Set over Set?

Theoretically, should I lose my entire stack if I have a lower set than the villain after the flop? I know this is a very broad question but any answers would be appreciated.

yes, unless you get lucky and straight or flush possibilities kill action.

Generally yes. Obviously there are situations where the answer would be no, but in the heavy majority of the time, you should be stacking with a set, and if they have a higher set you just got unlucky.

pretty much yeah uless the flops a scary one

Like Zach said - in a set over set situation, if you're holding the lower set then yes, you should be expecting to lose your whole stack.

The odds of it happening are 100:1 or something like that so you shouldn't be in the habit of folding your sets fearing a higher one and as a result... the hundredth time, yes you will go broke.

There are some situations where I guess you can get away from them, like if it's a very draw-heavy board and there are a couple of other players who you know don't bet without the nuts raising hard... but even if they've flopped a straight or a flush you've still got outs to a boat, and the chance that the could have, say, TPTK and a draw will still make it a difficult fold for me.

Yeah like I folded my set with 66 to a 689T board with 3 hearts when villain overbet shoved lol. As mentioned though it's first off villain dependent, second off board dependent and of course stack sizes as well. But in general, especially on the flop, if you have a set, you should never dislike getting your stack in. Even if the flop is like 3 in a row all of one suit the times when villain has a combo draw outweighs the times they have the straight/flush and even when they do you have outs to improve to a boat.

Example, not sure I did this right but basically 678 all hearts flop and villain will shove with a set, made flush or straight, or else 2 overs with the flush draw. This may be a bit wide because QJ with Jh may not shove just because they could be drawing dead but that cancels out the A5 with Ah type hands. Also just did the numbers with 66 instead of 88 (and giving villain the possibility of having 88). Even with the set over set possibilities, we have a 55-45 edge.

equity win tie pots won pots tied
Hand 0: 57.427% 55.92% 01.50% 100212 2691.50 { 8d8s }
Hand 1: 42.573% 41.07% 01.50% 73595 2691.50 { 77-66, AhKh, AhQh, AhJh, AhTh, Ah9h, Ah8h, Ah7h, Ah6h, Ah5h, Ah4h, Ah3h, Ah2h, KhQh, KhJh, KhTh, Kh9h, Kh8h, Kh7h, Kh6h, Kh5h, Kh4h, Kh3h, Kh2h, QhJh, QTs-Q2s, JhTh, Jh9h, Jh8h, Jh7h, Jh6h, Jh5h, Jh4h, Jh3h, Jh2h, Th9h, Th8h, Th7h, Th6h, Th5h, Th4h, Th3h, Th2h, 9h8h, 9h7h, 9h6h, 9h5h, 9h4h, 9h3h, 9h2h, 8h7h, 8h6h, 8h5h, 8h4h, 8h3h, 8h2h, 7h6h, 7h5h, 7h4h, 7h3h, 7h2h, 6h5h, 6h4h, 6h3h, 6h2h, 54s, 5h3h, 5h2h, 4h3h, 4h2h, 3h2h, AcKh, AdKh, AhKc, AhKd, AhKs, AsKh, AcQh, AdQh, AhQc, AhQd, AhQs, AsQh, AcJh, AdJh, AhJc, AhJd, AhJs, AsJh, AcTh, AdTh, AhTc, AhTd, AhTs, AsTh, Ac9h, Ad9h, Ah9c, Ah9d, Ah9s, As9h, KcQh, KdQh, KhQc, KhQd, KhQs, KsQh, KcJh, KdJh, KhJc, KhJd, KhJs, KsJh, KcTh, KdTh, KhTc, KhTd, KhTs, KsTh, Kc9h, Kd9h, Kh9c, Kh9d, Kh9s, Ks9h, QcJh, QdJh, QhJc, QhJd, QhJs, QsJh, QcTh, QdTh, QhTc, QhTd, QhTs, QsTh, Qc9h, Qd9h, Qh9c, Qh9d, Qh9s, Qs9h, JcTh, JdTh, JhTc, JhTd, JhTs, JsTh, Jc9h, Jd9h, Jh9c, Jh9d, Jh9s, Js9h, Tc9h, Td9h, Th9c, Th9d, Th9s, Ts9h, 54o }