Abbreviated wheels are mathematically designed to arrange a group of numbers into lines that guarantees secondary prizes. The logic of using a 3 if 3 wheel is to match 3 of the numbers and have a 3 number match. There is also the possibility of matching 4 or 5 numbers and having more 3 number matches, a 4 number match and/or a 5 number match.
"Logic is mostly a 'if this then that" scenario."
The logic is the conditions we set and the math is what we should expect by meeting the conditions. A 3 if 3 of 15 numbers wheel has 57 lines so that must be compared to other 57 line bets. The odds against any 57 lines having a 3 number match in MM is 5.37 to 1. By setting the conditions that 3 of the 15 numbers will match, we can get a guaranteed 3 number match by "if this then that". Since only 18.6% of any 57 lines will have a 3 number match, the 3 if 3 wheel will slightly improve the chance of winning a jackpot over 81.4% of any 57 lines.
"Every game probably has its "own" special logic formulas, and what works for NY will not always work well for OH. However I am sure some of the underlying random principles apply for both states."
If both are 5/39 games, a 2 if 5 of 39 numbers wheel eliminates the random factor. The results of a like number of drawings probably shows about same amount of numbers being drawn more than average. By successfully using some of those numbers in smaller groups of numbers, the effect would be slightly improving the chances of winning a jackpot in either game.
The answer to "Can math and logic improve chances of winning a jackpot?" depends on what we are comparing it with.
Mathematically, by playing more lines, we're slightly improving our chances of winning a jackpot compared to playing 1 line. By playing a 2 if 5 of 56 numbers wheel, there is always a 2 number match so that in effect slightly improves the chances of winning a jackpot compared to any 46 lines and certainly more than by just playing 1 line. Use each of the 46 bonus numbers and the 46 lines are guaranteed to be part of the 2.5% of all tickets winning a prize. That effect lowers the cost of play by at least $2. Doesn't sound like much, but the same bet can be made 24 times for the same cost of making 23 bets.