How Many Moves Ahead Do You Calculate?


In the past month, I played maybe 15 casual games of chess, and from these, I discovered a few things about calculation that I had overlooked in my otherwise tournament-heavy experience. I was able to learn new things precisely because the games were casual, and thus not subject to the competitive mindset. In most of them, I talked to my opponent as I played. These were against lower level players, and to help them out, I sometimes discussed my thought process mid-game. This was also a chance to explain to non-competitive chess players what goes on through an experienced player’s mind. Here are some of the things I found myself explaining:

1. It is NOT necessary to calculate several moves ahead.

Perhaps the most common misconception about chess is that a player needs to think 3, 4, 6, or even more moves ahead to win.

In reality, for the vast majority of moves, thinking even one move ahead is sufficient. Once you play enough games, you develop an intuition that will guide you as to which pieces to move, when to move them, and where. For example, I’ve played dozens of games that opened with the Sicilian Dragon, quite a few of them in rated tournaments. When I play a new game that opens with the Dragon, I instinctively know which strategies work and which ones don’t, and my thinking time is spent on figuring out the differences and trying to exploit them. That is, I can think about refining a strategy instead of inventing one. This saves a lot of time.

Sometimes, however, you will need to calculate an exorbitant number of moves ahead. I recall a game in the 2006 National Open that ended up in a rook and pawn endgame.  On the last move of the game, I thought for perhaps 40 minutes, calculating no fewer than 10 moves ahead. When I played that move, my opponent thought for an entire hour and then resigned. What made the position so complicated? Here’s what was going through my mind: pawns dangerously close to queening, rook and pawn checks, queen checks after 2 pawns queening, mating nets, as well as king positioning. This is an extreme exception though, and most of the time I don’t calculate over two moves ahead.

2. A balance between intuition and calculation is important.

As I mentioned above, intuition plays an enormous role in chess. With it, you feel like you “know” what to do. Should I attack the queenside or the kingside? Or should I try to break open the center? Should I trade a bishop for a knight? Should I push the g-pawn or the h-pawn to start the attack? Instead of calculating such things from scratch, you can often use intuition to develop a preliminary answer, and then use calculation to confirm or deny your hunch. This is incredibly useful in a tournament setting, where your clock is ticking.

One can go the other extreme and rely too much on intuition, or rather, too much on generalizations. At some point in a game, I was winning by a knight for a pawn, a pretty huge material advantage, but had slightly less board space than my opponent did. A third-party was watching the game, and told us that he thought my opponent was winning because he had more space.

I disagreed with the third-party because, based on the current board position, the space advantage did not make up for the material deficiency. In fact, I thought it did not even compensate a loss of one pawn, let alone two pawns (the equivalent of a knight for a pawn).

3. You don’t have to calculate every possible move.

This is why humans were able to beat even the best of computers for so long. We lasted until 1996. Even though computers could calculate orders of magnitude faster than the human brain at that time, and even before, they did not do the calculations in as smart a manner. For instance, say we are in some position in the middle-game, and that I have 20 legal moves, to each of which my opponent has 20 replies. Then to calculate just one move ahead, I would have to look at 400 positions to fully cover every scenario. (In chess lingo, a “move” consists of one move by white and one move by black.) To calculate two moves ahead, it would be 400², or 160,000 positions. For a human to do this, even analyzing one position per second, it would take several hours to compute. Now suppose you want to calculate 10 moves ahead: 400^10. This is roughly 10^26 positions to analyze. Even a computer analyzing these at a billion (10^9) positions per second would require 10^19 seconds, or 300,000,000 years. It would be impossible for a human.

So how is it possible that a human can calculate 10 or more moves ahead? Well, we (unconsciously) use a technique called pruning, or ignoring certain moves. For instance, out of the original 20 moves, only 3 of them look interesting at all, and the other 17 seem either accomplish nothing or are silly moves that lose material immediately. For a full “move,” this would be 9 positions, and calculating 10 moves ahead would give 9^10 = 3.5 billion positions. This is much more reasonable, but is still an extravagant amount. What happens in real calculation is that many moves are forced, in which there is only one response. Other times, one or two of the three interesting moves degenerates into a clear position at which you can stop calculating. Thus in calculating 10 moves ahead, it is possible that you may only need to look at 15 final positions, which is much less than 3.5 billion or 10^26.

