How Did Casinos Figure Out Their Advantage at Blackjack?

We all know that today casinos use computers to calculate odds on various casino games. How did they do this before the age of computers? For example, in the 1950s, how did they know that in blackjack, double after split was an advantage to the player? How did they come up with the rules that defined the game at that time?

[Editor's Note: We asked Arnold Snyder for his take on the history of basic strategy, which he was more than happy to provide, as he always is.]

The rules of casino blackjack, in fact, were derived over decades via trial and error because the casinos never did figure the game out mathematically. The game they offered in casinos in the 1950s was pretty much dead even. In fact, a perfect basic strategy player had about a 0.1% advantage over the house. But no perfect basic strategy players existed. The house profited from player errors, though no one knew which strategy plays were erroneous. They just knew the house made money.

The card games that were precursors to blackjack a couple hundred years ago were not offered in casinos back then as a house-banked game. These games were similar to poker in that they were banked by the players who took turns being the dealer. In time, the rules became more standardized and players figured out the optimal rules and strategies via personal experience.

There were a few legendary players back in the 1950s who’d developed casino blackjack strategies very close to perfect basic strategy simply by dealing hundreds of thousands of hands to themselves and recording their results. The first really accurate basic strategy was, in fact, devised and published in 1956 by four men in the armed services who spent years using adding machines to calculate the best strategy, but the casinos took no notice of their book which did not have a big publisher.

The recognized “gambling experts” in the 1950s were very clueless about optimal strategies and their advice no doubt made a lot of money for the casinos. So, until Ed Thorp’s best-selling Beat the Dealer came along in 1962 with a computer-devised winning system, the casinos didn’t worry much about the precise odds on the game. They just knew they were making money on it, and if it ain’t broke, don’t fix it.

How did the early casinos figure out what their advantage was at blackjack?

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gaattc2001 Dec-10-2019

Here's a link to the original paper...

Baldwin et al., Journal of the American Statistical Association 51:275, 429-439 (1956), downloadable as PDF. According to the late Peter Griffin, this paper is the progenitor of all serious (theoretical) work on Blackjack.
https://www.tandfonline.com/doi/pdf/10.1080/01621459.1956.10501334?needAccess=true

And some more information on Baldwin et al.:
https://en.wikipedia.org/wiki/Four_Horsemen_of_the_Apocalypse_(blackjack)

I played my first hand of Blackjack in Reno in 1968. They had single-and-double-deck games for $1 to $200 and $5 to $500, dealt almost down to the last card. I think most of us would agree that the game has deteriorated somewhat since then.
Cheers.https://www.tandfonline.com/doi/pdf/10.1080/01621459.1956.10501334?needAccess=true
And a Wiki article with some more information on Baldwin et al.:
https://en.wikipedia.org/wiki/Four_Horsemen_of_the_Apocalypse_(blackjack)

Mikescud Dec-10-2019

payouts

I've also been told the "old" way of payouts was 2-1 on BJ's. Probably another advantage they didn't realize was so significant.

Boogieman888 Dec-10-2019

Really?

Long before computers there were mathematicians that could figure odds. I'm sure those involved with the first casinos figured every angle they could to separate a player from their money. Don't try to tell us they went into this venture blind.

Kevin Lewis Dec-10-2019

It isn't that hard

I doubt very much that "no perfect basic strategy players existed." The trial-and-error method of dealing out thousands of hands was available to anyone who had a deck of cards, was meticulous, and had lots of time on their hands. I suspect that there were hundreds of skilled basic strategy players. After all, they wouldn't exactly have broadcast the fact.

I also suspect that the casinos had at least a rough knowledge of proper basic strategy, and observed that almost all players habitually made the wrong decisions. When those players stood on hard 16 or on soft 18 versus a 10, or hit a 12 with a 6 showing, the casinos knew they were making money, even if they couldn't exactly quantify their advantage. They just knew what happened in the soft count room at the end of the shift.

O2bnVegas Dec-10-2019

"make 21" strategy

I've never played when there wasn't at least one at the table who thought the objective was to get as close to 21 as possible, disregarding the dealer's card.  Table mates often try to enlighten them, and they might go with it a time or two, but you can tell they don't really get it and don't really believe it.  Especially when their "mistake" wins. D'oh!

Daniel Dec-10-2019

DanMin

I believe the late John Scsrne predated those mentioned and well before computers were used. He "Cased" the deck; High Count Cards vs. Low Count Cards. He was "Mob Connected" as a consultant so you know he was good. Published books on all types of gambling.

[email protected] Dec-10-2019

Boogieman888

When I first started going to Las Vegas in the early 1990s Treasure Island had an entire double bank of 10 $1 Full Pay Deuces Wild machines.  Mostly they sat empty.  At that time no one had run the computer programs to figure out the correct strategy, so they had no idea that those machines had a 100.7% expected return.  So if the casinos hadn't figured out the game by the early 1990s, I have no trouble believing that they didn't in the 1950s or earlier, either.
Yes, the probability theory was known, although modern probability theory is based on discoveries made in the 1930s, but even so it took the power of computers to really solve the problems.  It's easy to determine the probability of a given hand from a random deal, but much more complex to determine how the use of a strategy impacts those probabilities.  Bayesian theory didn't really become ascendant until the 1950s.

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