The three-drop rule of thumb
If by the end of your third turn you cannot see a path to a pure sequence, take the first drop. The expected value of dropping after the third draw is positive on almost every hand, regardless of what the closed pile is offering. The deadwood you would have accumulated by turn ten is higher than the 20-point penalty.
When middle drop is correct
Middle drop is correct when you have drawn cards but the geometry of your hand has worsened. Examples: you drew a fourth high-value face card, you drew a duplicate of a card you already held, or you watched two opponents pick from the discard pile the cards you needed. The penalty is 40, but it is still cheaper than the 80-point full count.
Dropping in Pool vs Points
In Pool Rummy, dropping is even more powerful than in Points, because the deadwood you save carries forward across deals. A 20-point first-drop in Pool keeps you well below the 101 elimination threshold. The conservative player stays in the Pool for longer; the aggressive player runs out first.