What Lies Beyond the Board?

What Lies Beyond the Board?
by Frank Frigo – 28 June 2006

I am often asked to compare the strategies of backgammon and poker. While the games certainly have some similarities, the biggest distinction is in the available information and where the information is located.

Poker aficionados are quick to point out that in backgammon every piece of intelligence is on the board in front of you. Poker on the other hand requires the need to handicap the hidden or indirect information.  How my opponent bets, holds his cards, reaches for his chips and darts his eyes all may (or may not) be providing me clues toward some hidden information. While none of these clues provide any certainty, the savvy poker player will handicap this information and combine it with what is known (i.e. chip stacks, his hole cards, his position and of course the pot odds). Is backgammon really so different?

The answer is yes and no. Most of the valuable information is indeed on the board and the bots have shown this to be true. Snowie and GNU can both play at a world class level without knowing a single thing about their opponent. The scary thought is how good they could be if they could profile their challengers. Much has been written about adjusting one’s play based on skill differentials. Walter Trice and Jake Jacobs wrote an entire book on the subject (“Can a Fish Taste Twice as Good”). Based on rating differentials, the authors offer up a number of optimal strategies to exploit skill variance. Match equity tables were developed to reflect the skill (ELO rating) differences among players and these tables can greatly alter certain key doubling decisions in matches. As in poker, backgammon also has some indirect information which should not be underestimated.

A successful backgammon player derives an advantage in two ways. First, he must strive to make technically optimal plays and avoid making errors. Secondly, by providing his opponent with difficult decisions, he can gain from his opponent’s errors. Keeping ones error rate to a minimum is obviously very important in the outcome of a backgammon match. But it is the error differential that really matters. Direct information (that which we see on the board) provides us with most of the tools we need to control our own error rates. It is through the indirect information whereby we may exercise some influence over our opponent’s choices and subsequently the error differential.

Efficient doubles are all well and good, but having a strong suspicion that your opponent will pass a proper take, or take a proper pass can be a significant advantage. This suspicion can be derived from their body language or simply from a player’s history. If the signals are strong enough, there may be justification for skewing doubling decisions beyond what is technically correct. Just as in poker, knowing whether a player is generally conservative or aggressive can be very helpful. Checker plays as well as cube decisions, can be used to exploit the indirect information. Consider an aggressive player who is prone to overextending his position during blitzes. This is exactly the type of opponent we should like to “minor-split” against early in the game. Their deep and loose hits will often translate into an early racing advantage for us. Another example might be an opponent who is a solid checker player, but has a very difficult time assessing races. If I perceive this player to also be a bit aggressive, I am going to be far more likely to give a late cube in a somewhat murky race – a situation in which they will have a chance to make a blunder.

When assessing the value of indirect information, here are some of the key characteristics we should consider when profiling our opponent:

• Overall Skill Level
  • How strong is my opponent and how does their level of play compare with my own?
• Conservative or Aggressive
  • In what types of positions are these traits likely to surface?
• Body Language
  • Do they look eager or passive when I am considering the cube?
• Temperament (Steam Factor)
  • How likely are they to gather their wits after a tough loss?
• Ability to count pips
  • Is my opponent a recent convert from online backgammon to live tournaments?
• Skill in assessing match equities
  • Can my opponent adjust for the difference between money games and match scores?

The reason this information is referred to as “indirect” is because there is no certainty in how someone will behave. While I know exactly how the checkers and cube are positioned on the board, I must handicap the behavior of my opponent. The bots can shed some light on behavioral handicapping as well. Consider the following position:

While Red’s position has become fairly strong, this is not quite a “proper” double.  However, if there is a 12% or greater chance that White will pass, the double becomes correct. This is because Red’s decision to double costs him about .05 points when White correctly accepts and gains about 0.4 points when White incorrectly passes.

What might Red know about White’s skill level? Is he conservative? Is he steaming from a tough loss last game?  Is he sitting with his arms folded or eagerly leaning forward? There are some instances where a strong case could be made for an opponent passing this double 1/8 times. Without any additional information beyond what Red sees on the board, he should just play on. In practice however, a double could hardly be faulted.

The assessment of indirect information is not an exact science and can even be used against us if we are not careful. However, a little information is often better than no information. So the next time you are laboring over a tough backgammon decision, don’t forget to take a gaze across the board to see who is sitting on the other side.