I'm curious in which case player posts big and small blinds simultaneously in Texas hold'em game. I recall it has something to do with letting button go through all players before joining the game.
At a casino, when you first sit down at a Hold’em table, the rules vary as to whether you have to post blinds (even if you’re out of the normal blind positions for that hand) in order to be dealt a hand. Posting Blinds in Texas Hold’em
House rules vary. Some places don't require you to post any blinds at all when sitting down at the table, other places do.
Some require you to post a big blind and I believe that some will require you to post the big blind and the small blind simultaneously so that you end up paying the full amount for the blinds without having to charge you in two separate hands, that could be tricky to manage without having a button or a chip to indicate that.
I think this is the only occurrence where this can take place.
A lot of places you have to come in on a big blind in cash games (tournaments you never miss a blind).
You can typically wait for the blind to reach you or post a big blind to get a hand, you can post whenever you would like. You can let the blinds pass and post in position behind the button. Some places allow you to post between blinds, and some places will let you "*buy the button" by posting both the big and small blinds directly under the gun. If you missed a blind you can also buy the button if you are directly under the gun. Whenever you miss the blinds you will have to post both a big and small blind or wait for the blinds to get to you before receiving a hand. If you miss just a small blind you will need to post just a small blind to get a hand or wait for the blinds to reach you. A posted small blind is always dead, meaning it is not part of any call or bet you might make in turn.
*Buying the button is when you post both blinds and then receive the button on the next hand. You can only buy the button when the button is in the seat directly on your right and the player(s) on your left are due the blinds. Those players get a one hand reprieve on the blinds.