Board & tile games
No cards here, and no hidden information either. Everything is on the board in front of both players, which changes the nature of the mistake you are about to make.
Card games hide things. Board games mostly do not, and that single difference reorganises everything. There is no bluffing in Chess and nothing to deduce in Checkers; if you lose, it is because your opponent saw further than you did. That makes these games less forgiving and, for a lot of people, more satisfying.
Chess is the deepest game humans have designed with sixty-four squares, and it is genuinely unforgiving: one careless move against a decent opponent decides the game. Checkers looks simpler and is subtler than its reputation — compulsory captures mean the board can force you into a losing sequence you can see coming and cannot avoid. Reversi, or Othello, is the sneakiest of the three, because holding more pieces in the middle of the game is often a disadvantage; the corners decide everything and beginners spend twenty moves handing them over.
Backgammon is the exception in this group: it uses dice, so luck is genuinely present, and the skill is in playing the odds well over many rolls rather than calculating a single line perfectly. It is also the oldest game here by a wide margin, with recognisable ancestors in the Near East thousands of years ago.
Mahjong Solitaire is the odd inclusion — not the four-player Chinese game but the single-player tile-matching puzzle invented for computers in the 1980s. It asks for pattern recognition and a little forward planning, and it is by far the most relaxing thing on this page.