I am in a debate about the odds for making a royal by suit. WhoIsPhaedrus posted in 2005 that the odds against a royal in 7 cards was 34,421 to 1. This number looks pretty close.

Are the odds of making a royal for instance in Clubs in 7 cards, with having the first two cards of the royal dealt to you, are 4 times this number (137684 to 1) or is it? I can't seem to get the formula to work with this.

Help
Getandgo