What’s the estimated number of iterations to collide? Kangaroo-style

How many iterations do you think it takes to get a collision? This isn’t your usual kangaroo setup. Both Wild and Tame can move both ways. We’re dealing with a 135-bit puzzle here. There’s a total of 1.9 trillion for Wild and 1.9 trillion for Tame. You can’t have Wild collide with Wild or Tame with Tame. The only possible collisions are between Tame and Wild. I’m not using distinguished points in this scenario. Can anyone estimate how many iterations, on average, it would take for Tame and Wild to collide? Does the birthday paradox factor in here? I’ve tried asking 5 different AI, and they all gave me different answers.

I think 12

I think that is too low. Collision happens only to wild and tame.

Here's the correct answer, in line with how you stated your problem parameters: Between zero iterations and an infinite iterations. Because you can't know if a collision will ever occur (even if you find a way to store all the visited points, which is already the #1 limiting and bottleneck factor anyway). You may also get lucky and hit the target when your first Tame gets born. You seem to ask the same question over and over, when you should have already had the answer if you'd actually spend 5 minutes to do some basic math, instead of asking stupid questions without any actual context whatsoever.

I want to know the average collision. There too many visited points it impossible to store them all.

Puzzle 135 is 134 bits, so if you don't screw up the parameters and the algorithms, then you can expect somewhere around 2**66 to 2**68 group operations until the first collision. It can be more, or it can be less. In terms of cost, you're looking at somewhere between 100k and 1 million $, depending on luck.