A raw October day is no match for the warmth of Ashley and Nicholas Ritchie’s home in Brewster.

They bought a three-bedroom Cape last year for just over $240,000 — far less than market value — through an affordable housing lottery.

The house has a woodstove and a cathedral ceiling in the living room and plenty of natural light, and it’s on a quiet street where their three young children can play.

“We really lucked out with this neighborhood,” Ashley said.

With Barnstable County median sale prices in the 700s, the Ritchies couldn’t find something on their own that worked for their family. So they decided to try entering lotteries for deed-restricted affordable homes.

Homes that carry wealth restrictions written into the deed — and must sell below market value — have become an appealing

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