The Man with a Golden Formula

by JP Massar aka Mr.M


While there are many blackjack card counters who have won a fair bit of money from casinos, they have not really made a significant dent in the casinos' profits. In fact, precisely the opposite has happened. The popularization of card counting, since it was first developed by Ed Thorp in the early 60s, made blackjack a more popular game. And, over the years, more blackjack players at the tables has translated into more blackjack profits for the casinos.

But there may be one person who actually caused the casinos to lose more than $200 million in profits. Believe it or not, this person remains completely unknown to the general public. Let me tell you a little about him and the story behind his accomplishment.

The Challenge: Finding a Shuffle Tracking System that Works

Back in the earliest days of the MIT Blackjack team (circa 1980), the idea of being able to exploit the various shuffling procedures the casinos used was in the wind.

Referred to by most card counters then and now as shuffle tracking, the idea is pretty simple: locate a bunch of Aces and Tens (a 'packet') as the current shoe is being dealt and watch where they end up as the cards are shuffled for a new shoe; when those cards are about to come out as the newly shuffled shoe is dealt, start betting big.

But the MIT Blackjack Team had a problem. If you're in the middle of playing through one of these packets you've tracked, how do you estimate the true count so that you can bet and play appropriately? How do you take maximum advantage of your newfound knowledge?

Neil and the MIT Blackjack Team Find the Solution

This is a hard problem, and there was no obvious answer. But it intrigued a certain member of the MIT Blackjack Team. We'll call him Neil (which is not his real name because he prefers to remain anonymous). Neil was extremely good at math (even for an MIT student), and soon enough derived a mathematical formula that provided the solution: given information about the cards tracked in a packet and possibly the other cards they were shuffled into, the formula would calculate the appropriate true count as a player played through the packet. Neil called it 'The NRS formula', for 'Non Random Shuffle', and ever since the MIT Team has used the term 'NRS' to refer to everything involved with shuffle tracking.

It turned out that while the formula itself was complicated, it was relatively easy to use; for any given shuffle pattern the NRS formula would reduce to something that a trained card counter could employ with sufficient practice. Bingo! (Or should I say Snapper!?)

The MIT Blackjack team soon adopted this new technology, and for a time the casinos (especially those in Atlantic City, where we mostly played) didn't know what hit them. We would sit for hours and hours at the same table 'doing the NRS' on shoe after shoe, using betting patterns that defied any rational explanation in terms of standard card-counting techniques. It was a lot more fun than darting in and out of casinos trying to lose the pursuing card-counter catchers in Atlantic City. Or staying a step ahead of the 300-lb. guards who were trying to grab you in Las Vegas so you could be read the trespass act or worse!

The Blackjack Casinos Fight Back

But this essay is not so much about our (temporary) success using NRS; rather it is about the casinos' faux victory. Because eventually the casinos did figure it out -- one of their more talented supervisors had an 'aha' moment after watching team members play for hour after hour: "Yup, these guys were tracking cards through the shuffle and betting accordingly." How did we know they found out? The most obvious reason was that over a period of months, one by one, the casinos changed their shuffle procedures. And they started stopping us from playing again. And eventually one of their supervisors actually told us he had figured it out!

From a straightforward, very quick shuffle, the casinos went to intricate and time-consuming shuffles. They invented double and triple shuffle passes, flips, insertions and other moves designed to make it virtually impossible to track packets of cards through a shuffle. And they implemented these procedures for every shoe they dealt, at every table, 24 hours a day, 365 days a year, and as far as I know they are still doing it (where there are still shoes that are hand-shuffled).

And the Casinos Pay for Their "Victory"

Now let's make some kind of rough estimate as to how much the casinos lost by doing this. Assume 1000 BJ tables with shoes worldwide, each making $100/hr. Assume 3 shoes per hour, or 20 minutes per shoe. Further assume these additional shuffle procedures take an extra 30 seconds per shuffle. That's 1.5 minutes per hour of extra down time, or a reduction of about 2.5% in dealing time per table, or about $2.50 lost per table per hour.

Now let's multiply that out over a ten year period: 1000 tables x 24 hours x 365 days x 10 years x $2.50 = $219,000,000.

Hey Neil! That's more than $200 million dollars the gambling public is indebted to you for saving them, and that the casinos' would rather have had in their coffers. And you're also responsible for thousands of dealers shuffling interminably while bored patrons who haven't a clue as to why look on.

Here's to Neil, this shoe's for you!

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