About the moves reduction
The moves reduction forces the opponent to waste his moves to eliminate the gaps in his chains while you eliminate the gaps in your chain (figure 1). The forcing means that the opponent has no choice, i.e. otherwise it will worsen the position of his dots (figure 2).
The aim of moves reduction increases the chance to encircle your opponent. By reducing the moves in remote areas of your chain you can improve the situation at the end of the chain.
Figure 1 - The gaps are formed during the struggle between chains (left), the attacking red chain performs the moves reduction, so the blue chain has to close the gap (center), the attacking red chain gets less moves to encircle the blue chain (right)
Figure 2 - The gaps are formed during the struggle between chains (left), the attacking red chain performs the moves reduction but the blue chain doesn't close the gap (center), the red chain penetrates through the blue and encircles it, then the blue chain rescues from encirclement the end of the chain (right)
Both players close the gaps in their chains. So you should reduce the moves when you have more chances to encircle the opponent earlier in the situation of mutual encirclement. Then you need to take care of protection of your dots from encirclement (figure 3).
Figure 3 - In a situation of mutual encirclement the blue chain has fewer moves to encircle the opponent (left), the red chain performs the moves reduction but it gives an advantage to blue chain to complete the encirclement earlier (center), the right choice for the red chain is try to break the blue chain at the weakest dot and escape from the encirclement until it is too late (right)
Ways to reduce the moves
The moves can be reduced by creating a threat to break the opponent's chain or capture its part. This can be done using standard attacking techniques: forks, nets and dummy dots (figures 4-5).
Figure 4 - The blue chain makes the moves reduction using the threat of fork. So the red chain has to fortify itself. The number of gaps in the blue chain is reduced by one. The number of gaps in the red chain remains the same (gif animation)
Figure 5 - The red chain makes the moves reduction using a threat of encirclement through the possible net in the blue chain. So the blue chain fortifies itself. The number of gaps in the red chain is reduced by one. The number of gaps in the blue chain remains the same (gif animation)