About Luck and Skill in Backgammon and Poker

About Luck and Skill in Backgammon and Poker

by Frank Frigo – 16 November 2006

The two most frequent questions I am often asked about backgammon are:

1. How much of backgammon is luck?
2. What takes more skill; backgammon or poker?

In light of our recent misguided legislation in the U.S. regarding online gaming, these questions are probably more relevant than ever.  For many of us in the gaming community, our pursuit of intellectually stimulating games is under attack.  Strangely enough, backgammon and poker are the victims of a campaign to protect family values.

When I see my children playing board games instead of watching television it makes me proud.  They are learning about risk management, critical thinking, sportsmanship and a host of other disciplines and values that will help them throughout their adult lives.

Just what are Senator Bill Frist and company thinking?  And what exactly does this have to do with the security of our ports?  OK enough of my rant; let’s get back to answering the difficult questions.

The answer to how much skill lies in backgammon is a complicated one.  Let me start by making what I believe to be several factual points about the game:

• Every decision in Backgammon is a skillful decision
  • With the exception of forced moves, every choice requires a skillful assessment of alternatives
  • Some choices carry more weight than others but all are affected by some amount of skill

• A raw beginner (someone who has just learned the basic rules and a few general strategies) would have almost no chance of defeating a world-class expert in a 25-point match
  • The expert would almost certainly be greater than a 95% favorite

• There is great parity among top players
  • Among experts, it is rare to win more than 60% of open level matches over the long haul

• There is extreme volatility as a result of the dice
  • Single game winning chances can swing 5 to 10% on the opening moves and up to 100% in late game situations

• Skill is based on more than just the fundamental knowledge of the game
  • Temperament, preparation and execution matter a great deal

Several years ago I read an article by Bill Robertie on “Complexity Levels” in various games of skill.  These levels were defined by the number of tiers between expert and beginner whereby a higher level could defeat the lower level 75% of the time in a lengthy contest (say a 25-point match in backgammon).  Not surprisingly, games such as Go and Chess ranked at the top of the complexity scale.  While this analysis shed some light on parity it did not ultimately answer the ‘luck vs. skill’ question.

Even though there is really no easy way to definitively slice the pie between skill and luck in backgammon, one thing is clear.  It is absolutely a game of skill.  It is the parity of the participants that fools our perception.  In a sense, this is no different than any other game or sport of skill.  When the competition is close or evenly matched, extraneous factors or luck will likely make the difference.

I propose that perhaps the best way to determine the skill level in any game is to do the following:

1. Choose a worthy format for the competition.  In the case of backgammon let’s use a 25-point match.
2. Determine the percentage of time that a raw beginner could be expected to defeat an expert in that format.
3. The resulting percentage is the luck factor.

For instance, the game of Roshambo (rock, paper, and scissors) would be considered nearly 100% luck in a best-of-19 game format.  As much as the so-called experts might squawk over this fact, consider the following.   I could teach a five-year-old a random algorithm that would disable an “expert” from garnering any edge.  Before you doubt a five-year-old’s ability to behave randomly, consider how easy it would be to have them construct a pattern from the dial of a wrist watch, or a simple nursery rhyme unbeknownst to their opponent.

Now on to the Poker question.  Let’s consider a heads-up no-limit Texas Hold-em competition between an expert and a raw beginner.  We will set the blind structure in the most skillful way possible.  If the beginner simply goes all-in on every hand he will guarantee that the match will be decided on a single hand at some point.  While this is far from the optimal strategy, it assures the beginner of being no worse than approximately a 3:1 underdog.  That’s right; imagine a five-year-old who just knows the most basic rules of no-limit hold-em sitting across from Phil Ivey with an even chip stack in the final showdown of the World Series of Poker.

Using a basic “all-in all the time” strategy, the beginner should have at least a 25% chance of pulling down the championship.  To see why this is true, recognize that Ivey will have to push all-in at some point and his stack will be covered by the beginner.  The longer he waits the more he gets blinded out.  He will likely push when he believes he has a reasonably dominant hand.

The experts may debate the optimal defense to the beginner strategy but I expect Mr. Ivey would not lay down a hand that is a 75% favorite against the random beginner hand (a pair of tens, for instance).  Furthermore, if Ivey does win the showdown hand, the beginner may have already accrued enough blinds to stick around a bit longer.

While I love both games very much, I have to offer my apologies to the poker community.   Poker is a fascinating game but it definitely falls short of Backgammon in the skill department.  But that isn’t what is most important.  What needs to be clear to the general public is that Poker and Backgammon are both games of skill and should be treated with the respect they so richly deserve.  We can only hope these cherished games will ultimately be immune to the irrational pressures of Washington’s finest.