to move to avoid the risk. Bill Robertie gives the following guidance for these situations:

The first metric we want to calculate is the crossover count. A crossover is simply a move of a checker from one quadrant to another, or from the bar to the opponent’s inner board, or from the inner board to the bearoff.

Next we employ the following rule of thumb:
>If you trail by two or less in the crossover count, play safe. You’re doing well enough in the race that there’s no need to take additional risks.
>If you trail by five or more in the crossover count, take two checkers off and leave a blot. You’re a big underdog in the race, and you need the extra checker speed.
>If you trail by three or four, you’re in a grey area.

In the grey area, decisions depend very much on the exact arrangement and count of checkers in the inner board. You next want to look at all of the following considerations and see if they point toward one play or another.
(1) If you trail by three crossovers, tend to play safe. If you trail by four, tend to bear off.
(2) If White has a blot in his board, tend to bear off. If no blot, tend to play safe.
(3) If taking two checkers off brings you to an even number of checkers, tend to bear off, otherwise tend to play safe.
(4) If you have a speed board, tend to play safe, otherwise tend to bear off. A speed board is one where Black’s home board spares are heavily concentrated on the one and two points, which implies that small doubles are more likely to bear off four checkers through the bearoff. With a slower board, where the checkers are spread evenly across points, small doubles often won’t save a roll.

The above is taken from a problem solution on the Backgammon Forum at 2+2 Poker Server. http://forumserver.twoplustwo.com/138/backgammon/problem-week-39-solution-651194/

Game Winning Chances When You Have One Checker on the Bar and Checkers Off

This is another bearoff situation where you have borne off several checkers and end up with one checker closed out on the bar. The following assumes that Red has a fast board (all checkers on the lower points) and white has the idea bear off position with a closed board and the spares on the 6, 5, and 4 pts. Then the cubeless winning percentages are:

% to win in reference positions
N off	1	2	3	4	5	6	7	8	9	10	11	12
Red	4.5	7	11	15	22	30	39.5	51	58	69	76.5	84
White	95.5	93	89	84	78	70	60.5	49	42	31	23.5	16
d		2.5	4	4.5	7	8	9.5	11.5	7	11	7.5	7.5

The last line shows the difference for red (the player on the bar) by having one more checker off than is in the top column.

This table can be used not only to aid in doubling decision but in  making decisions about the best way to play certain rolls that force you to leave a blot in the bearoff. It is taken from an article by François Tardieu in which he discusses using this information to make these types of decisions. The complete article can be found at http://www.gammonlife.com/writers/07tardieuart1.htm.

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