How can I win big at the casino in Dragon Quest VII?

Like with many games of chance, in RPGs, your best best is going to end up being save-scumming. Meaning: Keep playing the games of chance and saving when you win, then reloading when you lose. This can take a lot of times, however, so it's up to you as to how long you wish to keep this up, for.

A guide written by David Fisher at gameskinny.com has some other information that could prove beneficial in the casino, of this particular game.

Note that a key point of this guide is to select Pilgrim's Rest [Past] as it allows for closer access to a priest (for saving) and several advantages over the [Present] version, which are discussed at length in the guide.

The main point of the guide describes buying a nominal amount of coins and using those to play Lucky Panel over and over until the coins run out, and then selling the proceeds. (Lather, rinse, repeat.) He also suggests that if you do wish to play the slots, make sure to use the machine on the far right as it has, inherently, better win chances due to having 2 chances to win, instead of the 1 that other machines have.

The strategy suggested for the Lucky Panel game involves simply using your first six free selections to clear up the top of the board, and writing down what you see, so that you can more easily solve the rest of the board. The main point of this is to select those cards consecutively, so that it's easier to divide the board in half, in your head.

If you didn't run into matches in those, then it assumes that the lower half of the board will have your match. Like all card match-up games, however, it's purely chance, and you'll have just as much luck selecting anything, as long as you write down what you found. By revealing the tiles in order, you simply help to avoid revealing the same tile, multiple times, wasting your limited number of card picks. (Watch someone play these games, randomly, sometimes, and you'll see that revealing the same card once, twice, three times, or even more, is common.)

Note that if you do end up, by chance, finding several matches in the first two rows, then you're back to pure chance on the lower rows, since you don't know where their pairs are.

He does emphasize to avoid finding the match for the shuffle card, however, since it will ruin all of your notes.