Doubling in Running Games vs Backgammon

In running games, there are four types of doubling situations: last-throw situations, situations that can be calculated, no-miss situations, and formulaic situations.

Last-throw situation

If you’re in a last-throw situation, where your opponent is guaranteed to bear off on their next turn, you should double if you have an advantage. The following scenarios are the closest:

• When you have one checker on your five-point and one on your two-point, you should double because you have 19 winning rolls and 17 losing rolls.
• you only have 17 winning rolls and 19 losing rolls.

Understanding Other Calculable Situations in Running Games

When you have either one checker on your eight-point or one checker on your four-point and one on your three-point, you should not double because

The category of “other calculable situations” in running games can be somewhat subjective and depends on the level of effort one is willing to expend. Achieving a highly accurate answer may require calculating the outcome of up to 1,296 games, a convenient number because it is 36 x 36. However, this level of calculation is not practical or feasible during the game itself. Instead, it is something that can be done at a later time if one wishes to know what to do if the position arises again.

While most players may not be interested in this level of analysis, there are still some relatively simple situations that can be worked out with ease. These can offer valuable insights into the best possible moves, and can be especially useful to intermediate and advanced players seeking to improve their skills.

In the diagram provided, there are 19 throws out of 36 that can result in a win for you. While you may be tempted to double if Black’s one man was on the one, two, or three points and bound to come off in one throw, it’s important to consider the overall situation. If you miss and Black has 27 throws that get him off and nine that do not, he will win three-quarters of the time when you miss. If you double him, he will double you back and you’ll have exactly one chance in four of winning. Therefore, it’s immaterial in the long run whether you accept or drop.

If you assume you will drop, you will lose the game on all those 17 throws out of 36 when you fail to bear off in one throw. However, if you had not doubled, Black could not have redoubled you and on average, you would have won one-quarter of those 17 games, in addition to the 19 you won by bearing off on your first throw.

In essence, doubling may seem tempting since it can result in winning twice as much when you do win, but it’s not worth it in this scenario. If you don’t double, you’ll win more than 23 games out of 36 and lose less than 13. Therefore, it’s advisable not to double as the advantage of winning twice as much is far outweighed by the extra games you win by not doubling.

No-Miss” Situations in Backgammon: An Overview of a Highly Advantageous Position

No-Miss” situations in Backgammon occur when both players have all their checkers on the 1-point, or most of them on the 1-point and the rest on the 2-point, with one or two checkers on the 3-point. In such situations, it is highly likely that any dice throw will bear off two checkers, and any double will bear off four checkers. To determine the appropriate strategy, the following simple rules apply:

• If you need one less turn to bear off your checkers than your opponent, without throwing doubles, then double your opponent.
• If both sides need five turns to bear off their checkers without throwing doubles, then offer the first double but do not redouble.
• If both sides need four, three, or two turns to bear off their checkers without throwing doubles, then doubling or redoubling is appropriate.
• If you need more turns to bear off your checkers than your opponent, then refuse any doubles. If both sides need the same number of turns, then accept if that number is 4 or more, and refuse if it is 2 or 3.

Formulaic Situations in Backgammon

In running game situations, a formula is necessary to make the right decision. There are two formulas, one for those who prefer a simple approach and the other for those who are willing to invest more effort.

The easy formula involves doubling Black if their pip count is 10% or more than yours. If Black doubles you, you should take it unless your pip count is 15% or more above theirs.

For more accurate decisions, here is the most precise formula for running game doubles. As White, follow these steps when deciding whether to double:

1. Calculate your pip count.
2. Calculate your adjusted pip count by adding two pips for each man you have left, one pip for each man on your one point, and subtracting one pip for each point where you have a man in your home board.
3. If your adjusted pip count is 25 or more, add 10%. This gives you the ‘doubling number’, denoted as ‘D’.
4. If Black’s adjusted pip count is D-1 or higher, offer them a double or redouble. If it is between D-2 and D-1, offer a first double but not a redouble.
5. If Black offers you a double, accept if your adjusted pip count is less than D+2. Otherwise, drop.

While this approach may seem complex, it’s not as challenging as it appears. By using this formula, you can play better than 99% of players in this area and feel confident in your decisions.