May 11, 2023
I live not too far from the Mardi Gras in Las Vegas. It’s on Paradise Road, between Sands Avenue and Desert Inn Road. It’s a small hotel with a casino in the lobby, with perhaps twenty or so machines, some of which have video poker. It’s a somewhat obscure place: When I mentioned it to a well-known Las Vegas-based professional gambler who is a friend, he said he hadn’t heard about it. He wondered if it was a 15-machine place.
But Mardi Gras is not as obscure as my friend thought. vpFREE2 has a page on it which lists a single video poker game and provides information on its players’ club too. Las Vegas Advisor also lists the place on its Players Club Bonus Points page. What you can find from these sources, is that its slot club returns 0.1%, the best game reported there is 7/5 Bonus Poker (98.01% return), and that it has 20x points on Saturdays from 12 noon to 9 pm. These days, it’s also advertising 10x points at all other times, so the slot club is basically 2% on Saturdays when the promotion runs, and 1% otherwise.
I have been to the casino a few times, and here’s what I found: First of all, the machines don’t generate tickets. They take your cash, but when you are done playing and press the cash-out button, you need to wait for a slot attendant to come and pay you. They don’t usually have large notes either, so you will probably get paid in twenty-dollar notes. Second, the players club staff may not be very knowledgeable about the promotions. When I asked them a specific question about a promotion that typically any other players’ club would be able to answer, they said they didn’t know. I suggested they ask someone higher up, and they suggested I come back another day! Another time, I overheard a player asking the slot attendant what he should do now that he has forgotten the PIN number to his player’s card. She told him that the people who can change the PIN numbers are only there in the morning and he should come back some time before noon!
I don’t know what else you can do with slot club points there, but you can definitely convert them to Free Play easily on the machines. You put your card in, press the “redeem” button on the panel next to the card, and easily convert your points to Free Play.
Enough about the logistics. What makes the place interesting is that it has a promotion on Wednesdays. Here is what the casino website says: “Among the most popular examples is FREE-bate Wednesdays, when players earn a 25% rebate for their losing play.” Now that’s something to try!
I asked the Wizard of Vegas forum about the promotion, but no one appeared to know about it. So I had to try it for myself. I decided to go there on a Wednesday, prepared. (I don’t enjoy driving very much, so I didn’t want to waste a trip just for scouting.) I did a first run of my loss rebate program based on what vpFREE2 knew they had: 7/5 Bonus Poker at $5 a hand. It gave me exit points and reported a positive return, so I went in and tried it. I played the game for a while, lost some money, and left for the day. A few days later I went back, put my player’s card in, and found that I had a ton of points. It was the 25% loss rebate, given back to me in the form of points. I played them and left, with less money that I had started with.
That’s the nature of a loss rebate. You win over the long term by losing less when you lose. By figuring out the optimal exit points, you make sure that your winning sessions and losing sessions average out to a positive expectation. Sometimes you win and leave without getting any rebate, sometimes you lose and get some of your loss back and hope for better luck next time.
But how do we calculate the exit points? Well, I’ve written about the methodology on vidpoke.com before, which you can read about here. I am thinking about creating an online loss rebate tool, but that will take a while to get ready (there are too many input possibilities to sort out). In the meanwhile, you can either trust my numbers, or try to reproduce them yourself. (If you tried and arrived at different numbers, please tell me: there’s a chance I may have done my math or programming incorrectly.)
The first thing we need to do is get exact numbers for everything. Loss rebate exit points are sensitive to small changes in the parameters of the game.
We start by finding out what games are available. We don’t need to be very thorough and find every single game: we are generally interested in games with higher volatility (also known as variance) and games with higher returns. A higher volatility is better for loss rebates, and so is a higher return. The situation becomes more complicated when you need to find the better game between a lower volatility-higher return game and a higher volatility-lower return game. For these, you need to run the loss rebate software.
