Analysis of a complex yet peculiar comping system

Hello I have recently stumbled into a casino that offers the following promotions which I think offers considerable advantage on some games I've found with some numbers and reasonings. I hope the Wizard or anyone with decent statistics and probabilities knowledge can chip in and give me their opinion.

The casino offers a number of baseline points from which parallel accrual applies in the form of freeplay. Freeplay can be converted in either Non Negotiable chips at any denomination (minimum 100, maximum 10000, valid on all table games except poker or bingo games) or Slots credits (valid on all slots except video baccarat or video roulette) NN chips are retained by the player should he win the bet. So in total you have:
- Status points (determines your class level (6 in total), that will determine your FP points multiplier. The higher the class the higher the multiplier)
- Baseline points (main tier that tells your eligibility of all running daily or weekly FP's and additional promotions/raffles, etc)
- Dining coupons (determined by baseline accrual)
- Daily FP Booster = Get additional FP credits
-Weekly FP Booster = same as above for accrued weekly baseline points

I will post the currency and credit numbers in $ dollars (it is a different currency, will look inflated in value but it's to give you an idea)

The Dining coupons are as follows:
20 BL points = 50 $ dining coupon / or sandwich voucher
80 BL points = 200 $ dining coupon / or small noodles box voucher
250 BL points = 250 $ dining coupon
500 BL points = 500 $ dining coupon
1000 BL points = 700 $ dining coupon
1500 BL points = 800 $ dining coupon

The value of these coupons is cummulative. That means that if you obtain 250 baseline points in a day, you are getting 3 coupons (250 + 200 + 50) for a total of 500 $ worth of dining value valid in all restaurants and bars here which are numerous. Furthermore, some food bar establishments run by the casino directly will apply additional 15% to 20% discount if you pay with vouchers getting yet more value.
There are 6 class levels all with different multipliers. For simplicity I will label Class 0 the lowest (0 multiplier, means 1 baseline point gives $1 worth of freeplay)
The highest Class 6 will have a multipler of 2.5 x (1 baseline point gives $2.5 worth of freeplay) I myself am on Class 4 with a multiplier of 1.8 x. The status points run very similar with baseline. As you get higher you need more points to make it to the next class.
The Daily FP Booster is as follows: Get 400 BL points on a specified weekly day, get an additional $1000 FP. 1000 BL points will get you $4000 FP. 2500 BL points will get you $12500 FP. Runs at least once every week
The Weekly FP Booster is as follows: Get 2000 BL points in a week, get $4000 FP. 5000 BL points will get you $10000. 8000 BL points = $16000 FP. 15000 BL points = $30000 FP. 50000 BL = $100000 FP 100000 BL = $200000 FP. The highest amount of 150000 BL will give you an extra $330000 FP

The FP credits are in the form of "cashier" points that can also be used to pay for shopping, dining, hotel rooms, etc as with most casinos. I redeem it mostly for FP. Class 4 also has options to get hotel rooms for 400 BL a night redemption in a typical airport crash type of hotel that's in the complex. I am positive the higher classes will have rooms in the best hotels around here, possibly even with some nights given for free. Moreover, with 250 BL daily, you are getting a free tobacco pack (prime brands) If you are not a smoker, you could just resell it legally (which would be easy over here) for about $140 per pack (the currency is not dollars but to give you an idea)
There is I am sure additional comps as you promote to higher classes but I am not aware of, as some may be unpublished (I didn't know about the hotel rooms until I promoted, for example)

