There is no "the lottery" but I'll talk about the one I know about without googling, the Powerball. Its grand prize has a chance of 1 in 292mil and it has some smaller prizes. The 2nd prize is 1mil with a chance of 1 in 11.7 mil so it's irrelevant (the 2nd prize doesn't help you because even if you bought many tickets, there is essentially zero chance of winning the 2nd prize ten times.). $4 buys you 2 tickets so your chance of winning 10mil is 1 in 146mil (though you'd win much more than 10mil).
Now to blackjack. Assuming you only played basic strategy and didn't count cards, your chance of winning 10 million in blackjack would be even worse than the Powerball unless you could request a table limit of 400k or not far from it.
The table limits are key because your chances would be maximized by wagering as much as possible in an attempt to reach your target in as few hands as possible. Without table limits your chance would be in the order of 1 in 13 million, but in reality there are limits which would severely hurt your chances.
We can get a ballpark estimate of your chance by treating each hand like a 46.36% coinflip (no splits, doubles, blackjacks or pushes). With a 400k max wager you'd want to go all-in until $525288, then start betting 400k each hand. This would give you a chance of .4636^17 * [1 - (5364/4636)] / [1 - (5634/4636)^25] = 1 in 113 million. (I can explain this calculation if a geek reading this is interested.)
But a max wager of 100k would reduce your chance to 1 in 1.4 trillion!
I don't know how realistic it would be for you to be granted a larger wager than 100k. If you told them your plan was to turn $4 into 10mil in as few hands as possible starting with a freshly shuffled shoe, they might grant you more freedom than a typical player. I'm guessing the largest limits are to be found in Macau.