Felt for the back of a wooden board?

I would like to apply green felt to the back of my 50-year-old wooden 21" Drueke chess board. I used the board a lot as a kid and in college in the 70s and 80s. I haven't used it much over the past 30 years, but recently caught the chess bug and bought a nice set of pieces for it. I play with the board on my dining table, and would like to protect the table and board from scratches. Can anybody recommend a source for adhesive green felt? I looked on eBay and Amazon, but only found sheets and small sizes. I'd like to be able to cut a piece 21" square, not a patchwork. I presume that adhesive felt is the way to go. Or should I glue non-adhesive felt fabric to the board? (Also, is this a good idea in the first place? The board is hardly in mint condition, as I played plenty of games on it and no doubt spilled beer and pizza on it in my youth. I've used some liquid scratch remover polish to make it presentable again.) Any advice would be appreciated. Thanks

How much felt are we talking about? The whole 21X21 or just in the corners? My suggestion is to not felt to whole bottom of the board. Go to Walmart and get some of those self adhesive thick black or khaki colored pads and place these of the corners of the board. Works really well and you can protect both the board and table with very minimal material used. Keep it simple. 

I agree 100% with HaveRum and  Knightsfork on the minimalist approach of using felt rounds on the corners of the bottom of wooden chessboards. My Drueke style board from Brad at Colorado Wood Worker over at Etsy was made without any felt protection. I obtained my felt rounds from the same website from a company called "Flower me Boutique" which sells a multitude of colored felt round swatches in various sizes to choose from. They come without adhesive but a good wood glue applied thinly will do nicely for this purpose. Those felt rounds in coffee color (#59) are 2" in diameter. Here is the link to the felts and the 2 photos as follows. The reason for the difference in light variations is because the first photo was taken with artificial soft white lighting and the second with natural daylight which gives the appearance of showing 2 different boards, it's just the lighting. FYI. As follows;

https://www.etsy.com/listing/183740962/felt-circles-2-1-color-16pcs-felt-circle?ref=shop_home_active_68

The wood ultimate chess set is on the board.

The underside of the board with the coffee-colored 2" diameter felt rounds. 

Thanks, folks. After reading your advice, I decided to use four adhesive felt rounds. I had some felt floor protectors for the bottom of chair legs that work well.