But the effect of pushing one card closer is much smaller than the effect of skipping it. If, for instance, you're playing a no-trash sea hag game, and the only way you can really afford a province is on a tactician turn, playing sea hag while their tactician is not in the discard is probably a good idea. Even if hitting another card is N times more likely, skipping the tactician is probably more than N times as impactful. One mistake people make when analyzing stuff like this is assume everything is linear, but it's not.
Your first sentence is true but misleading, because it doesn't take into account the likelihood of each of those things happening. It's like lottery odds. Say you get 9,999 people to put $1 in a lottery. One name is drawn, and winner takes all. Should you pay $1 to join the pool (bumping the pot up to 10,000)? Well, the effect of winning would put you up $9,999 instead of down $1. But you've only got a 1 in 10,000 chance to win, while you've got a 9,999 out of 10,000 chance of losing. It's a zero-sum game.
Arbitrarily cycling an opponent's deck is like that. You stand a remote chance of hurting him badly, and a great chance of helping him slightly. It averages out to even, UNLESS you know something about the quality of his draw pile vs. the quality of his discard pile. Only then might arbitrarily cycling have a net positive or net negative effect.
A few ways you can have some clues about an opponent's draw and discard piles:
* What cards he's purchased since the last shuffle. Greens or no?
* Have Rabble attacks hurt the quality of his deck?
* Did the purchase of an Inn improve his draw pile?
* Have you been counting his cards and noticing what he's discarded since the last shuffle? (Your Tactician example falls into this category; I'm not disputing that.)
Lacking any information like this, though, cycling arbitrarily will break-even over the long run.