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The diabolo should make a big round around the sticks, starting from down, going left then up and back down. Try to do that, there will a small knot in your strings.

In order to escape from this, you must make a round around the left stick with your right one. Hold the right stick with your two last rigth fingers. Make the right stick approach the left one. with your index (your first finger after the thumb) and your thumb, take the right stick from the other side of the left stick. (your last fingers are above the the left stick, thumb and index are above.)

for fluidliness, think about pointing the right stick toward the diabolo.