Gavier looks to have covered the ground with a good answer, but can I suggest it's well worth learning how to set up your 4-jaw independent?
Self-centring 4-jaw chucks aren't anything like as popular as the independent type because independents can do much, much more. They can grip odd shapes and align work to spin accurately on any centre, as needed to turn ovals or bore precisely placed holes.
Setting them up is indeed a bit of a faff but it's surprising how quickly it can be done after the operator has put in enough practise. For some reason, 4-jaws are only supplied with one chuck key which makes aligning the job much harder. Far better to use two keys in opposition. Make one if necessary.
Briefly, assuming it's round for simplicity, gently grip the work in the 4-jaw as close to centre as your eyeball permits, perhaps using a centre in the tailstock or the jaw markings to get near. Then mount a DTI to measure the job's horizontal displacement, put a pair of opposite adjusters level, and turn the job through 180° to find how far out the job is horizontally. Use the two chuck keys together to push the job sideways as necessary to halve the difference. Repeat until the centre is correct on both sides, but probably not up and down. Don't overtighten the jaws. Once the job is centred horizontally, turn the chuck through 90° and do the same with the other pair of adjusters.
Check the true centre has been found by turning the chuck through 360° whilst watching the DTI. When centred correctly, shown by the DTI barely moving as the job turns, tighten up taking care not to disturb the setting.
Measuring with a DTI is convenient for centring round objects, but much the same technique works on irregular shapes, where the centre is defined with a centre-pop or other reference. Basically the job is rotated and tweaked with two keys until the centre point stops moving against some reference. It may help to reference the point against a fixed centre in the tailstock, or with a tool in the tool-post, but it can also be done with shims, or any other aid. Old-time turners did it with a stick of chalk.
With practice the process completes surprisingly quickly, and it has the advantage of being more accurate than any self-centring device. There are guys who use 4-jaw independents for everything because it takes longer to change to a self-centring chuck than it does to align work very accurately in a 4-jaw. If stranded on a desert island and only allowed one chuck, a 4-jaw independent is by far the best choice.
Can't claim myself to be super-quick, but I cracked my faff problem by spending a couple of days doing nothing but adjust various lumps of metal in my 4-jaw. As with parallel parking I'm not brilliant at it, but my 4-jaw is conquered! Practise, practise, practise…
Dave
Edited By SillyOldDuffer on 15/03/2021 09:21:23