Why Can’t Journalists Who Write Articles About Gambling Understand Math?

Almost a year ago I wrote a post reacting to the story that a gambling whale had crushed Atlantic City with the benefit of a generous loss rebate that the casinos offered him.  I was suspicious of the claim that loss rebates were the secret to his success.   This week, we get more details about that story – courtesy of an Atlantic article titled “The Man Who Broke Atlantic City.”

It turns out that high roller Don Johnson not only got a generous loss rebate – 20% discount on losses per session – but he also got the House to change the rules, whittling down their edge to less than 1/4 of a percent:

“He won’t say what all the adjustments were in the final e-mailed agreement with the Trop, but they included playing with a hand-shuffled six-deck shoe; the right to split and double down on up to four hands at once; and a “soft 17” (the player can draw another card on a hand totaling six plus an ace, counting the ace as either a one or an 11, while the dealer must stand, counting the ace as an 11). When Johnson and the Trop finally agreed, he had whittled the house edge down to one-fourth of 1 percent, by his figuring. In effect, he was playing a 50-50 game against the house, and with the discount, he was risking only 80 cents of every dollar he played.”

It’s at the end of that paragraph that the errors start.  See, Johnson doesn’t get back 20% of the losses on each hand, he gets back 20% of the losses on each session.  So, no, he’s not risking on 80 cents of every dollar he played.  Which leads to the next point:

“In a 50-50 game, you’re taking basically the same risk as the house, but if you get lucky and start out winning, you have little incentive to stop. “

No – actually, flip that and reverse it:  if you get lucky and start out winning, you have EVERY incentive to stop!  Since you only get a rebate on your overall session losses, your edge comes from being able to quit while you’re behind and pay less than you owe.  When you’re winning, your loss rebate doesn’t come into play, but you will still “want” to quit and start anew, as I’ll explain in a moment.

The article, after going into depth about how good a blackjack player Johnson is – how he knows the correct play for every situation, and how he knows the math stone cold – then quotes him thusly:

“So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing. “I was already ahead of the property,” he says. “So my philosophy at that point was that I can afford to take an additional risk here, because I’m battling with their money, using their discount against them.” “

No.  That’s not right at all.  You’re failing to use their discount against them: you’re getting no value from it if you keep playing when you’re “far enough ahead” !!!   Let me put it this way:  pretend you’re up a million, and you’re betting $ 50k a hand.   let’s just pretend that each hand is 50/50 win/lose (it’s not, but indulge me for simplicity’s sake).   So each additional hand has no positive expected value for you (nor any negative expected value).

However, if you pick up your million dollar win, walk across the street to the other casino who will give you a 20% rebate on your losses for the session, and start to lose – say you lose $ 1MM now – you’re MUCH better off.  You only have to pay $ 800k to the new casino (they rebate 20% of the million dollar loss), but you won a million at the first casino – you’re still up two hundred grand.  On the other hand, if you stayed at the first casino and proceeded to lose back your million in winnings, you’re now flat – because it’s all the same session so you don’t get the benefit of the loss rebate.  Capiche?

So how did Johnson do it?  Did he aggressively implement super short sessions to take maximum advantage of the loss rebates?  Based on the quotes in the story, it doesn’t sound like that’s what happened.   Additionally, we are regaled of the story of how he won every single chip in the rack during a session at Caaesars:

“the dealer at Caesars refused to fill the chip tray once his earnings topped $4 million.

“I was ready to play on,” Johnson said. “And I looked around, and I said, ‘Are you going to do a fill?’ I’ve got every chip in the tray. I think I even had the $100 chips. ‘Are you guys going to do a fill?’ And they just said, ‘No, we’re out.’”

He says he learned later that someone at the casino had called the manager, who was in London, and told him that Don Johnson was ahead of them “by four.”

“Four hundred thousand?” the manager asked.

“No, 4 million.”

So Caesars, too, pulled the plug.”

That also doesn’t sound like it had anything at all to do with loss rebates.  As I’ve explained already, loss rebates aren’t a factor when you’ve won every chip in the rack!

There’s another meaty story worth reading, called “Foxwoods Casino Is Fighting For Its Life,” where they mention Mr. Johnson:

“Butera told me about another blackjack player who had recently beaten several Atlantic City casinos for more than $15 million. According to published reports, the player, a Pennsylvania businessman named Don Johnson, won $5.8 million at the Tropicana in just 12 hours. The word in the industry was that Johnson benefited from his own solid strategy, a run of great luck and rules that were tilted too much in his direction. He apparently was allowed to bet relatively small amounts when the deck was not in his favor, and up to $100,000 on a single hand when it was. (Also, under typical casino rules, if a blackjack player is dealt two aces, he can split those aces and play two hands, but if he gets another on the next deal, he can’t split again. Johnson was allowed to split aces a third and even a fourth time.) “

In other words, they are saying that Johnson basically created a game where the house had virtually no initial edge, and then gained his own incremental edge by counting cards and betting a huge variable spread (ie, bet $ 5000 when the count is crappy, and $ 100,000 when the count is good and the player has an edge).   A friend of mine who played blackjack professionally as part of the MIT card counting team explained to me: “There’s no way they let him bet massive spreads based on the count.  That information has to be wrong.”  I agree with that assessment, but unfortunately, we’re left without good answers.

Did Johnson just create a neutral EV, high variance game and get lucky?   Did the way in which he actually implemented his loss rebates vary significantly from the absolutely backwards explanation in the Atlantic article?  Were the casinos completely idiotic, allowing him to walk in and play 1 hand, get a rebate and leave?  Were they idiotic by allowing him to implement a huge bet spread in accordance with the count?   None of these explanations make any sense to me – aside from Don Johnson being the beneficiary of some positive variance good luck.

The Man Who Broke Atlantic City

Foxwoods Casino Is Fighting For Its Life




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