The impact of gammons on backgammon doubles is significant and should be taken into consideration when deciding whether to accept or reject a double. In situations where a gammon is possible, accepting a double and losing the gammon can result in a loss of three points, as opposed to a loss of one point for losing a single game. However, if there is a 50% chance of winning and a gammon is the downside risk, accepting the double would result in losing four points once and winning two points once, leading to a balance of losing two points, which is the same as refusing the double. Generally, if the chance of winning the game is equal to or greater than the chance of losing a gammon, then accepting the double is recommended. Otherwise, it is advisable to drop the double. It should be noted that in practice, the situation is usually more complex and there is a possibility of losing only a single game even if a gammon is lost.
The previous section on doubles in backgammon towards the endgame emphasized the importance of accepting doubles even when the odds are against you. However, in the middle game, the average player should exercise caution before accepting doubles. Beginners often fail to consider that a seemingly favorable situation can quickly turn into a losing gammon. While there is no definitive rule to determine whether accepting a double is the right move, it is helpful to consider whether you are more likely to win a single game or lose a double. With experience, you can develop a better intuition for these situations. In this section, we provide examples of common positions and guidance on what to do. This will not only help you in those specific situations but also teach you how to approach other positions.
A Guide to Holding Game Doubles in Backgammon
In this section, we will examine the strategy for doubling in common situations where one player has a high anchor game, meaning they have moved all their back checkers out while their opponent has established an anchor on either the 4-point or 5-point.
Let’s examine Position 1 where Black has moved his checkers from the backgammon board while White is holding the 5-point anchor. Black is trying to advance his checkers towards his home board while avoiding leaving any blots for White to hit. White is aiming to hit any blot that Black leaves or win the race by rolling higher numbers than Black. Though Black has an advantage, White still has resources. The question is, should Black double?
Before answering that, let’s consider the pip count, which is the total number of pips or points left to bear off. Black’s pip count is 119, and White’s is 131, meaning Black has a 12-pip lead, representing roughly 10% of his pip count.
In a straight race without the possibility of hitting a shot, a 10% lead would be enough to double. However, in this position, White has a chance of hitting a shot, and he typically has a better bearoff position than Black. Hence, Black’s winning chances are below 70%, and he does not yet have a double.
In high anchor holding positions like this, Black requires more than just a minimal racing lead to double. To determine how big a lead Black needs, let’s examine Position 2.
Please examine Position 2.
In the current position, Black’s pip count is 119, and White’s is 139, giving Black a lead of 20 pips or approximately 16% of his pip count. In a straight race, this lead would justify a double from Black and a clear pass from White. However, Black’s lead is not quite large enough to force a pass from White in this high anchor holding position.
Despite this, White still has a clear take due to his combination of racing and hitting chances, which give him a winning probability of just over 25%. Furthermore, White is highly unlikely to be gammoned from this position, meaning he can take as long as his winning chances remain above 25%.
If Black wants to force a pass from White, he will need a bigger lead. To explore this further, let’s consider Position 3.
Please examine Position 3.
Position 3 is similar to Position 2, but with two of Black’s checkers moved from the 13-point to the 3-point, increasing the pip count to 99 for Black and 139 for White, a lead of 40 pips. One would think that this is an automatic pass for White, but surprisingly, it’s still a take. Black’s winning chances are only slightly better than Position 2, by about 1%.
The reason for this is that Black gains in one asset (racing chances) but loses in another asset (timing) simultaneously. While Black is now less likely to lose the race, they are more vulnerable to being hit as they try to clear the 13-point. These two assets move in opposite directions at roughly the same rate, resulting in similar doubling and taking decisions for both positions.
In most 5-point holding games like these, White has a straightforward take, and Black needs a lead of about 15% in the pip count to make a good double. By keeping these rules in mind, you can avoid making errors with the cube in these common situations.