Category: Card Games

Casual Gaming, Fierce Competition

By , September 3, 2009 12:36 pm

Every Sunday night, my friend Jimmy ( organizes a small, local Sunday Night Poker game.  And every week he tempts me to get my visa and make it out to Brooklyn to play with his buddies.  With our without me, the game goes on, and every Sunday night there is someone who gets to walk home with a little more cash in their pocket.

I think this is a fairly common thing to do amongst groups of friends.  I mean, I think we’ve seen this make it into every RoCo (Romantic Comedy) ever made, and boy do those movies know how to parody every day life.  But an interesting problem was brought up when we were looking over how to rank each player.

Now, as typical (fill in day of the week) Poker Nights go, there are some people that are there every game, and then there are some who can rarely be bothered to visit Brooklyn that frequently.  That leaves us with a bit of problem since games tend to vary in size, as well as vary in who is playing on a given night.  We couldn’t simply tally up how many first to last place finishes everyone has to accurately rank a players skill.

Also, since the number of players can vary, this means that the difficulty of winning a particular game changes as well (the more players there are, the more you have to defeat to be the winner).  This throws another wrinkle in the ranking systems since winning an eight player game is harder to do than winning a three player game.  And then, how do you rank the random friend who came once and ended up winning?  Should he live forever as the best poker player your game has ever seen?

I did a little research and I found a pretty good way to rank players based on the size of the game, how rich the buy-in is, and where people finish in the game.  This equation came from, and it does a pretty job of creating separation between who finishes first and who wears the asshole hat (college reference anyone?):

equation2In this equation, B represents the buy-in, so the higher the stakes, the more points you can accumulate.  Also, since E, which is the number of entrants, is also in the numerator, a player gets more points for winning larger games.  P represents what place you finish in, so the further down you place, the larger the denominator, and the less points you can get.  Pretty cool.

The only problem I have with this system is that it rewards players who play a lot, and doesn’t penalize players that lose a lot.  With the scoring system, a player that plays a whole lot games and finishes in last place in all of them can outrank a player who plays a few games and actually wins them.

A better system would be to figure out relative points given the size of the game, and its a fairly simple adjustment to the equation.  We simply subtract out the points for what the average finish would be.  Those that finish above average, get positive points, and those that finish below get negative points.  Since losing games does not penalize you to the same magnitude as winning games reward you, a player can actually make up ground very quickly by winning games.

Now if you still find yourself at the bottom of your rankings, you may just have to suck it up and admit to yourself that you are not very good at poker.  And if you really still want to keep playing, we play every Sunday night so just give me a call.  I can even sell you a pass to the pool on the roof.

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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