Millions of Americans have been angry at big Wall Street banks ever since the financial crisis. Having taken huge government bailouts at taxpayers' expense, they turned right around and tried to levy a bunch of new fees on their customers, including Bank of America's (NYSE:BAC) ill-advised attempt to lift debit-card fees to $5.

But living well is the best revenge. In that spirit, let me point you to the best single way you can beat big banks at their own game: Take advantage of big rewards on the credit cards they offer.

What the banks want
You don't have to do much digging to find lucrative rewards on credit-card offers. Capital One (NYSE:COF), Bank of America, and Citigroup (NYSE:C) all have offers that provide $100 bonuses after you spend $500 on purchases during the first three months you have your account. American Express (NYSE:AXP) currently offers a $150 bonus on it Blue Cash Preferred card if you spend $1,000 during the first three months. And JPMorgan Chase (NYSE:JPM) goes a lot further, as one of its consumer cards offers 40,000 points for those who can spend $3,000 in the first three months, while a business card offers 50,000 points for $5,000 in spending. Those points are worth $400 or $500, respectively in cash, or 25% more for airfare or travel spending.

The reason banks offer you all this money just to take a credit card from them is that they expect to earn back everything they pay out and more over the course of their relationship with you. Between the merchant fees they collect from the businesses where you use your card as payment and the interest, late charges, and other fees that most people end up paying regularly, big banks have run the numbers, and they're not stupid. On average, banks will prove to be the big winners in these deals.

What you want
But even though most customers might end up on the losing side of the stick, you don't have to. That's because you don't have to give the banks what they want. Instead, aim for what you want: to maximize your rewards while giving the banks as little revenue as possible.

To do that, you need to do three things:

  • Find credit-card deals that give you substantial upfront introductory rewards, preferably with minimal requirements to earn them.
  • Meet whatever requirements the card companies impose to get your reward.
  • Pay off the card bill immediately, taking advantage of the grace period to avoid interest charges.

Whether you keep using that card depends on whether it continues to give you ongoing rewards that are attractive compared with its peers. For instance, some cards keep giving you cash back on your purchases, with higher rates often applying to purchases in various categories. If taking advantage of those rewards is worth whatever annual fee you'll have to pay to keep the card, then continuing to use the card makes sense. If not, then you can move to another card and repeat the same process.

Worth the hassle?
Getting new credit cards just to reap big rewards does come at some cost. Frequently opening and closing card accounts can have a modest negative impact on your credit score, even if you never make late payments and stay current on those accounts. Moreover, eventually, banks catch on to customers who aren't profitable for them, and so you might no longer get exclusive offers that pay you large cash rewards to open further accounts.

Nevertheless, the pleasure of beating Wall Street banks at their own game is worth almost as much as the hundreds or even thousands of dollars in card rewards you can collect following this strategy. It's not for everyone, but for many, the payoff is worth the effort.

Fool contributor Dan Caplinger owns warrants on Bank of America and JPMorgan Chase. You can follow him on Twitter: @DanCaplinger. The Motley Fool recommends American Express and owns shares of Bank of America, Citigroup, and JPMorgan Chase. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.