Payday 2 – What is the Highest Achievable Dodge Chance?

While there are currently no exact numbers on what causes an escape missions, I've noticed the following by observing when we get escape missions after completing the main segment of the mission:

• If no alarms are ever set off, there is no escape
• If you have the Expert Driver asset, there is no escape
• If you leave during an assault, there seems to be a very high (practically guaranteed) chance of an escape
• If you leave after an assault, before the next assault, there seems to be a reduced chance of escape
• If you leave after killing all enemies in a wave, outside of an assault phase, there seems to be a reduced chance of an escape
• Once you have set off an alarm, killing civilians will increase the chance of an escape mission

Ultimately, escape missions are there to prevent the "quick and dirty grind" - if you want to go in loud and don't prepare properly, expect an escape to happen.

I've seen and heard a lot about this ambush.

From my experience, finishing the day one without triggering the alarm will insure you to avoid it. The wiki seems to confirm it:

Note: If you have successfully completed Day 1 in stealth, you will not be ambushed on Day 2.

It also says that

If you have not successfully completed Day 1 in stealth, there is a chance you will be ambushed though it is random, it is possible to go loud on Day 1 and have no ambush on Day 2 if you escape during the hostage phase.

I've also seen a guy putting an ECM jammer on the cell phone instead of answering it, before the second phone call. He wasn't sure, but thought it would reduce the chances of an ambush.