Okay, so as far as the gaming goes, I believe I have identified slow pace games with low house edge where the rating is superior to your expected loss. One of these games is Baccarat. As you get higher in limits, the number of players sitting tends to be fewer, increasing the rate of hands per hour and diminishing the comping value. However, as the higher limits are rated much higher, this may be ideal to get extra comps (and therefore freeplay) To get an idea of the current rating in different tables I have collected a number of samples on my sessions, including baseline points earned, profit and loss amount, and time. Over here you get rated based on time spent at the table, not on actual betting, so this may create an opportunity. Available tables are from $1000 minimum bet per hand , $2000, $2500, $3000, $5000, $7000, and the highest $8000. There is actually higher at $10000 and above but only made available for high rollers on invitation.
I'm choosing the $3000 full tables where I am able to play between 4 and 6 hands per hour. For this calculation just say 5 hands. That gives me a total of $15000 wagered at a expected loss of 1.3466% = $202 per hour. The standard Baccarat game of choice here is called the Super 6, which is a commision free that pays 1/2 to 1 if the Banker makes a "super 6" (any six) Some side bets like 12 to 1 on super 6 of 2, or 20 to 1 super 6 of 3 are available, also pairs, ties, etc. As taken from the Wizard of Odds I have chosen the appropriate house edge for a combination of banker and player bets.
The rating collected on all my samples averages about 85.85 baseline points per hour on that limit (I have collected about 56 sessions so far ranging in time) I have noticed that I get higher rating if I tend to bet progressively regardless of whether I win or lose. Let's just say to adjust for further diminishing over time that I pick 70 baseline points per hour which is very realistic. This gives 70 baseline points x 1.8 multiplier equals = $126 FP. As part of the daily promotion of 1000 gives $4000 FP, this would have a value of (70/1000) * 4000 = $280 FP. The weekly promotion of 2000 gives $4000 FP would have a value of (70/2000) * 4000 = $140 FP
So total value in FP is -202 + 126 + 280 + 140 = $344 per hour profit that is without adding yet the extra value in dining and tobacco and other comps. My question is in regards to volatility, the bankroll I would need to avoid risk of ruin assuming these figures would give an approximate return of $51000 per month playing about 750 hands per month as it stands. If the number of three standard deviations applies, that means I could finish between -$200000 down or up on any given month, is this correct? So what bankroll do I need to avoid a risk of ruin?
Also consider the rating on bigger tables. $5000 has an average accrual of 264.05 Baseline points per hour over 6 sessions. $7000 has an average of 325.05 per hour over 3 sessions. $8000 has an average of 403.36 per hour worth of baseline points over 4 sessions. As the value in comps ramps up here, is it worth it to use a progressive system (like a paroli type of system) trying to "promote" yourself to the higher tables? On $5000 tables sometimes I can sit with many players and skip hands. On $7000 or $8000 almost exclusively either me with someone, or by myself. Given all these implications I would like to have an idea of the variance involved. Thank you so much if you read until the end.

Welcome. Good questions…. But I think it’s a LOT of work to give you an answer. And it’s never as ‘simple’ as you think. Many of your assumptions are guesses. Like how many hands you can sit out? Like what is the real value of a ‘noodle box’?

Hopefully someone here has a few hours and the DESIRE to figure it out!

Interesting numbers. They sound like very Asia / Macau-like numbers given the conversion of $50 to a sandwich voucher. Mind mentioning where you're seeing this?

If I'm understanding correctly, the most efficient way to do this would be to presumably do 2 days of the daily promotion hitting 1000 BP each time to collect 4000 FP twice. This would also allow you to collect the weekly promotion of another $4000 FP?

So basically you're trying to earn 2000 BP a week which equates to 2000 * 1.8 + 4000 + 4000 + 4000 = $15,600 in FP value.

To hit 2000 BP a week, by your conversion of $15,000 in total wagers = 85.85, to hit 2000, you would need 2,000 / 85.85 * 15,000 = $350,000 in total wagered over 2 heavy days of gambling per week.

At a house edge of 1.3466%, that's a total loss of about $4700. So taking things at face value, it does seem that the $15,600 in FP does make up for this.

With regards to your actual vol question, to hit $350,000 in the at a 3,000 betsize, you would need to bet about 117 times.

Just using Excel random number generator and a huge column for a Monte Carlo sim, at the end of these 117 $3,000 bets, your results are (excluding FP earned):

Median case: -$3,000 (max drawdown -21,000)
10th Percentile Case: -$45,000 (max drawdown -54,000)
5th Percentile Case: -$57,000 (max drawdown - 66,000)
1st Percentile Case -$81,000. (max drawdown - 87,000)

In my few 3000 simulations, I did see drawdowns of $120,000
The standard deviation from the sim for each run of 117 hands is about $33,000 - this seems in line with intuitively each hand having a $6000 swing. So 117 hands would be sqrt((6000/2)^2*117) = $32,449 SD.

You clear the -$15,600 mark to breakeven with FP 68% of the time. (-$15,600 is about the 32nd percentile)

Keep in mind this was a pretty rough guess and I'm not the most mathematically minded. Just wanted a crack at it and hope someone can correct my thinking.

Also, 5 hands an hour trying to hit 117 hands over 2 days means playing for almost 12 hours a day.

EDIT: For a month, let's just shortcut this and do 4 weeks.

Convert our 117 hands to 4 weeks which is 468 hands. sqrt((6000/2)^2*468) = $64900 standard deviation.
Expected value of 468 hands is 468*$3000 * 1.3466% = -$18906.
If we wanted to be safe within 3 standard deviations, -18906-(64900*3) = $-213,600, We'd want a bankroll of about $220,000

Quote: SOOPOO

Welcome. Good questions…. But I think it’s a LOT of work to give you an answer. And it’s never as ‘simple’ as you think. Many of your assumptions are guesses. Like how many hands you can sit out? Like what is the real value of a ‘noodle box’?

