The House Always Wins IV

 is a quest in Fallout: New Vegas

Quick walkthrough
Mr. House asks the player to convince the Omertas to ally with Mr. House. The player can achieve this by completing How Little We Know, or killing all the Omertas. Upon doing either, the player must then return to Mr. House. If you have previously done either, the quest will mark as completed automatically. House will pay you anyway, just to avoid discouraging you. Alternatively, the player can just refuse to surrender his weapons upon entering the casino and thus turn the Omertas hostile. There is no need to kill any of them, leaving and speaking to House will fail the quest but allow the player to proceed to part 5. This is the fastest way to pass this section but forfeits the rewards.
 * Completing The House Always Wins: IV will cause the player to fail Beware the Wrath of Caesar! and Render Unto Caesar.

If you have already finished How Little We Know by siding with Nero and Big Sal, then you will automatically fail part IV when talking to Mr. House, unless you can pass a [Speech Check of 50] and tell him the Omerta's plans and then say you infiltrated them in order to gain their confidence.

Detailed walkthrough
For more information please See the side quest How Little We Know.