Table Games Loss Discount Math: What am I doing wrong?

A thread in the comps section got me thinking about the loss discounts offered to big players, one of whom is a roulette player which is an easy game to use as an example when working out the math.

If you get a 10% loss discount if your losses hit 50k for example and you play even money bets on single-zero roulette, for each $1 bet the EV would be:

Without discount: (1 * 18/37) + (-1 * 19/37) = -0.027 .... as we all know, a -2.7% HA against you.

With 10% discount on losses: (1 * 18/37) + (-0.9 * 19/37) = +0.024 .... you have a 2.4% advantage since you win 100% on your winning hands but only lose 90% on your losing hands.

Now I know it would only kick in if the player lost 50k but if a player decides to play only until he loses 50k or wins 50k wouldn't he come out ahead?

I feel like I"m oversimplifying this. In fact I'm sure of it. I feel like my brain is barely operating at 20% today. But what am I missing? My hunch is I'm ignoring some effect of the asymmetrical payoffs over multiple hands but I just can't see it right now.

Thoughts?

 

I think you're missing the fact that the HA is a prior-to-event calculation.
Once you lose the $50K (or whatever your loss limit is), the after-the-event HA is 100%. Even when they rebate you 10% of that loss, they have a guaranteed win from you of $45K (or 90% of your loss limit).

 

What you are doing wrong is applying the discount to each individual spin. That would only be the case if you always went to the casino and played one spin, then collected your discount.

I believe they apply this for the total trip. So assuming it is going to people who are gambling a lot its a lot more like taking 10% off the house edge, because they aren't getting a discount on all the spins they lost, but rather the spins they lost minus the spins they won. I would imagine that makes the overall edge tough to calculate without simulations, because it would change based on playing conditions.

For example, for 100 spins at 100,000 a spin, then you checkout and collect loss discount if you lost. To figure out the house edge, you'd need a probability distribution of the possible outcomes and their likelihoods, then you would discount all the loss outcomes by 10%, and multiply each outcome by its probability (and divide it all by 100 to get your edge per spin, or you could just look at EV for the session)

It still could be gamed. Someone posted a link in Natedogg's thread about a guy who beat Atlantic City by negotiating a bigger discount and running short high variance trips. Then again, there is nothing that says they have to offer you this discount. They give the most stuff to the worst players.

 

The problem with your math is that you are applying the loss discount at all times.

 

I tried my above example in excel and found that the house edge decreased from 2.7% to about 2.16% for the iterations listed, or an expected loss $215517 if betting 100k per spin.

In fact, its an edge for the house for any number of spins over 1 at a 10% loss discount.

House edge needs to be somewhere around 0.41% before you'd have an advantage over 100 iterations per trip. Of course, there are other comps you would get for the play. But its tricky whether to factor them in, as it assumes you would be spending that money if you didn't get the comp, which I would imagine is seldom true.

 

But if you were playing at multiple locations in one trip, you could maximize your benefit by playing where you're losing. So if you start a trip and you're up at one property, you could move to another and start over at zero.

 

Yes, you could, but certainly at roulette with a 10% loss discount, it would still be very hard to turn the edge in your favour.

And we are assuming all casinos would offer you the loss discount, even though you would end up doing a hit and run (literally get up a bet or two and walk) at most of them.

Didn't Nate say he had to play a certain # of hours/day to get his discount? Or was that airfare?

 

That's right guys. Thanks! I got so trapped into one line of thinking I couldn't see that this only made sense for 1 hand, but not since you're applying the discount to the net loss over multiple hands. Serious blonde moment! (nothing against blondes, I love blondes)

Nevyn I knew I could count on you to apply your brute force excel approach to it By the way I was the one who linked to that article in Natedog's thread. That story was in my head too but that AC gambler negotiated abnormally good terms both on his discounts and on the rules of the BJ game he played.

mike that's true. Despite the dumb flaw of my approach, a High Roller can game the system a bit over multiple casinos. Which from stuff Nate has posted sounds like most of them do take advantage of that.

 

This time it was only semi brute force. Used the binom.dist formula for each individual outcome (how many out of X spins you win). Just used excel to combine it all. Doesn't take long at all.

 

Actually, you made it way too complicated.

The HA if you lost $50,000 is 100%. Forget all the other math. It does not matter. You lost 100%. All of the $50,000 in this case.

Nothing left to figure.

 

And he had the bankroll to back up making large bets when needed. It I recall, at one point he cleaned out the entire chip rack from a high limit BJ table (that's when they stopped him from playing any longer). That's not just good rules and a good rebate. That's big wagering and good luck!

 

Also to clarify that for normal non-negotiated discounts, it is 5% for 50k and 10% for 100k.

Also you would have to still put in the 12 hours, since there's no quit loss until it gets to 300k.

I guess it is possible to bet 50k on one hand, lose it, then go play pai gow poker at 25 dollars a hand for 11:59...but that would be like slow torture...

At 300k, you can do a quit loss and not have to play 12 hours, but you would have lost 300k-30k-14k-4.5k=252.5k

 

the bottom line is the OP is semi-right in that by gaming the loss discounts and playing at multiple casinos you can work the HA much more in your favor. for example, if you make a big win at one property, you switch properties. if you lose there, you collect the discount and pay off the loss with your win from the one property. this is exactly what natedog did last trip and it paid off big time for him. he won 1M at Wynn and lost 1M at V/P. but he only had to pay about 800k at V/P, so he effectively "won" 200k for nothing.

if you work the system like this, you can come ahead even when you break even or lose a little. this is the same thing that a big BJ player did at AC a while back that got some execs fired. he got huge loss discounts when he lost and got them to let him start a new trip at any time. so he'd win 1M and then instantly start a new trip. then maybe he'd lose the 1M back and then he'd get his 20% discount, pocket 200k on breaking even and start a new trip. do that enough times and you can definitely beat the house.

 

OP is oversimplifying it, but he isn't wrong. Some of you are though.

Loss rebates are beatable. Especially at roulette. There is a damn good reasons promos are normally restricted to even money bets.

Probably the same logic the guys at the AC Trop had. I'd hope they were fired after losing millions to a single blackjack player.

 

This is right. I didn't want to kick up my own thread for it since others had already answered but I started to research it a bit that day and found a good article on the subject. It uses baccarat but the idea is the same and they used the same exact approach I used in order to show the problem with 1 hand, but then then branched it out over multiple hands which I neglected.

http://www.casinoenterprisemanagement.com/web-exclusives/discounting-player-losses

nostresshere a simple way to see the problem with what you said is if you look at it that way then ANY loss discount under 100% should be ok to offer by simple induction. But you already know, just intuitively, that can't be true.

 

That wouldn't work with my luck at pai gow. Even though its supposed to be a slow game I could easily lose that 2500 from the loss rebate on pai gow at 25 a hand for 12 hours. Trust me -- I've done it!