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SaidAchmiz comments on The Least Convenient Possible World - Less Wrong
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I'm not sure if I'm evading the spirit of the post, but it seems to me that the answer to the opening problem is this:
If you were willing to kill this man to save these ten others, then you should long ago have simply had all ten patients agree to a 1/10 game of Russian Roulette, with the proviso that the nine winners get the organs of the one loser.
What if one or more of the patients don't agree to do this?
Then you let him die, and repeat the question with a 1/9 chance of death.