I have no idea about the exact volatility and the exact return of the video slots at Mardi Gras. So for our purposes, we assume they don’t exist. We will focus on video poker. We don’t need to look at low denomination games too carefully either: Because they are at a lower domination, their volatility is definitely lower than the same game with the same paytable at a higher denomination.
Here is the video poker games I found at Mardi Gras, together with their denominations, their return, and their variance, assuming perfect play:
The game with the highest return is Bonus Poker 7/5. The game with the highest volatility is Super Double Double Bonus 50/6/5. We probably don’t need to look at anything with both a lower return and a lower volatility than Super Double Double Bonus 50/6/5. That leaves us with Bonus Poker 7/5, Double Bonus 9/6/5, and Super Double Double Bonus 50/6/5. (Don’t worry, I have run the loss rebate software for the other games too, to show you how much you can expect to win if you prefer playing those games.)
Now we need to figure out exactly how much the slot club returns. You should play the Free Play on the game with the best return, which is Bonus Poker 7/5. The denomination you play the Free Play doesn’t matter in figuring out the expected value of the Free Play, so you may decide to play it as fast as possible at $1 per coin or as slow as possible at 2¢ per coin. Higher coin values mean more volatility, which you may enjoy or want to avoid. That’s your call. Either way, the slot club return will be 1%×98.01% = 0.9801%.
Then we run the loss rebate software with these parameters. Given the slot club return and the loss rebate function, for each game we input the distribution of its results, and it will calculate the exit points and the expected value of the loss rebate. Generally, depending on the parameters of the loss rebate, it can take a short time or a long time for the software to figure out those values. In the case of Mardi Gras’s loss rebate, it took more than 10,000 rounds of calculations for each game for the numbers to converge.
Here is what it found out for each game at Mardi Gras, played at the highest denomination available for each game at 5 coins:
If you want to trust my numbers and go play this promotion, you need to pay attention to a few things:
To maximally juice this promotion by playing the Super Double Double Bonus game, you need a large bankroll. There’s a good chance that you may go and play several times and each time you play, you lose your $1765. I don’t know how to figure out how large your bankroll should be yet, but I believe James Grosjean has some information about such bankroll considerations in his book, Exhibit CAA: Beyond Counting.
I’m assuming computer-perfect play for each game. The value of the loss rebate could be a little higher or lower if you don’t play perfectly. The perfect strategy for each game can be figured out using the Wizard of Odds Video Poker Strategy Maker and looking at the exceptions at the bottom of the page. Surprisingly, playing the basic strategy generated by the Wizard's Strategy Maker results in a higher expected value for the loss rebate than playing the game perfectly. According to my calculations, the loss limit changes to $1770, the win limit stays the same, and the expected value of the promotion increases by six cents, to $90.14. This is because the basic strategy generated by the Strategy Maker has a slightly higher variance, but almost the same return.
As is the case with the basic strategy for Super Double Double Bonus, it’s possible that modifying the strategy in some cases to make any game more volatile can result in a higher expected value for the loss rebate. I don’t have a good tool for calculating such a strategy yet, but I expect any gain would only be worth a few cents.
The perfect strategy for playing the loss rebate would be playing until you hit either the win limit or the loss limit. But there’s a chance you keep playing and it takes forever to hit either of those targets. It’s OK to quit at any time. You’d be leaving a positive expectation game, but you need to get back to your life too!
Stop playing if you lose the loss limit or you win at least the amount of the win limit. You’d no longer be playing a positive-expectation game.
It’s possible you would get mailers based on your play. Not knowing the formula for such mailers, I can’t assume any value. But if there would be any mailers, that’s extra positive expectation on top of the loss rebate.
Finally, the expected value of the loss rebate promotion changes if you have already won or lost some money. For example, assuming you play Super Double Double Bonus and you are already ahead $900, the expected value for continuing to play is $2.14. Similarly, if you are already behind $1600, the expected value for continuing to play is 72¢. The following table shows the expected values of the loss rebate for Super Double Double Bonus when you are ahead or behind a certain amount (I have limited it to multiples of $100):
Outstanding article! I should go over there and play it.