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IRC Poker Quiz #4

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spoonitnow

06-24-2009, 04:15 PM Post subject: IRC Poker Quiz #4

#1 (permalink)

Straight Flush

Join Date: Sep 2005

Location: IRC Chat Room

Posts: 5,406

If we hold 87, what is the chance that we flop a gutshot (4 out) straight draw? Include the times we also flop a pair or flush or flush draw, but don't include the times we flop an 8 out straight draw or flop a straight.

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nish81

06-24-2009, 04:40 PM

#2 (permalink)

Flush

Join Date: Jun 2009

Posts: 295

Alright, i've got the flu so excuse me if i'm way off here

Cards we need to flop a gutshot:
TJx
6Tx
59x
46x

Total possible permutations of flop cards:
50*49*48
= 117,600

Permutations of JTx possible
(4*4*48)*(6)
- 48 because the other J and T can still come, pairing the board, but still giving us a gutshot
- 6 because theres 6 ways we can get a JT on a flop (JTx, TJx, JxT, TxJ, xTJ, and xJT)
= 4608
Times four because theres four ways to get a gutshot:
1152*4 = 18432

18432/117,600 = 15.7% chance

anywhere near right?

edit: my corrections to my OP:
there are two more flops that work, J9x and 45x
the permutations of each flop are (4*4*44)(6) - 44, not 48, because four of the cards would complete the straight

leaving us with a new probability of 21.6%

<JustinSKS> Tha'ts why I fold my 33 to 72o, because 7 high beats, 1 pair, donk.

JR: lets do it JUAN
JR: mono e mono
JR: man to man
JR: HU4ROLLZZZZZZZZZZZZZZZ
Dealer: juan0984 folds

Keith

06-24-2009, 05:50 PM

#3 (permalink)

Full House

Join Date: Nov 2008

Posts: 1,336

in the following blocks of combinations take for example JTx. x cannot be 9 else its not a gutshot , nor can it be a 6 as the 6TJ combinations will be counted in the T6x block therefore for each subblock theres 8 ineligible cards.

6 blocks of combinations TJx,T6x,9Jx,46x,45x,59x.

each block can be made up as
(
JxT TxJ (4/50*41/49*4/48)*2= 1312/117600
+
JTx TJx (4/50*4/49*40/48)*2= 1280/117600
+
xJT xTJ (42/50*4/49*4/48)*2= 1344/117600
)
*
6 blocks of combinations
= (3936)*6/117600
=23616/117600
=20.08%

EDIT: as linaker has just pointed out double gutshots are not allowed either so they will have to deducted from my total. easiest way is to rework with 2 blocks with 8 ineligible cards and 4 blocks with 12 ineligible cards.

in the following blocks of combinations take for example JTx. x cannot be 9 else its not a gutshot , nor can it be a 6 as the 6TJ combinations will be counted in the T6x block therefore for each subblock theres 8 ineligible cards.

2blocks of combinations TJx,45x,

each block can be made up as
(
JxT TxJ (4/50*41/49*4/48)*2= 1312/117600
+
JTx TJx (4/50*4/49*40/48)*2= 1280/117600
+
xJT xTJ (42/50*4/49*4/48)*2= 1344/117600
)
+
4 blocks of combinations T6x,9Jx,46x,59x.
Tx6 6xT (4/50*37/49*4/48)*2= 1184/117600
+
6Tx T6x (4/50*4/49*36/48)*2= 1152/117600
+
xT6 x6T (38/50*4/49*4/48)*2= 1216/117600
)

= (3936*2+3552*4)/117600
=22080/117600

linaker

06-24-2009, 06:27 PM

#4 (permalink)

3-of-a-Kind

Join Date: Apr 2009

Location: UK

Posts: 70

Hope you get better soon Nish. You forgot to eliminate the 8 out SDs tho.

Cards to flop a gutshot:

a) JTx
b) J9x
c) T6x
d) 95x
e) 64x
f) 54x

In each case, 1 value of x will make a straight. ie 9 with JT makes JT987.
In cases b) to e), 1 value of x will make a double gutshot. ie 5 with J9 makes J 987 5, so we have an 8 out SD
In cases b) to e), 1 value of x will make an OESD. ie 6 with J9 makes J 9876.

