Strafe jumping allows you to span gaps slightly further than can be with a regular forward jump. You won't get as far as the long jump module allows, but you can still cross to unexpected lengths perhaps enjoying a bonus at the other side.

It exploits a physics trait in the GoldSrc engine in that by strafing and turning at the same time a player can gain more speed than can be had just by running forward. This is the same principle behind bunny hopping "bhop", unlike bunny hopping the goal is (usually) to make one jump -- not multiple chained.

It can help greatly to remap your mouse wheel scrolling in game to perform jumping instead of SPACE, both for this and bunny hoppying. This may sound strange but it frees up some stress from your keyboard hand. It also allows you to create multiple jump commands by scrolling more than one tick, which helps ensure your launch doesn't begin too late after you start to fall. You can do this by opening your game console and submitting the following commands:


Simplified, the steps of a strafe jump are:

1. Accelerate adjacent to the gouge, not forward toward it. Typically you'd be running 80 degrees adjacent, going forwards. (No strafe yet.)
   
2. At the point of launch simultaneously jump, strafe (hold A/D), and turn to face the destination platform.
   
3. Hold the forward and strafe keys until landed.

Have I oversimplified? Let's go over that more closely.

Let's take the following gouge. Obviously not making this jump results in very death, and the gouge can't be spanned with a forward jump.


The blue line represents the line of acceleration you need to take. Run forwards along it, not sideways, from top to bottom.

Where the blue line meets with the red line you need to perform the next step. Keep hold of forward (W) but you now need to begin strafing (A). At the same time with your other hand you need to turn to face your destination, and launch by scrolling the mouse wheel.

The turn should be quite a snappy angle change, not a curve. Curved jumps are better suited for shorter but faster jumping necessary for bunny hopping rather than spanning one gouge as long as possible.

Finally the red line should be your approximate trajectory through the air towards the platform. As illustrated it's OK to have a little bit of curve whilst in the air but the initial turn needs to be abrupt.


Looking again sideways:



The next jump looks impossible with the much shorter run up, but it takes the exact same steps. Just move as far back along the platform as you can to get the maximum acceleration length, though you can still reach full speed by the time you arrive at the point of launch.

Don't trust my images? You've got some nerve!

Just to satisfy your scepticism here's a recording of me making every jump in the chain to show it can be done.