Just buying *two* tickets most significantly increases the probability of winning--from 1/292M to 1/146M. That's the best bang for the buck. The increases drop from there.
Wrong. Using your math, all you would have to do is buy around 40 chances and you odds of winning would be about 2-1.
Instead of 1 chance in 292M a second ticket only gives you 2 chances in 292M. Buying 40 tickets gives you 40 chances in 292M.