Hopefully someone here has a few hours and the DESIRE to figure it out!
link to original post

Hi Soopoo thanks for coming in. I think this is more a case of someone who knows how to use Excel or any probability tool well. Unfortunately my knowledge in that area is limited. I go mostly by what I am reading in good sources. Note that there's very little guess in my assumptions, everything is based on real experience as I've been collecting those data every single session, I once experienced a problem with comps credited and decided to start tracking myself, and writing time spent, profit or loss made, comp count and put it all in a spreadsheet. I discovered this by chance but also making use of my experience in AP, and doing a lot of research in this and other casinos in this area, to their every little hook, corner and crevice.
Obviously I am not in this for the noodle or rice boxes (with the exception of some people who look forward to them, many of them who seem to be poker players, I used to be one of them) I mention it because the rating in Texas Hold'em is absolutely pitiful, about 8 BL points per hour. They all look like they haven't changed their clothes in days, and mind you many slots players look the same around here. Now they look at me eating some fancy dinners from the asian restaurant or casino bar and they wonder "how the hell is he eating that stuff?" The value in food starts accruing when you get more points, we all know food and drinks in casinos have huge mark-ups and are already overpriced, saying that the salaries here are very low and even though the casino catering is more akin to a 3 star hotel compared to the West (everything is substandard here), to a local here it would be like eating in a 5 star establishment if it makes sense. The food upstairs in the shopping mall where you can also use your coupons starts being more at the 4 star level, but it will cost you more coupons.

Regarding hands sit out, no need to sit out, you can remain sit at the table. I don't know how it works in Vegas, I've never been there yet but over here you can time your bets as you see fit provided you sit with a lot more people who do bet more frequently. This can only be done at the low or medium levels (from $1000 to $3000) where there is a lot of affluency of people and full tables can be found easier. From $5000 up you start seeing only 2 or 3 players per table, I have been able to do it on $5000 with 3 other guys because you have many high rollers here from Asia but it's less frequent than in $3000. Other people also time bets even though they are not AP because this is a place that is heavily entrenched in superstition, in a context that is already prone to superstition and hunch like is the game of Baccarat. They are looking for progressions, trends, you know the drill....I choose tables where there is a lot of side betting and a lot of money flowing in compared to the minimum bet, because the table will be likely making a profit on it for the day. I have noticed that my numbers consistently support the theory that these tables rate higher. It has nothing to do with my own betting or profit/loss on my bet. I have literally sit on tables where I've been only 1 or 2 hands for a few minutes and collect huge ratings even walking out as a winner. I have about 56 sessions data in $3000 and at every level up to $8000, I talk "averages" to reflect the fact that different tables will have different profits and you get rated by different types of people every time, so the numbers are realistic, they are actual and not a pie in the sky or some imaginery confection. Having said that though, the casino could easily take measures against my ratings and cut them radically, but I would know when this happens (comparing to the lower levels) and so far the data I have does not support these measures, which means I'm still under the radar. I choreograph my every move when I am in the casino, I am in the role of an impulsive compulsive gambler, but still I am conspicuous due to the fact that I am foreign (Westerner)

I could post a sample of my data but I don't know how to attach pictures here. I am doing/have done this also on Blackjack successfully but unfortunately the ratings are not as high even though still +EV (between 45 - 50 BP per hour) In fact this is how I started. The BJ over here is extremely liberal in rules (especially the Free Bet BJ)
I need to analyse other games like Pai Gow Poker, Pontoon, or Craps to see how they fare and I will be researching very soon. Unfortunately the edge in PGP is fairly high-ish (about 1.6%, standard game is Face Up PGP over here) minimum limit is $2000 but the pace is quite slow especially if there are 2 or 3 people minimum at the table, so if it's only a little better rated than BJ I could find +EV opportunities here

You are quite right when you say it's not so "simple". Because unfortunately this country is a shithole and there are many many problems over here. The customer service here, even though this is a luxury resort, is absolutely downright terrible. Zero ability to resolve any type of conflict in an environment where you're prone especially as an AP to have multiple issues, or initiative to provide resolutions. It's difficult to raise some questions when at the same time you need to keep under the radar

Quote: monodactyl

Interesting numbers. They sound like very Asia / Macau-like numbers given the conversion of $50 to a sandwich voucher. Mind mentioning where you're seeing this?

