June 30th, 2010 at 11:14:00 AM
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I'm struggling to get my head around this, and am hoping somebody may be able to help:

Your hole cards are suited connectors, what is the probability of making a straight, flush or straight flush on the flop? By the river?

I can work out the flush aspects:

On Flop: 11/50 x 10/49 x 9/48 = 33/3920

By River: 1 - (no other same suit cards) - (one other same suit) - (two other same suit) = 0.063999082....

But I have no idea with the straight aspects:

~ If I have A2, I would need 345

~ If I have 23, I would need A45 or 456

~ If I have 34, I would need A25 or 256 or 567

~ If I have 45, I would need A23, 236, 367, 678

etc.....

Please can anyone nudge me in the right direction?

Also, once I have the straight, can I add these two together or do I need to take something off (have I double counted a straight flush)?

Thanks in advance!

Your hole cards are suited connectors, what is the probability of making a straight, flush or straight flush on the flop? By the river?

I can work out the flush aspects:

On Flop: 11/50 x 10/49 x 9/48 = 33/3920

By River: 1 - (no other same suit cards) - (one other same suit) - (two other same suit) = 0.063999082....

But I have no idea with the straight aspects:

~ If I have A2, I would need 345

~ If I have 23, I would need A45 or 456

~ If I have 34, I would need A25 or 256 or 567

~ If I have 45, I would need A23, 236, 367, 678

etc.....

Please can anyone nudge me in the right direction?

Also, once I have the straight, can I add these two together or do I need to take something off (have I double counted a straight flush)?

Thanks in advance!

June 30th, 2010 at 11:28:16 AM
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That kind of math makes my head hurt, but, yeah, your flush calculation includes the various combinations that would be a straight flush.

I gotta assume that whatever you come up with for the straight would also include a straight flush.

It may help if you start by calculating the odds of the straight flush, and THEN figure out the odds for the straight.

I gotta assume that whatever you come up with for the straight would also include a straight flush.

It may help if you start by calculating the odds of the straight flush, and THEN figure out the odds for the straight.

I invented a few casino games. Info:
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June 30th, 2010 at 2:29:23 PM
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This is not an easy question to answer and is quite laborious. Check out

http://www.math.sfu.ca/~alspach/comp23/

http://www.math.sfu.ca/~alspach/comp23/

June 30th, 2010 at 2:48:26 PM
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I am led to believe that J+10 was once considered a better starting hand than A+K, because there are 4 ways to make a straight with J+10 but only one way with A+K.

June 30th, 2010 at 3:35:15 PM
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Thank you everyone, that is very helpful... Somebody on a different site directed me to Professor Alspach's site. Still trying to get my head around some bits of it, but definitely getting there!!

June 30th, 2010 at 7:01:58 PM
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Quote:PapaChubbyI am led to believe that J+10 was once considered a better starting hand than A+K, because there are 4 ways to make a straight with J+10 but only one way with A+K.

For straight only, probabilities:

hand offsuit suited

A,K .0330 .0309

J,10 .0709 .0666

Data from Alspach

P(win) 8 player game

A,K .2268 .26

J,10 .191 .2126

Data from Wizard of Odds