plz help....i cant figure this out

[SittingBull]

on my computer.I'm a computer illiterate. [img]/forums/images/icons/frown.gif[/img] No,I haven't considered the Str. cases.
Happy Pokering, [img]/forums/images/icons/laugh.gif[/img]
SittingBull

[Cyrus]

"I haven't considered the Straight cases."

You need to consider those cases too. As well as lots of others. The calculation of the exact probability of flopping only a 4-flush draw (not a flush, not a SF, not a straight, not a straight draw), when holding JTs, is extremely tedious! (Pairing your hand or a pair on the flop are acceptable.)

"I do not know how to use "EXCEL" on my computer. I'm a computer illiterate."

So am I! But I know how to use Excel a bit. Here's how to get the program to do Combinations for you: Say you want to calculate the number of ways you can combine 10 items 2 at a time without respect to order.

Open a new File. Write 10 in cell A1 and 2 in cell A2. Then click on cell A3.

On the Command Toolbar, at the top of the screen, there must be a command icon titled fx. Click on it.
(If the Toolbar doesn't contain that command icon, click View > Toolbars > Customize. Then from the box that opens, choose Commands > Insert > fx Paste Function. Left-click the mouse, keep it clicked and drag the icon of "fx Paste Function" on your toolbar. Presto, you have the fx icon on your Toolbar. Click CLOSE.)

When you click on the fx icon, another box appears. It contains all the functions you can use. Click on ALL in the left frame of the box, scroll down in the right frame and click on COMBIN. Then click OK.

Another box appears. (Bear with me because it's all a matter literally of two seconds as soon as you orient yourself!)

Click on the top row, titled "Number", to activate it and write in it

a1

then click on the second row, titled "Number_chosen", and write in it

a2

(Doesn't matter if you use proper caps or not.) This way, what you did is you ordered the program to accept the value that appears in cell A1 as the number of all the items you choose from, and the value that appears in cell A2 as the number of items in each combination. The answer should appear in cell A3, which is the cell that you have clicked on right before calling up the fx icon to perform for you.

Now, if it all went well (and I haven't forgotten anything!), you should click on OK, and then see the number 45 appearing in A3. That's truly C(10,2).

Change the numbers in cells A1 and A2 to fool around. Writing 15 in cell A1 and hitting ENTER, gives 105 in A3, which is C(15,2). Try also using some other functions from the fx icon in this manner, for example PERMUT.

Take care.

[BruceZ]

Or you could just click in a cell and type =combin(10,2). Done.

The calculation of the exact probability of flopping only a 4-flush draw (not a flush, not a SF, not a straight, not a straight draw), when holding JTs, is extremely tedious! (Pairing your hand or a pair on the flop are acceptable.)

It need not be extremely tedious if you know what the frick you’re doing, and choose an appropriate partition for the sample space. I claim you are not a proper judge of what must be tedious and what is not tedious, as I will now prove:

First of all, since we are allowing pairs, I’m assuming you want to allow 2-pair and 3-of-a-kind as well. If you want to disallow any of these, including pairs, let me know and I will do that just as easily, I would just have to change a few numbers in what follows. The probability we are after is equivalent to the probability of flopping exactly a 4-flush draw without the cards for a straight draw, since if we don’t flop the cards for a straight draw, then we don’t flop a straight either. We can always flop a 4-flush draw without the straight draw cards if we flop a 4-flush draw with no more than 1 of the 4 denominations 8,9,T, or K (more than one of the same denomination is OK, like 888 since we are allowing this). We can also always do it when we flop only the denominations 8,K. We can also always do it if we flop only 8,Q or 9,K so long as we don’t flop exactly 8,Q,A or 7,9,K, since these are the only double belly buster draws. These are all the cases, since the other combinations of two cards 8,9; 9,Q; and QK are straight draws. So now we count the cases.

No 8,9,Q,K: C(7,2)*27 = 567
Exactly 1 denomination of 8,9,Q,K: 4*7*30 + C(7,2)*12 = 1092
8,K: 2*3*7 + 1*33 = 75
8,Q but not 8,Q,A: 2*3*6 + 1*30 = 66
9,K but not 7,9,K: same as above = 66

Where I have added two terms, the first is for exactly 1 of the listed cards being a flush card. The second term is for either exactly 0 or 2 of the listed cards being flush cards, as appropriate to the case. Exactly 1 denominaton means multiple of same denomination still OK.

(567 + 1092 + 75 + 66 + 66)/C(50,3) = <font color="red">9.5%</font color>. This is the probability of a clean flush draw, exact to within the probability of a blunder, which in the limit should go to zero. [img]/forums/images/icons/laugh.gif[/img]

Now the probability of a flush draw including the times we also make a straight draw or straight is
C(11,2)*39/C(50,3) = 10.9%. So the probability of making a flush draw while at the same time also making either a straight draw or straight is 10.9% - 9.5% = 1.4%. The probability of making a straight draw or straight including the times we also make a flush draw is [ 3(12*42 + 4*33 + 6*4*2) + 4*4*4*2 ]/C(50,3) = 11.1%. Therefore, the probability of a straight draw or a straight is 11.1% - 1.4% = 9.7%. The probability of a straight including straight-flush is 4*4*4*4/C(50,3) = 1.3%, so the probability of a clean straight draw is 9.7% - 1.3% = <font color="red">8.4%</font color>. The probability of a straight draw or a flush draw or both is 9.5% + 11.1% - 1.3% = <font color="red">19.3%</font color>.

This is in agreement with the figures given earlier for the clean straight draw, but not for the clean flush draw. Since we used one to get the other, the earlier figures do not appear to be consistent with each other.

So in summary:

P(clean flush draw) = 9.5%
P(clean straight draw) = 8.4%
P(clean straight draw OR clean flush draw not both) = 17.9%
P(clean straight draw OR clean flush draw OR both) = 19.3%
P(both clean straight AND clean flush draw) = 1.4%

Now was that so tedious?

[SittingBull]