The reason computers are beating humans now isn’t because the computers think faster—it’s because they think smarter. If it can prune 20 moves into 3, then it might only need to calculate 3.5 billion positions to think 10 moves ahead. And at a billion positions per second, this would only take 3.5 seconds.


There were also some occasions where I played blitz chess (speed chess) and blind chess, though not concurrently. Speed chess is normal chess with strict time restrictions. This effectively limits the number of moves ahead you can calculate. It emphasizes speed over accuracy of calculation. This is also where experienced players perform really well, as intuition reduces the time spent dramatically. This is why in speed chess it can appear that the players are playing instantly and not thinking. They actually are thinking, but just in a different way.

Blind chess is also the same as normal chess, only you are not allowed to look at the board. You have to call out what move you want to make, and your opponent calls out the response, etc. The trick is about making sure you know where all your pieces are. The easiest way to do this is to keep a mental image of the board in your head, and memorize all the moves that occurred in the game. That way, if you are ever unsure of where a piece is supposed to be, you can play through the previous moves to track that piece’s location.

Overall, I treat normal chess, blitz chess, and blind chess as the same game; only a few changes in the thinking process are needed. So in response to the question “How many moves ahead do you calculate?”, my answer is one or two moves usually, more if necessary. How many moves ahead do YOU calculate?

Lock Picking, and Solving Problems

Days pass by normally, and often you don’t pause to reflect on them because they’re the same day, the same old routine. The little differences that set your days apart—these start to become annoyances and tidbits, even interruptions in your daily schedule. Until you have a day that is so bizarrely different from the repeated existence that it shakes your foundations of routine to the ground.

Today (or rather, yesterday, since I am passing the midnight mark as I am typing this) was one of those days: it was the day of the Cornell homecoming game, and I suppose attending a sports event was something I had not done for over half a year. But besides that, the intriguing part happened when a fellow trumpet player and I left a bit after half time, only to find the band room locked on all exits.

For the next part, I will let other people remain anonymous, though I doubt the Cornell police are reading this. And if you are, you need not be alarmed as there was neither criminal intent nor damage done.

The person with me is quite good at knowing how things work, so he naturally assembles a makeshift lock-picking set from some handy materials. This includes a trumpet lyre, a Cornell Homecoming pin button, and an iPhone. The iPhone was used solely as a flashlight (this was at nearly 9 pm), the lyre was used as a “torsion wrench,” and the pin from the pin button was used as a pick, i.e. the thing that any lock-picker in a movie uses to poke into the keyhole.

After perhaps 15 minutes of attempts, it is clear that the lock is too sophisticated. He mentions how he could only set the first “tumbler” in place but that the lock had five tumblers. Heck, I didn’t even know those things in locks were called tumblers.

While this was going on, I reflected on the nature of problem solving, and realized that the problems I solve in classes, whether they be physics questions that assume surfaces are frictionless, or math questions that deal with uncountably infinite sets—I realized that such problems didn’t help the slightest bit when I faced this real world problem of a locked door. Even the highest levels of theoretical math and physics wouldn’t help now.

I even joked at how, if this were some action movie, one of us could climb through the ventilation system and pop down inside the room and open it from the inside. Unfortunately, it is an old building and there is not a ventilation shaft to fit into.

That physical locked door in front of me was the ironic manifestation of the hypothetical locked door. Neither my friend nor I had the key. And without the key, there was no getting past it.

I exit the building temporarily to go to the Statler, and on my way out, I see some other familiar band people coming in. I tell them we tried to lock pick the door, and continue walking. When I came back a few minutes later, a remarkable thing had occurred: the door was open! My friend and the other band people were inside, and yet none of us had a key.

It turns out that one of the people I ran into on my way to Statler had done the impossible: he climbed through a ridiculously small opening in the top corner of the room where some utility pipes passed through, and successfully landed and opened the door from the inside. Of course, in the room where we spend so long lock-picking, there just happened to be a ladder.