Hi monodactyl thanks for replying I will answer your points one by one. The casino is based in Asia (not Macau) but saying that this is something that could be parched by the casino by taking actions against me, so I don't want to give the sensation this is some type of bonanza golden pot because I've been only at this a few weeks.
With that being said, I wouldn't be so quick to pack my bags and come over here because this country is an absolute craphole in just about every sense about everything (sorry but it's the truth) Also even if this continued on for a long time, this is only possible to make it +EV choosing low edge games with a slow pace which are overrated through the webs and in this casino they don't abound with the exception of Baccarat which is huge over here. There are very few slots that I can AP here, most are huge money pit jackpot progressives with really low returns that will just sap the green out of your wallet in no time, and because people are really superstitious over here, a lot of the clientele will be jackpot chasers that play like zombies even if that means they won't have any food on the table tomorrow.
So all this means that the scope for profitability is medium low. If you want to make it to Class 6 quickly you could just spin huge on the slots, Class 6 has many perks and you will be like in a 5 star hotel in every sense (free buffets for you, free private rooms with slots and catered things for you, etc, free hotel rooms, etc) but you have to generate a lot of spin and on the slots will come with a considerable cost to you. To do it "safely" on the slow low edge games and in +EV, it will take me about 8 months, that's provided they don't clip my wings before then

Quote: monodactyl

If I'm understanding correctly, the most efficient way to do this would be to presumably do 2 days of the daily promotion hitting 1000 BP each time to collect 4000 FP twice. This would also allow you to collect the weekly promotion of another $4000 FP?

No I think I maybe didn't make myself clear. The daily promotion happens once a week on a fixed day, you only have one shot a week, it happens every thursday. For my level Class 4 I need to hit 1000 baseline points on Thursday to get an additional $4000 in Freeplay. That is on top of the 1000 BP x 1.8 = extra $1800 FP I would normally get. The weekly promotions runs every week of the month, 2000 BP is the minimum required which will give you $4000 freeplay. From there you can opt to double your amount in freeplay at any number (5000 gives you 10000, 8000 - 16000, 15000-30000, all the way up to 150000 that gives you $330000 worth of FP)

So I am looking at 2000 BP weekly for $4000 FP, out of which 1000 BP will be done on Thursday to collect an extra $4000 FP. On top of that an additional 2000 x 1.8 applies to me (If I were Class 6 this would be 2.5 instead of 1.8) = $3600 FP. That is $11600 a week in freeplay alone. I use the Buster Blackjack table $700 minimum bet to play these chips which has about 99% convertible value.

The way this works is because waiting time is rated. The same amount of waiting and skipping rounds won't be possible as the limits get higher (fewer players) This is why if I wanted to obtain 5000 BP instead of 2000 BP (for $10000 FP) this now is more difficult to achieve in higher limits because you will be mostly sitting with 2 players or by yourself. If you want to do it at $3000 you would have to put a huge number of hours, can be done but it would be a real grind. This is about 714 BP every day of the week without rest, averaging 10 hours a day. That is 10 hours sitting time, a lot of the time you are scanning tables which will take you additional time, so I'd be looking 12 - 13 hours grind.

So my question is what bankroll I'd have to look at in order to avoid a risk of ruin, considering an average of 3.5 hours every day at an average of 70 BP given (being very conservative, my data supports much higher rating) playing the $3000 limits. I shall be adding on the Thursday to hit the 1000 BP mark I have to play more hours, about 5 or 6, the rest I will have to do with BJ, other table games if I can add them to the tag and some slots. I go to the casino about 26 days a month, so that is about 3.5 hours times 5 plus 6 hours times one, so I think a figure of 100 hours is more realistic and tuned in with reality. I will be placing between 4 and 5 bets an hour, as I am really good at timing my bets. So that is an expected loss of $202 per hour times 100 is $20200 per month (500 hands). So the last part of your post may be just about right, but only maybe. I am aiming for 250 points per day, even if I need only 200 points except for Thursday when I need 1000, because that will give me the 2000 weekly needed, but with 250 you get the 250 dining coupon so it's worth the extra 50 points for a total of $500 dining value comped up. The rest of time I may be going back to poker, even if I really hate it right now. The rating there sucks and I've gone on a massive downswing through no fault of my own, but I don't know what else to do. Everything else in this casino is massively -EV. There are very very few slots that I will play that are low or low med variance for this purpose, but the good thing is on some of them you can spin for as low as $1.

Back again to the Baccarat, because the rating at the higher tables ramps up considerably, I am thinking about doing a Paroli type of system. I did it once from BJ profits where I won $36000 in a session and went to the Baccarat tables. I started at the $7000 and brought two units to the table. If I lost, I would only flat bet, I would have $22k and would move down to $5000 with two units, if I lost I'd move to $3000 with another two units and so on. I would place one unit, if I won, then place two units, and from there repeat two units, until I had five units minimum to the next level, but would only risk 2 on the table. I moved up to $8000 fairly quickly and made a $100k profit once there luckily as I hit 6 winners in a row. I kept $30k profit and kept going back and forth, was able to last for 6 days playing full time before eventually busting up at the $1000 level. I collected about 2400 BP with the additional conversions in freeplay and all the rest, and still had a tidy profit at the end of it. This is how I found out about this loophole.
But with this comes a higher variance so I am afraid is this what may make me bust with a higher likelihood before I'm on time to convert the freeplay