It does not exist, but its vaporware form does not preclude those from seeking it. An "optimum" pattern percentage, of course, cannot exist either, as a 60% pattern is of "what"? A 60% pattern of 3/4 oz .of shot, or of 1-3/4 oz. of shot? And, what type of shot? Pellet selection for upland game is discussed in a bit more detail here: http://www.chuckhawks.com/pellet_size_upland_game.htm

Patterning a shotgun is the only way to really get a clue: http://www.chuckhawks.com/why_pattern.htm A 20 gauge 1-5/16 oz. load can, and has, outpatterned a 1-1/2 oz. 12 ga. load, and even a 2 oz. 12 ga. load as you can see. If you patterned, and discovered this for yourself, you'd never hunt with an "unpatterned" combination again.

Nevertheless, choke recommendations are endlessly made and remade, ignoring actual results. It is results that matter, not what a choke tube is marked, but we've known that for far too many decades. Sometimes, feathers may fly but the bird is just crippled or flies away. We may wonder why, but usually it is because just won't pattern our gun and don't want to think to too deeply. Feathers are not critically vital organs. A bird may be DOA with little feather disruption, yet lightly crippled with a perceived puff of them. Autopsies are tough to do with a lost bird.

However, the quest for the single "best" shotgun choke tube seems unlikely to go away. So, I will offer a suggestion, not because it is the best choice, or the "optimum" choice, but because I'm confident only that it is not the worst choice. If you don't have one, you need to try a Trulock Precision Hunter in "Skeet 2" constriction.

Theoretically, a "Skeet 2" provides half a notch better performance (patterns) than an Improved Cylinder choke, at the theoretical constriction of fifteen thousandths and the theoretical pattern efficiency at 40 yards of 55 percent. Another name attributed to "Skeet 2" is "Light Modified."

This is necessarily theoretical as constriction is defined from actual bore diameter, which varies. The quality of the shell directly affects patterns, and that of course varies by specific shotshell. Nevertheless, though I completely confident that this recommendation is wrong, it is the least wrongful choice that can be made.

There is some basis for this selection; the rationale being one of versatility. Skeet 2 is certainly not the ideal skeet choke for all guns; yet few of us shoot for a living. It is sufficient to go out and have fun on the skeet field, and for those who believe in a challenge it will likely prove to be at least marginally more challenging than a .002 - .003, as measured, skeet choke.

For sporting clays, it is another reasonable choice. Skeet 2 gets you somewhere in the vicinity for the majority of shots on the majority of courses. For casual five stand sporting clays, it is enough tube to have fun with from the 16 yard line.

For flushing upland game over dogs, it is a reasonable choice. For steel shot, that theoretically patterns a full choke notch tighter than lead, it gets you in the ballpark for decoying ducks.

All chokes have tighter centers than fringe areas. So, if you are perfectly on the bird, it can take you out farther than you might think. As long as we all insist that our paces all equal exactly one yard, maybe is really is good enough for government work. Using heavier payloads in quality shells may give us similar pattern percentages, but the same percentage of a higher pellet count is rarely a bad thing.

An extended choke tube, like the Trulock Precision Hunter, as a broad generalization, may offer a better pattern distribution (less patches) than a factory flush mounted tube. It may also do a better job with heavier payloads of shot, and larger shot sizes. It will also increase your effective barrel length a small amount, with a correspondingly tiny increase in muzzle velocity.

There is certainly no substitute for patterning several shells at 40 yards. However, George G. Oberfell & Charles E. Thompson (The Mysteries of Shotgun Patterns) found value in 10 yard patterns, showing that 10 yard patterns indicate expected results at 40 yards. Oberfell & Thompson patterned at 10 yards, counting the pellets OUTSIDE a 7 inch circle, mapping the relationship between that and 40 yard conventional results from 45-75 %. The fewer the pellets outside that 7 inch circle, the better. Using this quick and dirty method, comparing your Precision Hunter Skeet 2 to your factory IC or Modified tubes will likely surprise you.

So, that my best recommendation for a choke tube. It is wrong, of course, just like I promised. It is just the least wrongful suggestion that I have for "The One Magic Choke Tube."