Levitt and I just recorded a Q&A session for the Freakonomics Radio podcast, using the questions that all of you recently submitted. You’ll hear the results soon, probably in January. Thanks for the good questions.
One question we didn’t get to, from Tg3:
I have heard Dubner casually mention that he is a backgammon player. Are there ever Levitt vs. Dubner battles? More importantly, why is such a great game not more popular in North America?
Sadly, Levitt and I have never played. But it’s the second part of the question that got me thinking. Why not indeed? Off the top of my head, I’d say:
- Well, it’s not so unpopular, and there are those who say a renaissance is perhaps underway. My friend James Altucher and I have a running game (101-point matches) that we usually play in diners or restaurants, and almost inevitably a small crowd (or at least the server) will hang out to watch and talk about the game …
- That said, yes, it’s a fringe game. Why? I’d say it’s because too many people play it without gambling, or at least without using the doubling cube. Without the cube, a game that is intricate and strategic – because the stakes are higher – becomes an often-boring dice race. Once you use the cube, especially with dollars attached to points, the game changes completely because the most exciting and most difficult decisions have to do more with cube play than with checker play.
- Why is the game itself too often uninteresting? Don’t get me wrong: I love playing backgammon. But the fact is that the choice set of moves is in fact quite small. That is, for many rolls, there’s clearly one optimal move, or perhaps two that are nearly equal. So once you know those moves, the game is limited, and you need some stakes to make it interesting. Unlike, say, chess, where the options and strategies are far more diverse.
This last point, if arguable, got me to wondering: in what percent of backgammon turns would there seem to be clearly one optimal move – versus, for comparison, chess?
Since James is a superb chess player and also an excellent backgammon player (and a smart guy in general), I asked him. His answer is well worth sharing:
It’s an interesting question. Let’s define optimal first.
Let’s say a program has an evaluation function (EV). Given a position, the EV returns a number from 1 to 10 based on how good the position is for the person whose move it is. If it’s a 10, the person with the move wants to get to that position. The EV is a function of various heuristics added up (how many people are on the center, how many pips I’m ahead in the race, how many slots I control, how many loose pieces I have, etc). When it’s my turn, the computer looks at all my initial moves and finds the ones resulting in the best EV. It then looks at all my opponent’s responses to each move and finds the ones resulting in the lowest EV for me (this now propagates up to become the EV of my initial move). It then looks at all my responses to my opponent’s responses and finds the ones with the best EV (and does the propagation again). This is called min-max. Looking at all the best moves only is called alpha-beta search and is how most game programs work.
So the question is, what is “optimal?” On a scale of 1 to 10, if a move is 3 better than the next move, is that optimal? Let’s say it is.
In chess, it’s easy to see optimal moves. If someone does rook takes queen, then hopefully I can take his queen and it’s a fair trade. By far that will be the only optimal move. Other optimal moves lead to checkmate or great increases in material. Otherwise, its probably not optimal. In a typical chess game, maybe 5 percent of the moves have a value greater than “one pawn’s worth.”
In backgammon, I’d say its 10 percent. I’m saying this based on experience with Backgammon NJ [an excellent program, BTW], discussions with backgammon game programmers in the past, and I’m using 10 percent rather than 5 percent because backgammon is slightly less complex than chess. It’s not simple though. To be a backgammon master probably requires almost as much study but not quite.
Hope this was helpful.
Yes, James, helpful indeed – because I now know a bit better how you think about the game, which I desperately need to finally beat you in our 101-pt. matches. Thanks!