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#1
12-22-2005, 07:21 PM
 shutupndeal Member Join Date: Sep 2003 Posts: 31
Brain dead need help a sec

[img]/images/graemlins/confused.gif[/img] Can someone show me the forumla for how many times you will flop your suit for a four flush on the flop?
I know its easy but Im going blank here!
#2
12-22-2005, 10:55 PM
 DavidC Senior Member Join Date: Aug 2004 Location: Ontario, Canada Posts: 292
Re: Brain dead need help a sec

Pretty sure it's something like this:

52 card deck, 2 dealt to you, 50 cards remaining.

Possible deals ?? (50*49*48)/(3*2*1) = PD

Cards in a suit: 13
Cards left in your suit: 11

You want to be dealt ?? (11*10*9)/(3*2*1) = WD

And I think that leaves you with WD/PD as your chance.

---

This is my best guess, and it's based on the fact that you can get a flop any of 6 different ways with the same three cards (the cards could be "shuffled" differently). If there's a mistake, someone please help me out.
#3
12-23-2005, 04:06 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Re: Brain dead need help a sec

There are 19,600 flops.

You will flop a made flush 165 times . . . (11x10x9) / 3!.

You will flop a flush draw 2,145 times . . . (11x10x39) / 2!.

You'll flop a flush OR flush draw 11.47% of the time - approximately once in 8.5 times.
#4
12-24-2005, 12:22 AM
 Guest Posts: n/a
Re: Brain dead need help a sec

[ QUOTE ]
There are 19,600 flops.

You will flop a made flush 165 times . . . (11x10x9) / 3!.

You will flop a flush draw 2,145 times . . . (11x10x39) / 2!.

You'll flop a flush OR flush draw 11.47% of the time - approximately once in 8.5 times.

[/ QUOTE ]

Please can you give the details of the factorial equation you used here.
#5
12-25-2005, 07:01 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Re: Brain dead need help a sec

The flopped flush is the easier of the two.

There are 50 unseen cards, so . . . 50x49x48/3! = 19,600 (possible flops)

There are 11 cards of your suit; you need three to flop, so . . . 11x10x9/3! = 165

*

The figures for the flopped draw are done the same way but here we need 2 of your suit and one NOT of your suit (the inclusion-exclusion principle); if you don't do it this way you'll double count the flopped flushes. (In other words, you'll count them as both made hands AND flopped draws).

PM me if you want it explained in greater detail.
#6
12-25-2005, 07:07 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Re: Brain dead need help a sec

You got it.
#7
12-26-2005, 03:01 PM
 shutupndeal Member Join Date: Sep 2003 Posts: 31
Re: Brain dead need help a sec

Thanx so much!

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