The Playing 21 Blackjack Program -- Professor Edward O. Thorp

Professor Edward O. Thorp
“Was He Right?”

Realizing The Mathematics

In a time when everyone was blinded by the obvious, Professor Edward O. Thorp realized something about Blackjack not many before him came to realize; Blackjack was not a game of luck, but a game of skill. Thorp was influenced by Roger Baldwin’s 1956 published journal, “The Optimum Strategy in Blackjack.”

When no one seemed to take notice of Baldwin, Thorp did his own studies and invented something as synonymous today with the game 21 as a Blackjack. Thorp invented card counting. With his 1962 best selling book “Beat The Dealer”, Thorp took the gaming world by surprise. It was now believed that, without a doubt, the game was beatable.

Thorp’s theories spread like wildfire, about as fast as his book sold off the shelf. Casinos can now be accused of panicking, as they altered the rules of the game at the time to try and stay a head of the new wave of players. This alteration to the game by the casinos was not acceptable, and the Voice of the gamers was heard loud and clear. Casinos changed the rules back to the way they had been.

As history played out, the casinos were never affected by card counting. Thorp actually created an army of believers. These players believed that card counting could make them winners. They flocked to the tables and ultimately lost to the casinos in what we’ll call round one. The problem was that, even if Thorp was correct about card counting, you still had to know how to card count and play some sensible basic strategy. This is a problem for many, and what was basic strategy anyhow? Whom do you believe on what was the correct way to play the game, let alone card count?

Nice and Simple

What Thorp said on card counting was that the game was based on math, and not luck or superstition. Obviously to this day some people, usually guests of the casino, still don’t understand that part. Thorp was right, the game is all mathematics and, as McB Duplin stresses, every decision you make is either mathematically right, or mathematically wrong.

Thorp realized that the composition of the deck, the cards remaining in the deck, un-played if you will, had an effect, sometimes for the player and sometimes for the casino. Thorp valued the face cards as the cards most valuable to the player. When more face cards remained in the deck, the better the player’s chance of winning became.

Very simply, this was card counting. You didn’t have to be a mathematical genius to count cards. It helped if you weren’t a total idiot, but genius-level intelligence was not a must. A clear and understandable analogy of card counting is having 10 red marbles and 10 black marbles, and placing these in a bag. When you reach in, you have a 50% chance of drawing out either a red or a black marble. However, after you draw the first marble, lets say it was red, we can see how things have changed in the bag, albeit subtlety.

The composition of the marbles remaining in the bag has changed. There are now only 9 red marbles and 10 black marbles. Reaching in the bag again, now we have a greater likelihood of grabbing a black marble.

That is, in its most simple form, Card Counting. Thorp was certain in his “Ten Count” that the face cards were better cards for the players, than the smaller 3,4,5 and 6 (commonly referred to as bust cards).

Were Thorp’s Methods Even Correct?

McB Duplin was inspired by Thorp and his theories, but we were not believers in much of what he believed. Our beliefs and findings on the game Blackjack were actually, well, almost entirely the opposite of Thorp’s beliefs and findings. First let’s take a broader look at what Thorp believed. It should be stated Thorp’s theories were based on his probability and mathematics findings.

Thorp believed the 5 was the worst card in the deck of the player. When the 5’s were removed from the deck the player’s odds of winning increased. (McB Duplin Disagrees)

In Thorp’s Ten Count he stated a deck rich in 10-value cards was best for the player. He stated the reasons for this as follows:

A Player that is dealt a Blackjack is paid 11/2 to 1 (or 3-2), but the dealer only took the players wager. (McB Duplin Agrees)
When there are more face cards remaining in the deck, there are more Blackjacks and pat hands (hands 17 to 21) (McB Duplin Partially Agrees)
With a hand totaling 9, 10 or 11, the dealer can’t double down on a face card rich deck, but the player can. (McB Duplin Disagrees)
If the dealer receives a poor hand, 12-16, they must draw according to the rules and have a more likelihood of busting from a deck rich in 10-valued cards, but the player doesn’t have to draw on these hands. (McB Duplin Disagrees)
Computer simulations mathematically prove that a deck rich in 10-value cards favor the player where as a deck rich in low cards will favor the dealer. (The Playing 21 Program was going to prove this and all other theories once and for all.)

Why McB Duplin Disagreed With Thorp?

Man did we lose a few hours of sleep over this. Thinking Thorp may have been wrong, that was exciting. But asking ourselves how we could possibly prove we were right was the cause of all the sleepless nights. Seriously, can everyone still agree with Thorp, but us? Everything we said and thought was totally different! Thorp’s word has been gospel for forty years…and yet we based everything we had done on logic. Logically, Thorp was wrong, and we knew this. We knew without a doubt we had logic on our side, but we also knew logic was not math. Logic would tell a cribbage player he should be able to get a 19 point hand, but trust us, after two weeks of trying as a kid, it was not mathematically possible.

So math and logic are different. Thorp believed he had the math, and we believed he had neither. We believed Thorp was logically and mathematically wrong! What was driving us and pushing us so hard? What was totally convincing us that we were right and he was wrong?

