Question: In a game of Go, we were in a strange position. If my opponent moved at one point to put my pieces in atari, his pieces would get taken. If I moved at that same point my pieces would’ve been taken.

So if neither of us move at that point, are our stones dead?

How do you count this kind of position in the counting phase?

Answer: 
This situation is called [Seki](http://senseis.xmp.net/?Seki). Scoring depends on the ruleset you're using.
The situation you are describing is called a `seki` or possibly just a `point of contention` on the board. There are two ways to look at the situation. The first addresses the your questions and the second is a little more theoretical.

**First**

* It is the end of the game and both players have passed.
* If you both agree that that area is `unplayable` and a `seki` then those spaces are not counted for either player. For example, in Japanese counting you might just fill those spaces with stones from your bowls; move areas around for easier counting; and then determine the score.
* If either player `contests` the area then play resumes and that player will attempt to play in and capture the area. Play then ends again when both players have passed.

As you can see the area may or may not be in an absolute sense a `seki`, but that doesn't matter for the purposes of playing. Players can only play at their own level and see how to play through positions at that level. So, it is possible to incorrectly agree that an area is a `seki` or `dead` and belonging to either white or black, or any number of other errors. But, for the purposes of playing and learning, as long as both players agree that is how that area will be counted. You will especially see this kind of thinking during tournaments were there is no official observer for each game. It is then the losing players job, having agreed to the loss, to report the outcome of the game.

**Second**

Often times during post game analysis with a stronger player (s)he might explain that the area was not in fact a `seki` (or `dead` in the case of a life and death situation that was not fully played out) and that one player could have proceeded along some sequence of moves to capture the other. In these cases it doesn't change the outcome of the game it only changes the players' understanding of the game and how it "could" have changed.