BHN, Brinnel Hardness Number, is a number on the Brinnel hardness scale. A sample of the material tested is indented by a hard spherical ball of specified diameter with a specified force, and by the diameter of the resulting indentation, a formula gives you the BHN, which goes up as diameter goes down. The
Wikipedia explanation appears to me to be correct.
How hard you need for game is not as simple as giving a number. It is true that some hard alloys, linotype for example, cast too brittle for bone breaking, but that's not just because of the hardness, but also because of the particular alloy's structure. Veral Smith told how he had believed wheel weights, hardened as need be, were fine for all cast bullets until he moved to Idaho and found they shattered on bone in cold enough weather.
A general rule of thumb that has arisen is that if you keep the antimony down to about 2% (about half what a wheel weight usually has) then you can likely avoid shattering. However, such an alloy has to be heat treated to achieve the kind of hardness you have been talking about. Wheel weights, after all, are only around BHN 10-11 as cast. Losing half the antimony makes it less. But if you heat treat you can get back into the 20's. At that point the only other additives to be considered are tin and arsenic. Arsenic is needed for water hardening to take and stay, which is why chilled shot has a fair amount of it. Tin helps castability, but if it exceeds the amount of antimony, the hardened bullets lose their hardness more quickly over time.
So, if you want a hard bullet for hunting in all weather conditions, you probably need an alloy that is about 2% antimony and just under 2% tin and at least 0.2% arsenic. I've heard a quarter percent silver will help improve castability further, but haven't tried it. Then you need to heat treat to get over BHN 21 or so. It can take a couple of weeks after the quench for full hardness to be reached, so have patience there. Over time, whatever hardness you start with should fall to around BHN 21 and stay.
If all that alloy specification seems daunting, I would just cut cast wheel weight alloy 50:50 with lead, toss in 1.5% by weight silver bearing low temperature lead-free solder, and see how it does? There is some arsenic in wheel weights to start with, so you likely will have enough for water hardening with no added effort. If that proves untrue, try adding about 5% by weight of the extra hard magnum chilled shot to bring it up a bit.
