The Master Eye
As with all sports (with the possible exception of rifle & some types of pistol shooting), shotgun shooting is more straightforward when both eyes do the looking rather than just one. Two eyes see better than one and it is easier to ignore the barrels with two eyes open than with one closed. Keeping two eyes open gives the shooter one less thing to think about and it is more natural. Unfortunately, for various reasons this is not always possible.
The concept of Master Eye is an important one that must be determined at the outset. Quite simply, the Master Eye determines how the gun aligns with the target. Shooting from the right shoulder with the right eye as master the gun will align exactly with the target. However, should the left be the Master Eye then the gun will attempt to align with that eye. With the gun mounted in the right shoulder this will cause the gun to misalign to the left of the target. Similarly, should both eyes contribute equally to the task of alignment then once again the gun will misalign to the left.
With either of these problems there are several cures, the simplest being to shut the left eye early at the commencement of the shot, thus eliminating its influence. On the other hand, when the left is totally the Master Eye, and the right eye contributes nothing to the alignment process, then it is perfectly possible and preferable to learn to shoot from the left shoulder. Indeed for the beginner this will soon feel entirely natural and will allow two eye shooting. The third alternative, and not recommended (at least, not by me) is an S-shaped stock constructed with sufficient twist (known as cast-off) to bring the barrels directly in line with the left eye. This type of gun looks and feels awful, and if pride of possession plays a part in your gun ownership then these guns are best avoided.
There is one other problem caused by two eye shooting, and fortunately a rare one. This is difficulty with co-ordination. A few people, although apparently right eye dominant, find the timing of the shot difficult with two eyes open, and are also prone to firing oddly off-line shots, too. For these people one eyed shooting is the answer, and it will usually make an immediate improvement to their consistency.
So two eyed shooting is preferable where possible, but one eye shooting is no guarantee of poor shooting, far from it. World and Olympic Gold Medals have been won by single eye shooters who would have been struggling to make B Class had they tried to shoot with both eyes open. It can be fairly stated that any coach who insists that all his pupils shoot both eyes open regardless of whether it suits them or not does not know his job. I have encountered shooters who, while demonstrably left eyed, have been advised to shoot both eyes open and aim off several feet to compensate. This means shooting well to the right of straight targets, a long way in front of targets flying left to right, and behind targets flying right to left. This is, of course, complete nonsense and impossible to make work. If given this sort of advice ( except where it is intended simply as a one-off demonstration of just how far off line a left eyed shooter actually is) the best action is to quickly change coach.
Determining the Master Eye
Deciding this is of prime importance before embarking on your shooting career. It's not too difficult. To decide which eye leads simply tear an inch diameter hole in a sheet of card or paper (postcard size is about right). Pick an object in the distance and then quickly raise the card in front of your eyes. By alternately closing one eye then the other the lead eye is the one that sees the target object through the hole.
This process determines the lead eye but it does not mean that eye is totally in control of the aiming process. This can only be ascertained by shooting at straight targets with a straight-stocked gun.
The Under & Over Phenomenon
Many side-by-side shooters are obliged to use guns with stocks slightly off-set (cast) to compensate for minor misalignment caused by the eyes. Fortunately these same people can almost always use a perfectly standard over-and-under requiring almost no cast at all. This is probably due to the leading eye unconsciously picking up on the much slimmer profile of the O/U and eliminating the effects of the opposite eye.
Of all the basic requirements of good shooting sorting out which eye does what is without question the most important factor of all. Get this wrong and everything else is meaningless. Get it sorted on day one of your shooting career, or if that has long gone get it sorted now!