Destroying Atlantic City in blackjack

12 December 2012

By Frank Scoblete

Alan Krigman (columnist for Casino City Times) and John “Skinny” (below) have mathematical formulas showing why Don Johnson of Pennsylvania won more than five million dollars from the AC’s Tropicana. They all state unequivocally that the player had the edge for a relatively short while in which to hammer out a nice, fat win – and hammer such a win Don Johnson did. (You can read Krigman's article in his archive on these pages.)

The key variable in Johnson’s play had to do with a deal he made with Tropicana. They would give him back 20 percent of his losses. Now let’s take a really simple, simple look at how this win could accomplished. We’ll just use six hands to show how Johnson got his edge. This device I am using is nowhere near accurate but it does give you the flavor of how such a simple thing as a 20 percent rebate on losses can aid a player in getting an edge over the house, if the rebates are given after every individual session.

No Player Rebate:

Session 1: Johnson wins $1,000
Session 2: Johnson loses $1,000
Session 3: Johnson wins $1,000
Session 4: Johnson loses $1,000
Session 5: Johnson wins $1,000
Session 6: Johnson loses $1,000

No win for player.

Player Rebate of 20 Percent

Let’s take a look at a second scenario where 20 percent of a loss is returned:

Session 1: Johnson wins $1,000
Session 2: Johnson loses $1,000 ($200 returned)
Session 3: Johnson wins $1,000
Session 4: Johnson loses $1,000 ($200 returned)
Session 5: Johnson wins $1,000
Session 6: Johnson loses $1,000 ($200 returned)

Player wins $600.

Now obviously, my example is so simple that it is somewhat wrong on several levels. The house edge of about one-half percent has to be taken into consideration, as well as how long a session actually lasted. But a clear picture is being drawn … at least I believe it is.

Now look at this next scenario:

Session 1: Johnson loses $1,000 ($200 returned)
Session 2: Johnson loses $1,000 ($200 returned)
Session 3: Johnson loses $1,000 ($200 returned)
Session 4: Johnson loses $1,000 ($200 returned)
Session 5: Johnson loses $1,000 ($200 returned)
Session 6: Johnson wins $5,000

The win for the player is now $1,000 even though he lost five sessions and won $5,000 in his last session. By returning 20 percent, a push becomes a win for the player.

Final scenario: Johnson loses but still wins:

Session 1: Johnson loses $1,000 ($200 returned)
Session 2: Johnson loses $1,000 ($200 returned)
Session 3: Johnson loses $1,000 ($200 returned)
Session 4: Johnson loses $1,000 ($200 returned)
Session 5: Johnson loses $1,000 ($200 returned)
Session 6: Johnson wins $4,500

Johnson actually lost money here. He lost $5,000 but only won $4,500; normally a loss of $500. However, with the rebate he gets back $1,000 of his losses, so now – bingo! – he leaves with $500 more in his pocket than what he started with. He lost and won!

Now what if the casino only gave back 20 percent of the losses at the end of a trip of, say, five days? Would a single trip give the player the edge as I showed above? For that and for longer playing sessions I refer you to our three brilliant authors.


“Skinny” on Alan Krigman’s Analysis

Alan Krigman is correct about his premise that the edge will go back to the house the longer you play a single session. I concur with Alan that it is around 500 hands at -.40 percent and 650 hands at -.35 percent. But more importantly, he is correct that the longer you play a single session, you will eventually eliminate most of the advantage of the rebate.

My logic that he is correct is as follows:

What if you played an infinite number of hands? Eventually the variance would almost be eliminated and the end result would be extremely close to the exact house advantage. In that situation you would only be getting back 20 percent of the loss of the house advantage. Your net loss would always be approximately 80 percent of the house advantage times the amount you bet. If you continued to play in that manner, you would only be reducing the true house advantage by 20 percent.

But if you have a large enough bankroll to sustain extreme losing streaks and can play in the game long enough to overcome the variance that occurs naturally, you will still have an advantage over the house.

The key as he points out is to play short sessions. Perhaps you play one shoe at a time and quit. Then you come back later to play one shoe and quit. If the casino considers each one a session and rebates your losses for each of them, you can win over time.

You will be ahead at the end of some shoes and down at the end of other shoes, depending on which way the pendulum is swinging. Since you are getting 20 percent back each time you lose and keeping 100 percent each time you win, you still have an advantage. It is just not as big as I originally thought.

Let me use Krigman's figure of -.35 percent for the house advantage and 650 hands for the player advantage to be eliminated. With a 20 percent rebate, the player has a +9.685 percent favorable advantage on the first hand. That positive edge would decrease with each subsequent hand reaching approximately -0.001 percent (20 percent rebate) after 650 hands. It would decrease with each hand played for the first 9 hands in the following pattern +9.685 percent, +4.685 percent, + 4.685 percent, +3.435 percent, +3.435 percent, +2.810 percent,+2.810 percent, +2.420 percent, +2.420 percent.

In other words, it would decrease rather rapidly in the first few hands and continue decreasing at a slower rate after that. It would not be a linear decline but rather a curve that is steeper in the beginning and flatter at the end. So even if he played an 8 deck shoe (without counting cards there is no advantage to single deck) for approximately 80 rounds per shoe, he would still have an edge at the end of each shoe. After 80 hands the player should still have an advantage of around +0.575 percent.

As long as the player can settle with the house at the end of each shoe and get his rebate, I think this still gives the player enough of an edge that he can win without counting if he plays sound basic strategy.

Krigman has pointed out something that I did not think about in AC. I missed his point that the longer one plays, the more likely the session will end up close to the house advantage and eliminate the big advantage the player has early on in the session. That does not change my mind that a player with a big enough bankroll can overcome that with a rebate on losses agreement.

This is different than saying a player with a big bankroll can stay at the table long enough to overcome a standard house advantage. Gamblers mistakenly believe they can overcome the house advantage by "quitting winners" and using a stop-loss limit. Money management can not overcome a negative-expectation game because all the sessions you play become one long session. The sum of those sessions will become the equivalent of the "long run" in which case the variance is infinitesimally small and the net result is very close to the exact house advantage for the sum of all the sessions.

But with a rebate offer and a sufficient bankroll, one CAN indeed "quit winners" with a 100 percent win and stay long enough to overcome the 80 percent losing streaks.