What's the Name of That Book??? discussion

This topic is about
Yahtzee Croshaw
SOLVED: Adult Fiction
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SOLVED. Adult SF Short Story. Man wakes from cryosleep aboard spaceship. Ship AI is being cryptic and directing him to do odd things. Finds another crewmember, a woman, seems to be an empty clone. She dies of a mystery illness. Spoilers. Read in 2010-ish.
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Solved! It WAS by Yahtzee Croshaw after all! And it was a short story on his website from way back in 2006 called "The Hopeless Endeavour".
The board game, predictably, was Battleships.
The ship's crew is infected with a virus. The man is a clone of the last member, cloned in a state where he is just about to die from the virus, so every time the ship wakes up a new clone of him, he will only have a short time before he dies.
The ship AI has decided that the way to stop the spread of the virus is to destroy itself before the ship docks. However, the AI is unable to ask for its own destruction, so it is trying to give hints to the man to start the self destruct sequence without saying it directly.
In the end, the man and the AI play a board game (possibly chess), and the man realises what the ship wants. However, he succombs to the virus before he can set off the self destruct. The ship then wakes up a new clone of the man and immediately asks him "Would you like to play a board game?".
I read this around 2010, and it was either an ebook or (god help me) on a website. If so then I know there's a very slim chance of finding this. I thought it might be by Yahtzee Croshaw but I was wrong.
Thank you very much in advance!