this is one of those things that looks kinda complicated, but really isn't. everytime you drink, you have a 1/3 chance of dying, so you should only drink once.
the math:
if you drink first, you have a 1/3 (2/6) chance of picking the death bottle. and a 4/6 chance of not. half of those times (2/6), your opponent will drink the death bottle, and half the time you will in round three. so, you die 2/6 + 2/6 times, or 2/3 times. your opponent dies the other 1/3 of the times.
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