OK, first, Poisson distribution.
Second, a "trial" is one spin of each wheel; so, a trillion spins.
Third, for a trillion spins where the probability is one in a trillion, the expected value is one; that is, the most likely outcome, if you examine a trillion random events looking for a particular configuration with a probability of one in a trillion, is one.
There is a 37% chance that you will see zero, and a 37% chance that you will see one; and an 18% chance you will see two. There is a 6% chance you will see three, and a 1.5% chance you will see four.
What you're trying to do is say that there is only a slightly more than 1/3 chance of seeing a particular configuration of an event in a trial if the number of events in the trial is equal to the reciprocal of the probability of that configuration; but that is incorrect. What you REALLY want to know is, "if the number of events in a trial is equal to the reciprocal of the probability of a particular configuration of an event, what are the chances that I will see NO such events in a particular trial?" And the answer to THAT question is, 37%. There is therefore a 63% chance that you will see AT LEAST ONE such event in any given trial.
ETA: and apparently Myriad and RecoveringYuppie agree.
And here is a nice little calculator to play with.