I would say that the probability of any specific person finding a 1977 dryer coin is low, but the chances of a quarter falling out of a pocket and getting lodged between the drum and wall of a dryer for an extended period of time isn't as low as you would think (look at the number of coins @paddyman98 posted in an earlier pic). When you consider the number of people who carry quarters in their pocket, and the number of people that do laundry, the number of times per week they do laundry, the hundreds of millions of quarter that are minted each year and the it's been 41 years since you coin was minted, it wouldn't seem unreasonable for numerous 1977 quarters to have this type of damage. In addition, dryer coins tend to have raised rims and are smaller in diameter. I've seen many other quarters that only have the reeding worn smooth. Until recently vending machines, slot machines, payphones, and laundries relied on coins. Drop a quarter down a slot and its edge impacts another coin or metal component in the collection box. Do that enough times and the reeding along the edge wears down. Based on that, I would estimated that there are a lot of others in circulation, and it's not unusual to see multiple examples posted on coin talk
My 1977 quarter says in cod we trust. Where can I sell it lower than everyone else asking so it goes fast?
Well, you are welcome to show pictures but it sounds like you have a minor filled die. This wouldn't really carry any kind of premium.