I went through divorce in equitable distribution, and I ended up with the best case scenario - I not only did not have to sell the house (a condo in my case), but did not even have to buy XH out. But I had a lot of factors working in my favor, not the least of which being that XH was an idiot. (Yeah, I could probably be a lot more diplomatic than that, but if you heard the whole story, you'd probably be saying it too - everyone else has.)
In my case, we got divorced just as the housing values were starting to go up - our condo had gone up in value somewhat, but the value hadn't really shot up yet, fortunately for me. I had been paying for pretty much everything for years - the mortgage, the bills, the credit cards - he wasn't even giving me as much as a roommate would have, even though he made decent money. He didn't make as much as I, but it wasn't a drastic difference either. All his money had been going into running around on me, though I didn't know it at the time.
What's more, he had run up a whole lot of debt behind my back. When I talked to the lawyer, she said all the debt I had been paying, even if it was in my name only, since it was in support of the marriage, would be both of our responsibilities. All the stuff I didn't know about, since it was in support of his infidelities, would be his responsibility only. So, I took what the condo was worth and what our joint debts were at the time, and pointed out to him that if he insisted on getting half of the condo, he would also get half the debt, and he would end up owing more than he would get from the condo, plus the lawyer bills to fight it, and that the lawyer said all his debt didn't count, it was all his alone. Convinced him to just let me keep both the condo and the debt and not have to fight it through court to make it cheaper and faster.
I'm glad I did too - if I hadn't, we probably would have ended up in court right about the time the value of the condo more than doubled. Eeek!!!
I also had the advantage that he had been .... well, I don't want to go into details of what he had been doing, suffice it to say that he shouldn't have been doing what he had been doing, he needed money to fix it, and the only resource he had left where he could get the money was a loan from his Thrift Savings Plan (Federal employee version of a 401K). Since we were still married, he needed me to sign my approval to get the loan, since I still technicall had an interest in his retirement. Part of what we were agreeing to in the settlement was that we would each keep our own retirement (I'm also federal and have my own TSP), but I absolutely refused to sign it until our settlement agreement was signed and in place, assuring me that the condo was mine, that he couldn't claim any of my retirment, etc. I wasn't about to let him take out a loan that would basically gut his TSP without guaranteeing he couldn't touch mine first! He was ticked, but he had put himself in a very bad position, he needed the money very badly and very quickly, and he signed the settlement agreement.
So, in my case, circumstance and an XH who did some really stupid stuff helped me out a lot. What the lawyer told me when I first started out was that equitable distribution generally meant 50/50 split, but that it didn't HAVE to go that way. And that more than anything, you don't want to let it go to the court to decide it, you want to work things out with your STBX, and present the court with the settlement all worked out already. So what happens with the house will depend a lot on what you want, what your STBX wants, and how well you can compromise together. (Or, if you get as lucky as I did, how well you manage to hold him over a barrel.)
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P.S. I guess I may come across as being somewhat vindictive about the divorce and the settlement, but.... the factors that were important in it were that for about half of our 10 years together, he had contributed a small portion to the financial part of the marriage - maybe 1/4 at best. For the other half, his salary steadily increased, yet the amount of his contribution steadily decreased. When the A, the separation, and the D all came about, I got mad, and vowed I was not about to let him take all my hard work for all those years and just give it to that white trash "mouth" which, in my eyes, he'd already been stealing from me for. I felt he had contributed as little as he could over those years, so he should leave with as little as possible too.
But I doubt I would have gotten even close to what I ended up keeping if we'd had to have a judge do the dividing up. I kept most of the stuff in the house too. That's why settling out of court is a good idea. Less legal costs, and you're both more likely to come out with what you want.