Chess was never a game that sat well with Shepard. She really should have known what was likely to happen when Specialist Traynor invited her to play a game. The movement of the pieces and rules just didn't make sense to her. It was just too limited in certain ways for her to become comfortable enough with the game to excel at it.
That wasn't to say that she was terrible at all strategy board games. Most of the crew from the original Normandy had found that out the hard way.
There had been numerous occasions where no one could locate the Commander, only to find her and Urdnot Wrex of all people sitting on the floor of the cargo bay bent over a go board. No one else quite understood the game or the level of play the two were at. Garrus would, at times, wander over and try to divine what the hell was going on in those rapidly changing patterns of black and white, but inevitably gave it up as a lost cause. Kaidan knew enough of the rules to understand the basics, but the two would play kikashi on each other so often that even he couldn't tell who had the upper hand at any given moment until one of them threw their hands up in defeat.
Everyone eventually just accepted it as a thing that sometimes happened on the ship, and it really wasn't worth the headache of trying to do anything about it. That included everything from trying to stop it to trying to participate and especially trying to introduce the two to another board game about strategy.
(There was an incident where a crew member down in Engineering brought out a shogi board and taught Shepard and Wrex the game.
The game was subsequently banned after no one saw the two of them for three days and Anderson had called about five times trying to figure out where his wayward Spectre went and why she wasn't returning his calls. Joker used the threat of leaving out a copy of Risk in the cargo bay for months to get out of milk runs.)
After the SR-1 was destroyed and Cerberus brought her back to life, Shepard found herself missing those games. No one on the SR-2 played, and the goban and stones stayed buried in a drawer in her cabin. At least, they did until one night on Tuchanka. The crew had been going fairly hard for awhile, and after dealing with Maelon, everyone was pretty much emotionally drained. Wrex made a comment, and Shepard decided to call a short shore leave. It wasn't where a lot of the crew would have chosen, but it was better than nothing, and once the alcohol started flowing, no one really cared that they were on Tuchanka.
It was in the midst of an impromptu party that had started up (never underestimate the power of alcohol) that Samara looked around and realized that she couldn't find either Shepard or Wrex. Neither of them were near the bonfires or the kegs of alcohol, which was where she expected to find the two leaders. It had been quite a surprise to find them in a quiet corner, calmly drinking and heads bent over a wooden board and small white and black stones. They had both looked up briefly, then returned their attention to the board when she merely smiled and walked away.
So when Wrex was on board the SR-2 for the War Council, no one who had served on the ship at any point before was at all surprised to find him and the Commander sitting in the mess with a go board very late in the day cycle. (Chakwas, who was forever on a mission to make sure Shepard actually slept, just shrugged and said she'd count the Commander actually relaxing as a minor victory.) What was surprising was when another go board appeared in a corner of the mess with bowls of stones and a single black stone on the board.
On a whim, when she passed the board for the third time, Shepard placed a white stone. When she came by an hour later, another black stone had appeared.
Shepard never knew who she was playing against as the game continued. If she had to guess, it'd be one of the new Alliance crew. She never made it a point of finding out who her rather good opponent was. Something else was always more important, and honestly? She's kind of afraid that finding out who it was might scare them off. It's one of the small things she looked forward to in her day, and even if she didn't get a chance to make a move because the galaxy is demanding her attention that day, her opponent was always waiting for her next move, ever patient.
The game finally ended right before the Battle for Earth. Shepard cleared the board and put the stones back. She's about to walk away when something stopped her. She placed a black stone down on the board.
After the battle, after the Reapers stopped their attack, after everything, the board and single black stone were still in their corner, still in their opening move.
No one touched the board again.