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10-14-2005, 06:46 PM
if you hold 6-7, 7-8, 8-9, 9-10

in hold-em, what are the chances of making a straight if all 5 cards are rolled out?

thanks

10-16-2005, 11:09 PM
anyone? 71 people have viewed and no one knows?

yellowjack
10-17-2005, 01:37 AM
For all the connected cards you mentioned, you can make 4 straights using both cards. i.e. for T9: 6789T, 789TJ, 89TJQ, 9TJQK

Let's look at 6789T when you are holding 76. The board has to come T98xx in any order, where the xs are any card. Use C(4,1)=4 to denote the number of different Ts, 9s, and 8s that can come. Use C(47,2) for the any two cards at the end, and C(50,5) for the total number of boards.

P(76 hitting a ten-straight by the river)
(# of boards w/ straight) / (total boards)
3*C(4,1)*C(47,2) / C(50,5) = 12972 / 2118760 = 0.006122449

The probability of 34567, 45678, 56789 are the same, so I multiply by 4 to get: 0.0244897959

One card straights weren't included though. With 76, you can make 789TJ for a one card straight. For this, the board has to come 89TJx.
4*C(4,1)*C(46,1) / C(50,2) = 3.4738E-4

4 two-card straights and 1 one-card straight can be made with 76.

3.4738E-4 + 0.0244897959 = 0.24837, or 2.4837%.

The probability of the other connected cards, 87, 98, and T9 making a straight is the same as for 76.

BruceZ
10-17-2005, 03:50 AM
[ QUOTE ]
Let's look at 6789T when you are holding 76. The board has to come T98xx in any order, where the xs are any card. Use C(4,1)=4 to denote the number of different Ts, 9s, and 8s that can come.

P(76 hitting a ten-straight by the river)
(# of boards w/ straight) / (total boards)
3*C(4,1)*C(47,2) / C(50,5) = 12972 / 2118760 = 0.006122449

[/ QUOTE ]

It should be 4^3, not 3*C(4,1). Also, you are double counting cases where the board pairs, and triple counting cases where it pairs twice.

[ QUOTE ]
The probability of 34567, 45678, 56789 are the same, so I multiply by 4 to get: 0.0244897959

[/ QUOTE ]

Multiplying by 4 will triple count 3456789 and 456789T, and double count 345678x, x456789, x56789T, and 56789Tx.

[ QUOTE ]
One card straights weren't included though. With 76, you can make 789TJ for a one card straight. For this, the board has to come 89TJx.

[/ QUOTE ]

They were included by the C(47,2), more than once even.

I'll post a calculation later.

10-17-2005, 12:16 PM
thanks for the post...i know if you hold two suited cards, it's roughly 5 percent to make a flush...so i was trying to know what is the chance of making a straight (with both cards) once all five cards are out.

i was assuming it would be more than 5% since straights are easier than flushes to make.

yellowjack
10-17-2005, 01:54 PM
Wow, I was very wrong - humbled again. Thanks BruceZ.

binions
10-17-2005, 02:26 PM
With max strecth connectors (JT-54), you flop a straight 1.3% of the time, and flop an 8 out straight draw (open ended or double gutter) 10.5% of the time. When you have an 8-out straight draw, you will hit 31.5% of the time (using 47 unseen cards).

Of course, this includes all the times you flop a straight or straight draw when there is a 2 or 3-flush against you, not to mention paired boards, etc.

With suited cards, you flop a flush 0.84% of the time, and flop a 4 flush 11% of the time. When you do, you complete the flush 35% of the time (using 47 unseen cards).

Of course, this includes all the times there is a pair on the board and 4 or 5 to your suit.

Bottom line, with suited 0-gap max stretch suited connectors, here's how it breaks down to get a flop you like:

Suited Max Stretch Connector (JT-54)
0.84% flop a flush
1.22% flop straight w/o 3-flush board
(1.30% flop any straight)
10.94% flop a four flush
7.21% to flop clean 8-out straight draw (unpaired board, no 3 flush against, no 4 flush for)
1.85% flop clean 2 pair (no 3 flush board)
(2.02% flop any 2 pair)
1.45% flop trips or full house or 4 of a kind
23.51% = 3.25 to 1 against

Suited 1-gappers are 3.7:1 against flopping good. Suited 2-gappers 4.4:1 against.

10-17-2005, 03:16 PM
thanks, you da man.

so what is the chance of holding a nut straight after all 5 cards are out? (4-5 up to 10-J).

is it true that if you hold A-X suited that you'll make a nut flush about 5% once all the cards are out?

thanks

binions
10-17-2005, 07:21 PM
[ QUOTE ]

so what is the chance of holding a nut straight after all 5 cards are out? (4-5 up to 10-J).

is it true that if you hold A-X suited that you'll make a nut flush about 5% once all the cards are out?

[/ QUOTE ]

any suited hand is about 6% to make a flush once all the cards are out

any 0-gap connected hand is about 8.5% to make a straight (on any board, including flush boards and paired boards) once all the cards are out.

As far as nut straights, that depends on which max stretch 0-gap connector you are talking about. JT always makes the nut straight.

Did you know that every straight has a T or 5 in it?