Long before the Playing 21 Program came along, we had already spent 10,000 hours analyzing the game. We meticulously saved each bit of data and as we went, created more and more accurate information. Sadly, most of this work took place at the kitchen table, over years and years. We didn’t have the luxury of just buying a program like Playing 21.

Everything we did was based on what we had read. We didn’t just read a Blackjack book either, we read them all, anything we could get our hands on. Our card counting was what we knew. What we read in many books, Thorp’s theories. When you don’t have a computer program to prove these things, and apparently the people who had them for some reason weren’t selling them, you had to believe what you read and learned in the books. Suddenly, over night, everything became clear. All those cards flipped. All that legwork and all the statistics we kept, we had finally found something. Logically, the entire game Blackjack made sense for us from that point on.

What We Found

We found that the entire game Blackjack was based on one thing only. The entire game, every single hit and stand, split and double down, was based around the Dealer’s Up Card. The entire game revolved around it. It made sense why one hand you would stay with a hard 14, and the next time, against the same dealers up card, you would hit it. The Dealers Up Card changed everything.

Right about now, you might be thinking that isn’t anything new. You knew that already, and of course you make your decisions based on the Dealers Up Card, it is just common sense. Funny, but if you did just agree, you too contradict Thorp’s theories, and like us, just didn’t know it yet.

We went back over 10’s of thousands of hands. Wow, we were right. Collectively, every time the dealer flipped a face card as his up card, we were losing over 60% of the time. The count didn’t matter. Whether we were or were not card counting, in the end 60% was still 60%. We knew that when the dealer flipped a face card we were getting killed. Logically we all know this. Anyone who has ever played knows you get massacred when the dealers starts with a face card. We were on to something big. We were not losing that bad in the over all game, so where were we getting some of those heavy losses back? We think we knew, and so do you.

Again, going over all the statistics we found out, no matter the count, that when the dealer started with a smaller card, a 3, 4, 5 or 6, we won around 60% of the time. Amazing! When the dealer started with a low card, we did really well. We knew this all along from years of playing. Blackjack players always like the dealer having a low card up, that is when we win the most, doubling and splitting and making a killing.

Taking a Closer Look at Thorp

Immediately logic hit us, and we believed that, logically, Thorp was mathematically wrong in our belief.

We already knew that the only advantage the dealer has over the player, is that the dealer plays after the player. This is huge in the game Blackjack. If we busted, the dealer was already filing our money away to invest in the next million-dollar addition to the casino. Even if he busted on that same hand, they would never give us our money back. This had been documented before us, and was a big part of the house’s advantage over the player. The player could get this back by playing smart, the extra Blackjack payout, proper splitting and doubling down. Those were all key.

Suddenly Thorp’s theories looked weaker and weaker. Why were we betting more money when there were more face cards in the deck as Thorp told us to? If there were more face cards in the deck, logic told us, there was a better chance the dealer started with one as his up card. It didn’t matter the count, we’d lose 60% of the time.

If there were more face cards in the deck, we’d stand a better chance to get one in our hand. Any player’s hand with a face card is a hand that is never doubled or split.

If there were more face cards in the deck, the dealer stood a better chance of flipping one up, at which time we never split (maybe 8-8 and Aces we were told) or never doubled down (maybe 11), but those were good things for us, splitting and doubling.

If there were more face cards in the deck, we stood a better chance of getting a Blackjack, and get paid 3-2 compared to the dealers even money. Well, Thorp was right there, but would that be enough to over come all the negative? The “pat hand” argument was nothing; the dealer has the exact same odds of drawing a solid hand in 2 cards as the player does.

Thorp also said that if the dealer received a poor hand, 12-16, he’d have to draw, where the player could stay on this hand. Well, that made zero sense. What Thorp was actually saying is if the dealer started with a 2-6, we as players wouldn’t have to draw and bust out. Well, that was true, but if there were more face cards, the odds were against the dealers up card being a 2-6. We have the same odds as the dealer has of getting a 12-16 hand, but we have to play first. The times in a rich face card deck that the dealer had the face up, (more often then the lower cards), we’d have to hit first. When we hit before the dealer and bust, we lost, no matter his out come.

Thorp’s theories were all logically wrong.

When there were more smaller cards in the deck, there were more mathematical chance the dealer flips one as their up card, at which time we win 60% of the time. When the dealer starts small, we also take advantage by maximizing our splits, all hands, and our double downs, all 9, 10, 11, which we always knew were great hands for us.

Also, if there were more low ones in the deck, there were better chances of us catching two in the hand and making the 9, 10, 11 hands that we love to double down.

And yet all this time, because of Thorp’s theories, we always had our minimum bets out there, because there were more little ones in the deck. We just shake our heads when we think of all the years of lost opportunities.

40 Years of Ten Count

All these years later, and everyone was using the ten count. Every book we read, everyone supported Thorp. What made it harder to sleep at night was that all these books kept referring to these computer programs. I wish someone would have sold us one. Everything would have been much easier on us.

We knew we had no choice. To prove our theories, we had to develop the best Blackjack program ever made. The Playing 21 Program had begun.

What Did We Find and Who Was Right?