if a family member contests a will but is not listed on the will are they eligible for anything? what are the chances they will win the contest?

One of the requirements for contesting a will it that you somehow have a connection to the will and feel harmed by its contents. You either have to be named in the will but feel that you should have inherited differently, or weren't named in the will and should have been named in it, or would have received money if the person had died without a will.

You also must have a valid reason to challenge a will, such as undue influence, fraud, mistake, or loss of mental capacity of the testator.  Simply being upset with your inheritance amount isn't an actual reason to contest a will.

Quite frankly, will contests are difficult to win but without more details it's hard to say how strong a claim this family member can actually make.  You should consult a probate attorney in your area.

a lot of times the person that is not on the will is the one contesting the will because they did not get anything.  The person contesting the will has to prove that the will is invalid or that the person making the will did it as a result of some undue influence. Proving undue influence is not easy.  I unfortunately do not have enough facts to give you a definitive answer.  What i can tell you is that the person that wasd not named in the is probably not entitled to anything unless they can prove otherwise through witnesses or other documents.