Another idiom that means the same thing would be "all at sea."
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The image is of flipping a coin and not being able to tell if it comes up "heads" or "tails." You say this when you can't figure something out at all, as in "I just can't make heads or tails out of this report; can you rewrite it so that it makes more sense?"It means that you cannot understand something. Some thing that is really tough to understand. Some thing strange.
Expirimental probability is when you use an expiriment to find the probability of a certain predicament. For example: Let's say you flip a coin 10 times. Before you flip you guess that you flip 5 heads and 5 tails or 1/2 heads and 1/2 tails. You guess this because one side is heads and the other side is tails so its an even risk. This is theoretical probability. When you actually do flip the coins you get, lets say, 8 heads and 2 tails. This would make your expirimental probability 4/5 heads and 1/5 tails. That is because you based the evidence on an expiriment rather than a guess. The longer the expiriment is, the more accurate your evidence will be.
It means just what it seems to -- someone tosses a coin up and you try to guess which side will be facing up when it lands. "Heads" is the side with the person's face on it and "tails" is other side.
This isn't an idiom because it's just one word that's confusing. The word "ace" in this sense is slang. It means to score highly or make a top grade.
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