Pike come into their own against Kn and enemy foot. Against "missile-mounted", they are vulnerable and that, surely, is as it should be?
4-deep Pike vs Cv or LH is no different to 4-deep Sp of the same grade vs Cv or LH. It can be a tar-pit, as Toby opined earlier in this thread, but Cv(S) against (I) Sp/Pk can plow through in about 3-5 pairs of bounds if it gets lucky. (This is where paying extra for the Pk(X) would be worthwhile!)
Cv(O) or lesser against Pk(O+) is potentially a waste of both sides' time - but since the model is of the Cv throwing/shooting things at the Pike and the phalanx's response being limited to charging out and shoo-ing them away, it's not that unreasonable.
The way to try to force a result (for the Pike) is to be as aggressive as you can. In your bound, keep advancing into combat anywhere where you have, or can hope to manufacture, an overlap. Don't be afraid to stick a column into a hole in advance of its mates, even though the pals won't follow-up to catch up and you're probably conceding an overlapped (or double-overlapped) element next bound. What you're trying to do is force the Cv to repulse, or even better to spend elements (at least it gets them off the table). At 4:3 or 4:2 (don't forget you only get overlaps if your bound or it's side-edge to side-edge in the Cv bound) it's a slog but you will do it. Once the enemy line is broken up, it'll cost him a fortune in PIPs to get them all back in again, so your casualty accretion will generally slow down. And once you start punching holes, you can force columns into his (generally lower quality) reserves, flank the Cv elements that don't repulse/recoil (at 4:4 basic there will be plenty - you actually want to get results where half of the Cv get pushed away/spent and the other half win their fights!) so that you can kill them or even get around behind the Cv if the enemy is foolish enough to be without a back line.
It may seem counter-intuitive, but a decent width (6 or more) of Pk/Sp faced with non-impetuous Kn or Cv ought to get first charge in if they can - they hope to break up the enemy line and that the enemy will not then have enough PIPs to get all their elements back in.
I've not tested with Pk, but with Irr Sp(I) vs Cv it's generally a long slog but on even AP:frontage honours are about even. Reg Pk would be easier to force the overlaps with (less PIPs to turn) but cost more ME each time you have an unfortunate result.
Tim Child