Blackjack, Basic Strategy, Battle of Wits – Part II

By , July 20, 2009 11:06 am

A little over a week ago I started to talk about the strange (to me) occurrence of blackjack dealers encouraging their opponents to play basic strategy.  A few people have commented that this could have to do with the casinos playing on human psychology; folks who think they have a “system” will play at the casino longer.  This could allow the casinos to maintain a revved up atmosphere longer, and perhaps more sinisterly, give them an opportunity to pump us full with free liquor, which we all know hardly impairs judgment especially in a city with so little stimulation like Las Vegas.  All plausible thoughts, but what if the casinos have figured out a way to game basic strategy?  Inconceivable!

The foundations of basic strategy are built around a few key assumptions, but the two in particular that I’ll focus on in this post are:

  1. The deck is completely random
  2. The dealer’s face down card is a 10-value card (10, J, Q, K)

Basic strategy gives a player the probabilistically optimal play for every combination of the player’s cards and the single card the dealer is showing.  It assumes the dealers face down card has a value of 10 (assumption No. 2) and bases all hit/stand/double down/split decisions off of that.  Here is what a basic strategy chart would look like for hard player hands:

Basic Strategy

This is not to say that the reason why we assume a 10 value card is because that is the most probable value in a deck (16 out of 52 cards), a popular misconception.  The expected value of a card chosen at random is actually closer to 7, however working under that assumption does not yield the most optimal play.  This is primarily because both the player and the dealer have the option to draw more than one card until they reach 21.  If this wasn’t the case, the strategy would look like something like this (I did not work out the actual math behind this chart, this is more of a rough estimate):

Basic Strategy - Adjusted

This is very different from the optimal strategy, which is a testament to how brilliant basic strategy is.  As part of research for one of the most famous books on basic strategy, “Beat the Dealer,” Ed Thorpe tested its concepts on MIT computers and found it accurate to a couple of hundredths of a percentage point.  For their genius, the “Four Horsemen” of blackjack, the inventors of basic strategy, were recently inducted into the Blackjack Hall of Fame back in January 2008.

Now I don’t think that there is a great fatal flaw in basic strategy.  It is well grounded in probability theory and the strategic assumption on evaluating the dealers hand is clearly too legit to quit.  However, there is one teeny tiny detail that basic strategy depends on, and it’s that detail that rests squarely in control of the casinos.  That detail I’m referring to is the random deck, and I’ll get into my thoughts around how casinos shuffle decks and the implications on basic strategy next week.

Until then, check out the Blue launch of Wixity.  You’ll be able to browse and search for summer events in New York City.  We have been working very hard on it, and would love to hear everyone’s feedback.  If you are interested in more of the features, you can be invited to our our private beta by emailing me at

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4 Responses to “Blackjack, Basic Strategy, Battle of Wits – Part II”

  1. B says:

    I’m not sure if you’re implying that the house’s edge comes from the shuffle, but I believe it comes from the fact that the player must act first (e.g., if the player busts, he loses even if the dealer later busts as well)

  2. rishi says:

    lets go to vegas

  3. Rathan Haran says:

    Yea, the house edge is partly due to the player acting first in conjunction with other rules set up (like whether dealers hit on soft 17). Given these existing rules, basic strategy was developed to give the player the best odds, but it depends on a random deck. Without a random deck, the “odds” of basic strategy change dramatically.

    Rish, I’m in.

  4. N says:

    Dealers who know basic strategy encourage players to use basic strategy because it helps casual players win. When casual players win they are more likely to tip the dealer.

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