Without reading the entire will to make sure there isn't another gift somewhere, I would be guessing. However, based strictly on what you quoted above, it appears that the will contains a serious error. If the person who created the will (the "testator") is still alive, I suggest s/he go back to the lawyer who made the mistake and have it rectified immediately!
If the "testator" is not alive, then the will will need to be submitted to probate. There are (at least) 2 possible outcomes:
a) Mike Smith can try to prove that there was an error in the document and that he is supposed to receive the "entire" residuary estate or
b) the 50% that does not go to Mike Smith will pass by "intestate succession" to the "testator's" nearest surviving relatives.... if Mike Smith is a half-brother and there are no other siblings, then it would appear (based on the information you provided) that he would end up with the entire estate.
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It does appear as if there is a serious ambiguity in that provision of the will, based on looking at the text you have provided. A petition to determine entitlement to inheritance could be filed to have the court decide what this language means, and who is entitled to a share of the estate.
I would recommend consulting with an attorney familiar with probate law about what steps to take. Certainly, if the testator is still alive, they should redo their will, or sign a codicil, to clear up any ambiguity.
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Janet and John are spot-on- no attorney can really answer your question without reading the entire Will. There's just too much information missing (and the additional language the poster "provided" really doesn't help because it's out of context) and, based on what has been provided, there appears to be a very large, extremely significant gap regarding the "other" 50%.
Spend the money on an hour of an attorney's time to review the Will. Also, keep in mind that, if you (or others) decide to probate the Will via an attorney, the attorney's non-extraordinary fees are set by statute, so you should be able to get a handle on potential costs upfront.
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Because the will is ambiguous (unless other will language that you haven't provided clears up the ambiguity), a court would have to resolve the issue if the will isn't changed while the testator still is living. Two possibilities that spring to mind are that the whole share for Mike Smith might go to his kids or half of Mike's share might go to his kids and the other half passes to the testator's intestate heirs. Most likely circumstantial evidence (such as the drafting lawyer's testimony and file notes) could shed light on the intent. Lawrence Friedman, Bridgewater, NJ. Certified as an Elder Law Attorney by the ABA approved National Elder Law Foundation, former Chair NJ State Bar Association Elder and Disabilities Law Section, Member Board of Consultors of NJSBA Real Property, Trusts & Estates Law Section, Vice Chair Special Needs Law Section of National Academy of Elder Law Attorneys, and Master of Laws (L.L.M.) in Taxation from N.Y.U. School of Law.
Is there a provision before that labelled "Specific Bequest" that says "I give 50% of the estate to Mike Smith's children" ? -- in that case the will is not ambiguous. Absent that, you need an attorney to help you parse the document and to petition to have the court interpret it. You may also have a malpractice claim against the drafting attorney for a "scrivener's error" -- and time is ticking on getting both straightened out. If you are someone left out you may have an argument that this gap has created an "intestate share" which would go to heirs-at-law of the decedent. Get a lawyer fast.