Posts tagged: Blackjack

Blackjack, Basic Strategy, Battle of Wits – Part III

By , August 5, 2009 12:28 pm

Have you ever been on a blackjack table and accidentally hit a hard 14 with the dealer showing a 5 while playing basic strategy?  Replay it in your mind, you bust on the King, dealer makes his 21 on a 6, the entire table gives you the death stare, curses your first born, all while mumbling under their breath, “Never hit on a hard 14 with the dealer showing a 5 idiot. That King was the dealer’s bust card. We all would have won.”  Tough room.

First things first, those people have no idea what they are talking about.  There is no such thing as “that was the dealer’s bust card.”  The deck doesn’t know whether the dealer or the player is hitting or staying and the cards don’t change because of how someone plays their hand.  The probabilities that guide basic strategy haven’t been altered because someone does not make the optimal play and theoretically the dealer still has the same likelihood of busting (in practice though, since the deck has a fixed amount of cards, the distribution of remaining cards changes the underlying probabilities of basic strategy.  Card counting attempts to exploit this by identifying random deck distributions that happen to have a large amount of 10-value cards remaining).

The important thing to remember here is that basic strategy gives you the probabilistically best play given that the deck has a RANDOM DISTRIBUTION OF CARDS.  That means that if the deck is not random, basic strategy might not be the optimal play.  So what everyone should consider before baptize themselves in the holy waters of basic strategy is what it takes to make a deck random (and who controls what it takes to make a deck random).

To make a single deck random, the deck must be riffle shuffled about 7 times.  Since suit doesn’t matter in blackjack, and K, Q, J, and 10 hold the same value, you actually need to shuffle a single deck less, about 4 times, to make it random.  Most casino blackjack tables play with 6 or 8 decks at once which are shuffled together and played from a dealer’s shoe.  In order to randomize a shoe of 8 decks, it takes about 12 riffle shuffles.  Does your casino shuffle a shoe 12 times?  Probably not.  Most casinos shuffle a shoe 4 times, and that has some interesting implications when an entire table is playing basic strategy.

So let’s take a look at what happens to a shoe when the entire table is playing basic strategy.  The first thing is that anyone that has a strong hand on their first two cards (17+) is instructed to stay, and their cards remain on the table until the deal is over.  Players with weak hands play out their hands, and if they bust, the cards are removed from the table and placed in the discard shoe.  This begins to create layers of cards in the shoe; clusters of low cards placed on the shoe first, followed by clusters of high cards that were left on the table.  Since most casinos do not shuffle the shoe enough times, these layers loosely exist in the new shoe, and are further propagated when the entire table plays basic strategy (some people attempt to exploit this by using a technique called cluster counting).

Clustering of cards creates decks that are not random, which is one of the critical assumptions that basic strategy is built on.  This creates opportunities for dealers to win/push more hands than basic strategy predicts.  During a high cluster deal, a dealer is likely to have high cards to push, or even beat, the tables “strong” 19s and 20s.  In the case where low card clusters are being dealt, a dealer will likely have a low up-card, a situation where basic strategy dictates to hit against until about 14.  The thing is that since it’s a low cluster deck, the dealer  has a better chance to make a hand!  The player also has a better chance to make a hand, but basic strategy actually advises them not to try.  INCONCIEVABLE!

Basic strategy is still by far the best way to reduce the house odds, but since decks are not completely random, there is certainly room for improvements in game play.  For example, in high cluster deck situations, it may be worthwhile to split face cards, while in low cluster situations, taking another card to try to make a better hand may be your best bet.  Playing this way may add a little bit more excitement to the rule-based approach of basic strategy as you’d be trying to exploit the rest of the table playing the basic strategy system.  And if it pisses anyone off at your table, just turn to them and say “You fell victim to one of the classic blunders!  The most famous is never get involved in a land war in Asia, but only slightly less well-known is this: never play basic strategy against a dealer when deck isn’t random!”  I’d get a kick out of that if I heard that on a blackjack table.

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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Blackjack, Basic Strategy, Battle of Wits – Part I

By , July 8, 2009 7:04 am

After about a week and half in southern California meeting with advisers and VCs,  I made the trip to Las Vegas with a few high school friends to spend a few days … well, you know, it’s Vegas.  I hadn’t been to Vegas in close to seven years, partly because … well, you know, it’s Vegas and partly because of I’m not a fan of playing games where it’s not in my favor to win.  This was a lesson learned after losing three paychecks in a row playing blackjack at Ceasars during my younger day frequents to Atlantic City.  Now I only play the Powerball Lottery when the jackpot is probabilistically in my favor to risk the dollar (roughly over $150M).

Blackjack was the only game I ever played at a casino, and of course, in typical sadistic gambling fashion, I found myself hovering around the tables, mentally urging people to double down on eleven and stand on dealer six.   And as I kept rattling off the most efficient plays that basic strategy mandates, I started noticing that every player was doing exactly what I was thinking, and the dealers were encouraging the novices to do the same.  I began to wonder in a game where a casino stands to take more when people play ineffectively, why would the house encourage their competition to play the most efficient blackjack strategies?  I started to wonder whether the casinos knew something about basic strategy, much like the Dread Pirate Roberts knew a little something about iocane powder in his battle of wits with the great Fazzini.

Basic strategy outlines how a player should act in a game of blackjack by providing a probabilistic guideline to standing, hitting, splitting, or doubling down based on the combination of cards that the person has and the one card the dealer is showing.  Playing basic strategy dramatically decreases the house’s edge, and the exact amount varies by the rules of each casino (you can calculate those variations here).   There are other ways to increase your odds in a casino, like counting cards or group play, but these ways are heavily frowned upon (read as broken bones) by casino pit bosses.    So why is basic strategy so accepted, and almost so loved by the casino community?  My guess is that the answer lies in the assumptions of basic strategy, which are so often overlooked by the “amateur experts” looking to turn a paycheck into a dream.

I’ve been pretty busy over the last few weeks, so I’ll save the second half of this posting for next week.  Until then, I’ll leave you with this memorable scene from The Princess Bride.

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