Anticipation can be a postive or negative depending on what your horse is anticipating.
If you bring your horse to the mounting block and mount, but he takes off like a shot when you are half way into the saddle, he is anticipating the next move in the riding routine. Block, mount, leave.
If, on the other hand, he anticipates a coming action when he feels the slightest signal from the reins, and he prepares for some yet-to-be-requested action, his anticipation is a good, measured response. Current action, signal, prepare for cue. Perform.
Paired Cues: When a negative outcome is garnered for a particular response (ie: bit pressure for a high head), an animal will begin to avoid the response or find one for which a reward is offered (ie: avoidance or release of bit pressure). If the principle of paired cues is employed, body cues, leg cues, crop cues employed simultaneously all begin to signal the coming negative outcome (bit pressure). The animal will no longer wait for the negative outcome if it can be avoided by listening to the preceding cues. Thus BVB (Body cue; Voice cue; Bit cue:) turns into BV. Further it turns into very subtle B as experience grows and timing is refined.
Good training instills a readiness (measured anticipation) in your horse at all times in your presence. A horse who is “light” to the cue is always ready to perform.
If your horse anticipates in a negative way (the Block, mount, leave horse), his routine has probably gotten too … well, routine. He needs to have the routine made fresh with unexpected requests or a substitute maneuver in place of the anticipated “bad” behavior.
In the case of the “eager” horse at the mounting block, you should move to the block, mount, and stand … just stand. You can either do this enough times that you “extinguish” the rapid take-off altogether with a new anticipation (standing) or you should intermix the two routines so that the horse cannot anticipate whether you will leave or stand.