View Full Version : Higher flush on a 3-flush board

05-01-2005, 11:03 PM
You hold 2 suited cards and the board has 3 more of your suit (along with 2 more offsuit cards). What are the chances another person has a flush (assuming your opp plays all cards, even 23s)

05-02-2005, 12:51 AM
This is an inclusion/exclusion problem. There are seven known cards, 5 of your suit and two other. There are 45 unseen cards with 8 of your suit and 37 other. Assuming your opponent plays any suited hand the probability of one or more opponents having a flush are:


(8c8)/(45c8) = 23.79% for nine opponents.

with six opponents = 16.27%

with four opponents = 11.03%