This formula works...
I have sent over 300 Private Messages per DAY and have never been put in FB jail for it.
On any typical average day I'm sending over 100 Private Messages with no issues at all.
To be clear...
Most of these messages are to current FB friends of mine which by itself will keep you mostly "safe" from getting in trouble. But even when sending COLD messages to people you are NOT currently friends with, this formula will work to keep you out of FB jail.
The 2 things that will get you in jail with messenger...
1) When FB thinks you are spamming people by sending the same message to alot of people too fast. You will probably get a warning or maybe a time-out from being able to message people for a few hours.
2) When people that you message REPORT you to FB... this one can get you in trouble for sure.
1) Always use their name in the first message.
Especially if you are doing a copy / paste message to many people. This forces you to slow down a little bit and each message will not be exactly the same which shows the FB gods you are a real person and not spamming people. This also helps you create a connection with the person you are sending a message to by using their name. In your follow-ups to this person, you don't have to use their name but it's still good to do so sometimes when it's natural... like you are having a real face-to-face conversation with someone.... talk to someone on messenger like you would if you were with them in person.
2) Never send a LINK in your first message!
I actually don't send a link to someone until I've gone back and forth with them 2-3 times to create a connection and ask them some questions to QUALIFY them before sending a link to anything. After you have qualified them to make sure they are interested AND they have told you to send the info / presentation ... then send the link.
3) Space out your messages.
This is very important so FB doesn't think you are a robot or using a spamming program to message people. They do exist and I personally would never trust using one because FB is smart and if they catch you, they can put you in jail or even worse... completely shut down your entire profile ... DELETED! Not worth the risk. I would recommend sending no more than 10 messages in a row to cold prospects... (following the first two steps) then you can go back and message current friends and / or do follow up messages. There is really no limit to these types of messages to your current friends because you already have established a connection with them. Then after 20-30 minutes, do another 10 cold messages.... repeat. Within a few hours you will have sent well over 100 messages out in total.
It is very possible that your message to NON-Friends will go to their request / spam folder so they might not see your message. One way to increase the chance they DO get your message is to comment on one of their FB posts that you send a msg to them and ask them to check their inbox. Once they go look for it and msg you back, they will always get your messages into their main inbox on FB.
When people comment on your facebook posts requesting info, be sure to reply to their comment saying you have sent them a message... always take the conversation into Messenger. This will also help you boost your Facebook Engagement!