We're presuming that your home will be worth more later, that it will appreciate faster than inflation, and that no one discovers a toxic waste dump in your back yard. These scary things are not common but they have happened to people in your position.
If you're planning on selling the home someday, then you should count the home equity. If you think that you're riding the razor's edge on portfolio survivability, then take out the home equity and see if your retirement portfolio is adequately capitalized without it. That way the home gives you an equity cushion.
Reverse mortgages are only available to those 62 & older and they're not that common so their origination fees tend to be higher than other financing options (like a HELOC). Here's a Dollar Stretcher article
on the subject from Sep 2002. The article has HUD links for more research; HUD regulates these mortgages quite tightly to avoid fraud on the elderly.
The payout is based on the mortgager's actuarial estimate of your life expectancy. If you live longer then you "win", but once you die your heirs will either have to sign the home over to the mortgager or pay off the balance. That decision may be up to the mortgager but I'm not sure who has first claim to the equity. It probably depends on the wording of the contract.
It's not uncommon for private European investors to pay annuities to elderly homeowners in the hope that the homeowner dies before the annuity is wiped out. One of the world's oldest women died in France at, IIRC, the age of 122. The investor that sold her annuity paid it for thirty years before he died (and she outlived him for another decade).
Your best bet may be a HELOC or selling the home and moving to a cheaper place.