Life Saving Drug Situation

Using 5 doses for 1 person is ethical: you have the control and you use it to ensure he lives.
It is 100% that he lives, or 100% that he dies. That is a conscious decision in itself that shouldn't be taken lightly.

Assuming you take the option for 100% he dies, then you RISK a chance to live for the remaining 5 people.
You would be saying to 1 person, that they will die 100%, and the remaining 5 will have 20% chance to live.
Firstly, I doubt you'd be okay with a 20% (or wha-dever) chance to live, with the only other option being an unknown (death 100%? we don't know).
Second, this basically means that 5 people might live, or absolutely none will - that is the risk.
So when risking it, the choice is a guaranteed choice, or something that may end up significantly better, or just as easily significantly worse.

The remaining 5 people aren't given a 100% chance of death, meaning that giving all 5 doses to the 1 person is a better choice, as "100teath" doesn't exist in this option for any of them - you aren't making a decision to kill (or let die) anyone.

You could argue that the chance for 5 people to live is "worth it"; worth what? Worth that 1 person's life? Is it okay to condemn someone to death because of a CHANCE to save more numbers? The odds are against it anyway, and math proves that you're likely to come out to the same number of people saved regardless.
So why risk saving anyone? There is a chance you can save 5 people (worth), but you're likely to save 1 person (expected), but you're also potentially not going to save anyone at all (not worth).

When given a choice to definitely save 1 person, leave 5 to wha-dever may happen (death isn't certain - but even if it was, so is saving 1 life) OR to risk is and MAYBE save 1, 0, 5, 3? who knows how many....
The choice is to risk or not to.
Are you willing to play the game of chance with such a situation?
Funny thing is people gamble with worse chances all the time - look where that gets them.

I would most assuredly just save the 1 person - it's something that is known, not unknown; 100% success rate.
Better than telling someone that they will 100tie, and the rest that they have 80% chance of death too.
Another way to look at it is: why would you allow the possibility of all 6 dying? I don't even allow it to be an option.

6 people. (1 person lives 100%, 5 die 100%) or (1 dies 100%, 5 live 20%)
This, like you say, is a choice between guaranteed 1 person living, or leaving it up to chance where on average 1 person lives. (5 people taking a 1/5 chance)

101 people. (1 person lives 100%, 100 die 100%) or (1 dies 100%, 100 live 1%)
This again proves that on average, 1 person will live no matter which decision you choose. (even if there were 100 treatments)

So the question then is, do you decide to risk that 1 person survival rate, for more.
Telling 100 people they have a 1% chance to live...
You can go to a casino and figure out that thousands of people can play a game with 1% chance to win before someone wins (without any rigged game or machine).
Chance, randomness, is supposed to exactly define the unknown and/or unpredictable elements of something.

This means you're just as likely to have 0 survivors as you could have 2 survivors, let alone 3. 

Check this out:


A script to test the chances for 100 people. On the last few tests it happened to catch up, and the last test 4 people survived, just to reach the expected result out of the arbitrary number of tests chosen to take. (100 tests)
Try it for yourself and see: jsfiddle.net/ecb1kyn2/
(keep in mind that this test is for the remaining 100 people out of 101; 1 already died because they can't get the 100 treatments you are risking with the 100 people for 1% chance to live)

But after writing this script, I did notice something:
If you're just as likely to get 0 as you are 2, then in the scope of (0, 1, 2), there is a 2/3 chance to have a winning result.
So I ran the test a few more times, in groups of 3 to see the results:
1) 5 people / 3 tests = 166.67% 
2) 3 people / 3 tests = 100%
3) 2 people / 3 tests = 66.67%
4) 8 people / 3 tests = 266.67%
5) 4 people / 3 tests = 133.33%

So now I'm fairly convinced that either my script, or randomness, isn't accurate, or that I should risk it every time. :s