I guess I am having the most trouble describing what I do, because its been quite a while. Looks like I am going to have to hunt down a Simplex lock soon. First off, I always try the factory combination (24)3 first. Seems silly, but apparently for many years a very large user of Simplex locks, used the default combination. While I hope they have changed this, I fear that they havent. If a large corporation doesnt change the default combination, I assumed that most people wouldn't, and with my friends lock I was correct. Once he changed the combination, I tried to determine how far one of the tumblers needed to move. After determining just that one tumbler, I used that information to brute force the approximately 300 combinations that were left. I only needed to do about 20 before It opened.
Other bits of info that I would like to postulate for the average Simplex lock
1.) Joe User will almost never set a one push combination, be it a single, or multiple button push.
2.) (12345) also seems "insecure" to Joe User, and probably is never the combination
3.) Joe User will probably pick a 3 push combination. Think about what you would do if you were ignorant of picking, and went to set your lock. I guess that most users would pick at least one double push, but almost never a triple push. The default combo contains one double push, so Joe User probably things that this is a clever thing to do, and that any more than a double push will limit his possible combinations
While these are not hard and fast rules, and certainly if someone knows a bit about Simplex locks, I would assume they would not pick a "routine" combination. But, as these locks are used for high traffic areas, the special pushes would probably become inconvenient to demonstrate to most users.