Flops containing JTx, where x does not make a straight (ie the flop is not a combination of JT9):

(4*4*44)*(6) = 4224

(44 because the four nines are excluded).

Times six because there's six combinations to get a gutshot:

4224*6 = 25344

But there are 2 additional cards in cases b to e that make an 8 out SD. Number of J96 or J95 flops is

4 * 4 *8 *6 = 768

So 768 *4 = 3072 flops contain an OESD, so the number of flops that only contain a 4 out SD are:

25344 - 3072 = 22272

The chance of making a 4 out gutshot is

22272/117 600 = 18.9%

linaker

06-24-2009, 07:44 PM

#5 (permalink)

3-of-a-Kind

Join Date: Apr 2009

Location: UK

Posts: 70

Quote:

Originally Posted by Keith_MM

each block can be made up as
(
JxT TxJ (4/50*41/49*4/48)*2= 1312/117600
+
JTx TJx (4/50*4/49*40/48)*2= 1280/117600
+
xJT xTJ (42/50*4/49*4/48)*2= 1344/117600
)
*

This is wrong. If you think about it, you are saying that an AhJT flop happens more frequently than a JTAh flop.

In the first block you are working out the number of flops, given that the first card is a J and the third is a T. x can't be a 9 or a 6, so there are 42 possible cards for x. But we know the first card is one of the 4 jacks and the third card is one of the four Ts, so there are in fact only 40 possible cards for x. The same is true for the other blocks, since you have fixed the other two cards in each case.

In fact, you are double counting. In the JxT example you are including the T at position 3 in x, so counting it twice. This is why your xJT result > JxT > JTx.

spoonitnow

06-24-2009, 09:18 PM

#6 (permalink)

Straight Flush

Join Date: Sep 2005

Location: IRC Chat Room

Posts: 5,406

LOOK AT THE LITTLE BASTARDS GO AHAHAHAHAHAHAHAHAHHAAHAHAHAHAHAHAHA

Quote:

Originally Posted by Ripptyde

I only have 2 simple rules when I am coaching a new student.

Rule # 1: don't ask questions

Rule # 2: don't ask questions

I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.

a500lbgorilla

06-24-2009, 09:31 PM

#7 (permalink)

JESUS TAKE THE KEYBOARD

Join Date: Sep 2004

Location: This room is a good place to be

Posts: 8,379

spoonitdrunk at 5pm?

Smithers, use the amnesia ray.
You mean the revolver, sir?
Precisely.

settecba

06-25-2009, 12:35 AM

#8 (permalink)

Flush

Join Date: Aug 2008

Location: stealing blinds from UTG

Posts: 326

My "guess":

[C(4,1)*C(4,1)*C(40,1)*4+C(4,1)*C(4,1)*C(36,1)*2]/C(50,3)

(16*40*4+16*36*2)/19600=18.94%

This comes from the following flops:

1) J9x -- no T, no 6
2) JTx -- no 9, no 6
3) 6Tx -- no 9, no 5, no 4
4) 59x -- no 6, no T, no J
5) 45x -- no 6, no 9
6) 46x -- no 5, no 9

JR9477

06-25-2009, 02:11 AM

#9 (permalink)

Flush

Join Date: Aug 2008

Location: Iowa

Posts: 426

JR9477 is an unknown quantity at this point

18.29

(Josh)

spoonitnow

06-26-2009, 03:16 PM

#10 (permalink)

Straight Flush

Join Date: Sep 2005

Location: IRC Chat Room

Posts: 5,406

I'm surprised more people didn't comment on how surprised they were by this, but 18.9% is the winnar.

TonyB73

06-26-2009, 03:25 PM

#11 (permalink)

Flush

Join Date: Mar 2008

Posts: 414

Quote:

Originally Posted by spoonitnow

I'm surprised more people didn't comment on how surprised they were by this, but 18.9% is the winnar.

Why would I be surprised by 18.9%?

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