Nmartin
Nmartin
Joined: Jun 30, 2010
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June 30th, 2010 at 11:14:00 AM permalink
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!
DJTeddyBear
DJTeddyBear
Joined: Nov 2, 2009
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June 30th, 2010 at 11:28:16 AM permalink
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 invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
matilda
matilda
Joined: Feb 4, 2010
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June 30th, 2010 at 2:29:23 PM permalink
This is not an easy question to answer and is quite laborious. Check out

http://www.math.sfu.ca/~alspach/comp23/
PapaChubby
PapaChubby
Joined: Mar 29, 2010
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June 30th, 2010 at 2:48:26 PM permalink
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.
Nmartin
Nmartin
Joined: Jun 30, 2010
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June 30th, 2010 at 3:35:15 PM permalink
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!!
matilda
matilda
Joined: Feb 4, 2010
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June 30th, 2010 at 7:01:58 PM permalink
Quote: PapaChubby

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.



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

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