The fallacy of gray is a common belief in people who are somewhat advanced along the path to optimal truth seeking which claims, roughly, that because nothing is certain, everything is equally uncertain.
One who commits this fallacy may reply to the statement that probability of winning a lottery is only one in a million by saying: "There's still a chance, right?"
This fallacy makes a lot of sense once people notice very common and predictable emotional swings proximate to a possible attachment to an emotivist ("boo vs yay") or binary ("black and white") labeling of an entity, or situation, or system, or choice.
If someone says "Hurrah for X!" then X can often be attacked by saying that X is just kind of blah.
If someone says "Down with X!" then X can often be defended by saying that X is just kind of blah.
Either of these "blah" assertions could count as the fallacy, if that was the totality of the argument.
This fallacy is possible because it really is the case that a variety of ambiguous signals can exist in proximity to a complex object, and there truly can be a mixture of positive and negative aspects to any given thing in the world, and also objects can have aspects that might be instrumentally useful or harmful to different plans whose total net value is not entirely determined by any single local factor.
Also, a very normal response to complexity like this is for cognitive dissonance to lead the person to have some single simply up/down association... to achieve cognitive closure swiftly. People might call this tendency a bias towards certainty.
Then, knowing this bias exists, someone who wields the fallacy of gray can score debate points on people with a simplistic binary attitude, without seeming to strongly or obviously take sides.
This does represent a kind of progress or increase in power levels.
However, in calling the fallacy of gray a fallacy, some even better thing is imagined.
The better thing, simply put, is to become quantitative and detail oriented.
A VNM rational agent will have probabilistic beliefs, p, where 0<p<1, about what's likely to fall out of various choices, and a coherently linear model of value, v, with no behaviorally significant "natural zero". Then every option is basically assigned the value p*v, and the agent simply always make choices in favor of what the agent calculates gives the most utility, under uncertainty.
Suppose there is a choice between
something with p*v = -1,000,000 net utility under uncertainty or
something with p*v = -1,000,001 net utility under uncertainty...
...then the VNM agent simply chooses the option that is greater, or "less negative", and picks -1,000,000.
The negative sign, and all those zeros... that is just in the math.
The VNM agent feels no psychic cloud of badness because of the negative sign, or because of how big the number was.
If you want to insist that a natural zero in some resource (like a bankroll) does somehow exist in the territory, then you could put "the possibility of zeroing out the resource" in your map of the possible futures, and then model the consequences of having zero of that resource including all the long term cascading consequences into deep time, and then recover a linear ordering over outcomes that just happens to assign much relatively lower values to scenarios where the state of the system included having zero of some import resource with a natural zero at some point... But the utility score here is not "objectively lower" (like a big number with a negative sign), but rather it is relatively lower (like much lower than other options).
To say that someone is using the fallacy of gray is to say that despite not saying Boo or Yay, even so they are still speaking as if the people party to the discussion are only capable of emotive associative reasoning, not actual calculation in pursuit of any kind of detail-oriented assessment of options and trade-offs with costs and benefits that could be tallied coherently.