# How can a casino offer 99%+ RTP plus 1% cash back?

So I am checking out a legal, regulated casino and they have video poker with over 99% RTP (return to player) games. And then I also noticed they have a deal where by loading funds using a credit card you get 1% cash back on it. If you loaded the funds using their credit card method and say for example played a video poker game with 99.54% RTP wouldn't that make for a total 100.54% RTP and you could actually make money playing video poker ? Am I missing something ?

You are doing the math correctly.

• Start out with \$100.
• Get 1% cash back, so essentially you have \$101.
• Now, 99.54% RTP, gets you 0.9954 * 101 = \$100.54

So, on average every \$100 you play, you would make 54 cents. (It's far more likely that RTP is closer to 99%, in which case, the result is \$99.99, but let's say it's really 99.54%) According to an article from WizardOfOdds.com, this is not unheard of.

On the face of it, this sounds like a money making machine. But you have to keep in mind...

• How long does it take to "play" \$100? If it takes an hour, you're "making" 54 cents an hour. This doesn't seem like a particularly profitable means of making money. Even if it takes 5 minutes, you still are only making \$6.5/hour.
• How much are you spending to make this money? You may get free drinks, but probably you'll be purchasing food at some point. How much is that going to cost you?
• Are you good enough to actually achieve that kind of return on the game? The makers of the game can easily make it so complicated that no humans can actually play well enough to achieve that kind of payout level. There is a game mentioned on the Wikipedia article for Video Poker that has a payout of 100.1. But with the caveat that no one can play it well enough to achieve that....
• Do you have enough capital on hand to "ensure" you make money. Consider the following 99% game. (It's not video poker, but the point is to illustrate the idea.) You win \$1,000,000 with probability 1.99e-6, or you lose \$1 with probability (1 - 1.99e-6). How many times on average do you need to bet in order to win? You need to bet on average \$500,000 in order to win once. So, in that game you have to have \$500K cash on hand "on average" to win. This is an extreme case, but even for more "reasonable" games, the numbers are still in the favor of the house. You will go broke, before you hit the big money.
• Some cashback bonuses have conditions. For example, some casinos only offer cashback when you lose a bet.
• You have misrepresented the "capital on hand" issue with extremely unbalanced (ie lottery-style) games. Though individual players with low capitalization are each expected to lose, the casino's odds are always averaged over all players. Commented Mar 30, 2016 at 8:07
• @PieterGeerkens I disagree. I used that style game merely because it was easy to compute. With effort (more than I was willing to put in) I can create a game that "looks" more like video poker, but has capitalization requirements of any arbitrary value and an RTP of 99%+.
– John
Commented Mar 30, 2016 at 13:26
• I would add to this answer that some cashback bonuses have conditions. For example, some casinos offer cashback only when you lose a bet (as opposed to every single time). I would also add a reference to this article from WizardOfOdds.com, that explains how player advantage (as opposed to house advantage) is not unheard of with video poker. Good answer either way. I think you brought up two very good points: the cost of food/drink, and player skill. Commented Mar 30, 2016 at 14:21
• @Rainbolt add away! :) Excellent references and points.
– John
Commented Mar 30, 2016 at 14:25
• Assuming that you're not playing the \$1 you get as cash back (at least not immediately), shouldn't the formula for the expected return actually be \$100 * 0.9954 + \$1? Of course, that still works out to (exactly) \$100.54, so in practice the difference is negligible. Commented Apr 10, 2017 at 15:28