PDA

View Full Version : Odds of getting a Royal in Holdem?

AA suited
12-22-2004, 12:21 AM
I know the odds of all 5 of the community cards being a royal is 1:650k. (you have 0 of the royal cards on your hand.)

1) How about if you have 1 of the Royal cards in your hand?
2) How about if you have 2 of the Royal cards in your hand?

MortalWombatDotCom
12-22-2004, 02:38 AM
the total number of possible boards given your two cards s C(50,5) = 2118760. lets call that h.

if you have two royal cards (same suit), the total number of boards that make you a royal is 47*46/2 (pick the two cards that are NOT royal cards, their order doesn't matter).

(47*46/2)/h = .00051020408163265306 is your chance of making a royal

the number of boards that makes you a 1-card royal is
46 (pick the one card you don't use). so your chance of making a 1-card royal is 46/h = .00002171081198436821

if you have two possible royal cards (different suits) your chance doubles to .00004342162396873642.

if you have no cards T or higher, your chance of making a royal is 0.

AA suited
12-22-2004, 10:45 AM
what does that equate to? 1:? odds?

Lost Wages
12-22-2004, 12:58 PM
If the probability is P, then the odds are (1-P)/P:1

Lost Wages