[Insty]

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if I know for CERTAIN that my odds of beating an opponent in a showdown are exactly 50/50, and this opponent pushes all in ahead of me, are there any conditions under which I can call profitably.


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No. The best you can do is break even.

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I'd like to see a proof.


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I've managed to prove it for a winner takes all tournament. I can type this up if you think it would be useful.
It's a bit more complicated for a 5/3/2 payout structure, and I've not quite managed it yet.
Although I've simulated enough to be confident of the answer.

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As a corrollary to this problem, does the answer to this make sense given what we know about the relative value of chips in different sized stacks?

Ie - common tourney knowledge often suggests that calling with a suspected coinflip is wise if we have a huge stack in comparison. This is becasue the small stack's chips are worth more than ours and we may actually have pot odds to do so when considering the 'extra' value of shorty's chips.


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In the specified scenario it's never -ev to call when you have more chips than your opponent.
I thought that was interesting.

Insty.