Yeah, that's not what I meant. I did not mean to discourage you from trying, just trying to put you in the right direction.
Lemme rephrase that:
If you could do a strategy with the odds you are expecting, you would design a very efficient error correcting code. There's a thing called Hamming bound preventing that. Non-trivial cases when one happens to reach that bound have been mapped out since the 70s (for prime alphabets, so including binary). Mathematical proofs. One class is the one I gave you in the spoiler above. The other works for larger n.
In basic terms, every bit of information you add is another entropy generator that messes up the cases. Only in perfect settings one can separate entropy in different "jars" efficiently.
P.S. All of these codes are used in every bit of technology you currently use.