I just finished reading Ripley's "Unthinkable" . In addition to the "Competition" factor in crowd crushes, there's also crowd direction. If the crowd is headed in more then one direction, it aggravates the crush. In mt observation, there are three factors that need to be present for crowd crush. First, is crowd density. Second, is there needs to be some urgency. The last ritual of a weeklong pilgrimage, first come first serve resources, or a concert that's already underway. Lastly, is something to slow the crowd. A narrow passage like an entrance or exit or another crowd headed in a different direction.

Outside of outright avoidance, I don't know how to deal with crowds.

as an update, they've raised the fatality totals

Last body count is 1100. Roughly the same as the General Slocum disaster in 1904. More details are coming out as well. Like the General Slocum, it's not a single cause, but a cascade of mistakes

1) A group of 300 pilgrims departed the bridge early without being cleared to do so. They proceeded east on street 204, and intersected a group of 5000 going south on street 223 toward the bridge. Street 223 terminates at street 204, and the pilgrims on 223 would have to have gone west on 204 to reach the bridge. Fences lining the road prevented escape into the surrounding tent city.

2) Scheduling on the Jamaraate Bridge is notoriously tight, and as such, not very tolerant of out of position groups.

3) Street 206, which is the next intersection north on street 223, was blocked off. 206, if open, would have provided a relief path from the group headed south on 223. Why 206 was closed is still under investigation. The Iranian and Saudi goverments, not real friendly at the best of times (differing sects of Islam), are offering different reasons.

4) It was 47C (~117 F) at the time, which may have contributed to the early departure at the bridge.

5) Concerns about training of the Saudis in regards to crowd control. Specifically, why they were unable to compensate for the rouge group of 300 before it covered the 600M distance between the bridge and the intersection.

According to this , the number is now at 2,121.

When captured in such a dense crowd where you cannot even turn around - start breathing deeper, moving your chest up and down, instead of usual shallow diaphragm breathing. Try to keep the lungs half full all the time. Keep one of your palms locked over tightly closed fist under the chin, pressing the fist at the clavicles, and spread your elbows out a little at the chest level, like making a cage for your chest. Avoid spreading your legs too much while walking pinched between people, your leg might be captured tightly. If about to fall over something or somebody on the ground - use elbows to hang over the neighboring people and rise both legs over the obstacle, or step on it. If cannot withstand the pressure anymore push into others in perpendicular to the "crowd wave" direction (usually it goes along the "to the stage" or "to the exit" line), or even try to climb up a bit on your elbows, you are thinner down the legs, and people most likely will try to knock you off back, giving you some space for that. Been there done that.

In my experience, I found that climbing up on top of the crowd, spreading my arms and legs a bit, and either crab walking or rolling over the top to be quite effective. The people under me didn't like it much, but I got to the edge of the mob and was able to egress to safety. People were packed so tight that even if they wanted to they had no room to pull me back down once I got on top. Of course, there are caveats to such endeavors, but staying in the middle was simply no longer a viable option.

YMMV