Nmartin
Joined: Jun 30, 2010
• Posts: 2
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)?

DJTeddyBear
Joined: Nov 2, 2009
• Posts: 9594
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.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition.
matilda
Joined: Feb 4, 2010
• Posts: 317
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
Joined: Mar 29, 2010
• Posts: 475
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
Joined: Jun 30, 2010
• Posts: 2
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
Joined: Feb 4, 2010
• Posts: 317
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