Texas Hold-em Poker
Two suit problem
Question | Answer | Simulation Program | Program Answer | Conclusion

Question
Before the flop you get 2 of the same suit, what are you chances of getting the Flush, by the end of that game?

1. You have 2 know cards, leaving 50 different card that could come up on the next 5 cards
    POS = the 1st card there are 50 cards left, next card there are only 49 cards left and so on....
        50*49*48*47*46 = 254,251,200

2. To find the Odds of getting a flush, you need to know how many of them are flush hands
    Number of flush hands / Number possible = The odds: the chance ie: (.5 = 50% chance)

We will start by looking at all the ways it looks to win, then calculate, the odds of that, then how many, ways that can happen.
    Hand:    x = does not match suit, s = suit matches
    Odds:    (s s s s s) - you have 2 of that suit, so for the 1st card there is 11 of that suit in the remaining 50 (11/50)
                  2nd card (event 2) there are now 10 matching suits out of 49 cards (10/49)
                  Continue this for the next 3 event. To get the odds of all 5 events happening is (event 1 * ev2 * ev3 * ev4 * ev5)
    Count:   To get the number of times this will happen is (Odds * number of possible hands = POS)
 

Calculation hint: Since the divisor will always be number of possible hands (POS). We can skip calculating the odds, and go right to the Count. Count =  the dividends all time each other. Example for (s s s s s), Count = 11 * 10 * 9 * 8 * 7.

Answer:
So total count = 55440 + 308880*5 + 1467180*10 = 16271640
Total Odds = Count / POS about 6.4%

You might want to check my math!

6.4% Don't sound right to me. that means if you have 2 suited card before the flop, you only have a 6.4% of getting a flush.
I decided to write a program to simulate the problem, to check that answer with reality.

Simulation Program
Written in Visual Basic

Public Class test
    Dim Counter As Integer
    Dim ODDSc As Double
    Dim Hits As Integer
    Dim Cards(50) As Boolean
    Dim a As Integer
    Dim r As Integer
    Dim b As Integer
    Dim temp As Boolean
    Dim l As Integer

    REM Initalize
    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        Counter = 0 : ODDSc = 0 : Hits = 0
        For a = 0 To 10 : Cards(a) = True : Next
        For a = 11 To 49 : Cards(a) = False : Next
    End Sub

    REM "Timer1" is a Timer object, Sub trigger by Tick event
    Private Sub Timer1_Tick(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Timer1.Tick
        For l = 1 To 1000
            b = 0 : Counter = Counter + 1
            For a = 50 To 46 Step -1
                r = CInt(Int(Rnd() * a))
                If Cards(r) Then : b = b + 1 : End If
                temp = Cards(a - 1) : Cards(a - 1) = Cards(r) : Cards(r) = temp
            Next
            If b > 2 Then : Hits = Hits + 1 : End If
        Next
        ODDSc = Hits / Counter
        Count.Text = Counter.ToString REM "Count" is a text box object
        odds.Text = ODDSc.ToString REM "odds" is a text box object
    End Sub
End Class

Program Answer

After running the program for some 16,000,000 hands it came up with 6.401%. Math and program verified: correct!

Conclusion

If you have matching suits before the flop, don't expect a flush.
Examples:    2,7 suited should never be played. Now K,Q suited should, but not because they are suited, it only helps, adding
                   6.4% to the odds.

Links