I understand with a cutting board that mixing grains is a bad idea - the board goes through wet/dry cycles everytime is is used then washed, and people often only wash the used side of the board and lay it flat to dry - i always instruct the recipients of my boards to wash both sides equally and stand it up to dry.
and i have been told by those that make a lot of cutting boards that putting a cross grain border is a bad idea - and i get it - and i have made several dozed end grain and an equal number of face'edge grain boards. but no borders......
so i have made a chess board with a border. i am told it is going to crack. period. there are people who say they use cross grain borders with no problem. seriously two totally opposite sides to this.
BUT:
consider this:
1) a chess board is not going to get wet. pretty much will be inside a controled climate all its life
2) cutting boards dont get a finish. just oil. so water penetrates deeper when wet, and humidity as well.
3) i realize polyurethane is not a complete seal, but 3-4 coats of poly equally on all sides of the board will seal the pores somewhat and reduce the amount of moisture, how much who knows, but clearly it will seal better than no finish as well as better than just mineral oil. so its is sealed somewhat and will never get wet.
so my point is if it takes x amount of moisture to cause y amount of movement that will fail, then x/2 amount of moisture will not cause enough movement to cause failure.
i have also had some say that maybe it wont crack, but there will/may/could be other movement such that you will feel the joint if one side swells/shrinks - like a little lip - and i could live with that.
also consider that only the ends - in this case the walnut - borders are cross grain. the maple on the side is parallel to the face grain of the board
so wondering if anyone has any experience to share considering all the above - please see photos to illustrate my description
the basics: 1.25" thick, walnut and hard maple, though i also sumetimes use white oak and ash, squares are 2.25", total dimensions about 21x21". all glued with TBIII