The type of dice used can meaningfully impact this. The chance of a 2 or 12 rolling 2d6 is 1/36, the chance rolling 1d8+1d4 is 1/32. The chance of rolling 7 on 2d6, the most common result, is 1/6. The chance of rolling a 5, 6, 7, 8, or 9 on a 1d8+1d4, all equally likely, is 1/8 each.
Unlike you I can’t begin to remember the elegant way to find this. I also assume Randall would have it at least close to right.
A family in that sort of situation has considered many options. Willing the house to the brother is the easiest, the poster and their mother have reasons for opting against it. They are likely good reasons; in the broader sense, willing property to someone who cannot care for it can in many scenarios be a bad idea.
It’s dangerous to assume the brother would be safe from predation if he owned his home; the poster could do a lot worse than just not paying the bills. This person apparently lacks the ability to pay taxes and ensure proper maintenance. Even just to help with that, the poster will need access to their brother’s banking and tax info. If the brother is compliant it would not be difficult for someone to take advantage of that situation.
Alternately, using their legal ownership of the home the brother could potentially shut the poster out and might actively sabotage efforts to maintain and pay for the home. In that case the property could suffer substantial damage, become dangerous/uninhabitable, or even be lost despite the poster’s efforts. Many people have destructive tendencies.
The more certain way to protect the house for the brother would be to place it in a trust, but that’s not a panacea. Setting up an ironclad trust to prevent selling the house is great until the brother can’t get up the stairs, or the whole family decides to move to Canada, or the brother goes into assisted living, or the property value skyrockets. A trust will also have tax implications and potential costs that need to be considered.
I assume and hope the mother has been advised by a decent estate lawyer on their options. There are scenarios where willing a house to a sibling is the best course of action. I wish the poster luck and hope they’ll act in the interest of their brother for their entire lives.