You are standing in a forest and have just eaten a very deadly mushroom which will kill you in a short while. Fortunately magic frogs inhabit the forest of which a lick on the female frog cure all ills, while the male frogs do nothing but croak (the females do not croak). The females and males look identical and the probability of a frog being born a male is $50\%$.
You spot a frog at a distance ahead of you. Before you start running towards it, you hear a croak behind you. As you turn around, you see two frogs. You only have time to run and lick either the one in front of you or the two behind you. Which direction should you choose?
The question was inspired by watching a TED-Ed Youtube-video on it, and the solution is obtained by conditional probability, where we get a $1/2$ chance of survival if we run to the sole frog, while the survival probability is $2/3$ if we run to the two frogs behind us (the two frogs may be Male + Female, M+M and F+M, of which two of the cases guarantee survival).
Is everything fine? Is suggested solution and arguments absolutely clear? Or do you have some kind of dual thoughts? And if you do, but everything seems to be right, why can't you fully admit it?
Let us now imagine that at the same time our lucky guy that have just eaten poisoned mushroom hear male croak another lucky guy (probably his friend) eat another poisoned mushroom and he is looking at the two frogs and he see which one is croaking - so he knows which one is male. Obviously now our sharp-sighted friend doesn't care where he gonna run, because he has a 1/2 chance of survival in both directions. And as he doesn't care he can choose to run with his friend and what happens then... one of them is going to die with probability 2/3 and the other with 1/2? And if we repeat this experiment pure second guy gonna die much more just because of knowledge about which one is male??? Jeez... Mad, mad world! =) What is wrong with my thinking here?