It depends on the table. A Diamond has deep shelves which adds another dimension to the difficulty. 4.5" pockets would play pretty tough. If you are talking about a Gold Crown I which doesn't have shelves as deep as a Diamond, I would say 4.25" to 4.125" would play pretty tough. 4.5" on a Gold Crown I may play pretty easy.Thinking a table used mainly for 9 ball and 8 ball. For argument sake say a Diamond.
3 7/8...j.k. I would have a 3 7/8 GC, I would have a 4.125 diamond. I think that's perfect, but I love tight tables. I just played at Griff's and they have a really tight diamond blue label. I think it was 4.25. It was good, so I might go as loose as that.
I liked your post so muchFor roughly 550 and below Fargo players who are not likely to improve much over time for whatever reason, 4.75 or 5 inch corner pockets might be the way to go. Too much tighter and you may find that it takes the fun out of it. For 550-650 players, 4.5 inch pockets strike a pretty good balance where it is tough, but the game hasn't been dramatically altered too much like it can be with smaller pockets where cheating pockets and certain shot options becomes more limited, more cinch pool gets played, and the games get less offensive and turn a bit more defensive, etc. For 650 and up players, 4.25 to 4.5 inch pockets depending on personal preference and what you are after.