Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 07-11-2003, 09:48 PM
jaydoggie jaydoggie is offline
Senior Member
 
Join Date: Nov 2002
Location: davenport, ia
Posts: 237
Default probability of flopping 4 to a straight?

Is there a way to determine flopping 4 to a straight with connecting cards 45, 56, thru 9T, TJ?

If so what about cards like 57, 68 thru 8T, 9J?

Im no expert in math, i woulda never figured out 2 [img]/forums/images/icons/diamond.gif[/img] + 2 [img]/forums/images/icons/club.gif[/img] = 4 [img]/forums/images/icons/heart.gif[/img] without someone telling me.

thanks in advance
Reply With Quote
  #2  
Old 07-14-2003, 03:04 AM
doormat doormat is offline
Member
 
Join Date: Dec 2002
Posts: 84
Default Re: probability of flopping 4 to a straight?

jaydoggie,
I haven't seen this calculation done anywhere but I did see a similar post by Mike Caro elsewhere and as a rule find his calculations to be accurate. The example he gave was this: You have J Q, what is your probability of getting an open-end straight draw on the flop? He gives the answer of 6.04 percent. Since it is open-end, you must flop either a 9-10 or a 10-K. I would think that for the 9-10 part, there are 4 nines and 4 tens and then 40 cards left to fill the remaining spot on the flop (48 minus 8,since you eliminate the 8 cards which would make a 5-card straight), so 4*4*40=640, then multiply by 6 ways they can be arranged and double that because of the 10-K possibility and you get 4*4*40*6*2 / 50*49*48 = .0653.
However, this differs from Caro's calculation of .0604. If instead of using 40 remaining cards to fill out the flop, you use 37 instead, you would get 4*4*37*6*2 / 50*49*48 = .0604 exactly. So either my approach is all wrong or Caro somehow considers only 37 remaining cards instead of 40 - if someone can fill me in on why this should be, I would appreciate it.
Back to your question, if you are holding say 6 7, then you may draw 4-5 or 5-8 or 8-9 but none of the 8 cards that make a full straight. So my calculation, which may be wrong, would be 4*4*40*6*3 / 50*49*48 = .098. If you are holding 5 7 as in your next question, I would think the answer is the same as Caro's example of J-Q flopping a straight draw.
doormat
Reply With Quote
  #3  
Old 07-15-2003, 12:36 AM
Dynasty Dynasty is offline
Senior Member
 
Join Date: Sep 2002
Location: Las Vegas
Posts: 4,044
Default Re: probability of flopping 4 to a straight?

I'll give you the answers for JT-54. If you want the detailed math for this and all other hold 'em problems, I suggest you buy a copy of Hold 'em Odds Book by Mike Petriv.

Odds against flopping

a straight: 76:1
an 8-out straight draw: 8.6:1
a 4-out straight draw: 3.6:1
all of the above: 2:1

I had to do a double-take on those last two numbers. But, they are accurate.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 03:49 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.