psychprof
09-23-2003, 04:35 PM
I tried to do this myself, but would appreciate some verification. This is my first attempt at probability calculations.
Let's say I have Jh 5h and flop is
4h Js 3d
The flop gives me a runner-runner flush draw and a runner-runner straight draw. I have calculated the odds of making either the flush OR the straight, and I would appreciate it if you would check my calculations.
BTW, as my name indicates, I am a psychology professor so I have some experience with probability. However, my experience is mainly in the area of hypothesis testing with the normal curve, so standard probability calculations like the ones below are kinda rusty for me. I appreciate your time and corrections.
OK, I start with the easy one.
Probability of a runner runner flush (RRF)
P(heart on turn) = 10/47
P(heart on river given heart on turn) = 9/46
P(RRF)= 10/47 * 9/46 = .0416
*I forget the symbol for "given".
Probability of a runner runner straight (RRS)
P(A, 2, 6, or 7 on turn) = 16/47
If the turn gives me an open-ended straight draw (let's say a 2) then...
P(A or 6 on river) = 8/46
So the probability of completing an RR-OE straight is
P(RR-OE-S) = 16/47 * 8/46 = .059
If the turn gives me a gutshot straight draw (let's say a 7) then...
P(6 on river) = 4/46
So the probability of completing a RR-GS straight is
P(RR-GS-S) = 16/47 * 4/46 = .030
Probability of completing a RR-Flush OR a RR-GS-Straight
P(RR-F OR RR-GS-S) = .0416 + .030 = .0716 or a 7.2% chance
Probability of competing a RR-Flush OR a RR-OE-Straight
P(RR-F OR RR-OE-S) = .0416 + .059 = .10 or a 10% chance
In conclusion, the probability of completing a RR-flush OR a RR-straight are somewhere between 7 and 10 percent. Using the more generous 10%, this means I'm a 9:1 dog to improve the hand (to a straight or flush) and so I need better than 9:1 pot odds to justifying staying in.
So, if there's a $2 bet to me and the pot already holds $20 I have the odds to call (10:1).
OK, that took me a while, and I wouldn't be surprised if I were wrong in several places. I sincerely appreciate the time it takes you to reply and thank you for your help.
PsychProf
PS. Maybe I should have picked an easier problem to tackle as my first probability calculation in 10 years. LOL
Let's say I have Jh 5h and flop is
4h Js 3d
The flop gives me a runner-runner flush draw and a runner-runner straight draw. I have calculated the odds of making either the flush OR the straight, and I would appreciate it if you would check my calculations.
BTW, as my name indicates, I am a psychology professor so I have some experience with probability. However, my experience is mainly in the area of hypothesis testing with the normal curve, so standard probability calculations like the ones below are kinda rusty for me. I appreciate your time and corrections.
OK, I start with the easy one.
Probability of a runner runner flush (RRF)
P(heart on turn) = 10/47
P(heart on river given heart on turn) = 9/46
P(RRF)= 10/47 * 9/46 = .0416
*I forget the symbol for "given".
Probability of a runner runner straight (RRS)
P(A, 2, 6, or 7 on turn) = 16/47
If the turn gives me an open-ended straight draw (let's say a 2) then...
P(A or 6 on river) = 8/46
So the probability of completing an RR-OE straight is
P(RR-OE-S) = 16/47 * 8/46 = .059
If the turn gives me a gutshot straight draw (let's say a 7) then...
P(6 on river) = 4/46
So the probability of completing a RR-GS straight is
P(RR-GS-S) = 16/47 * 4/46 = .030
Probability of completing a RR-Flush OR a RR-GS-Straight
P(RR-F OR RR-GS-S) = .0416 + .030 = .0716 or a 7.2% chance
Probability of competing a RR-Flush OR a RR-OE-Straight
P(RR-F OR RR-OE-S) = .0416 + .059 = .10 or a 10% chance
In conclusion, the probability of completing a RR-flush OR a RR-straight are somewhere between 7 and 10 percent. Using the more generous 10%, this means I'm a 9:1 dog to improve the hand (to a straight or flush) and so I need better than 9:1 pot odds to justifying staying in.
So, if there's a $2 bet to me and the pot already holds $20 I have the odds to call (10:1).
OK, that took me a while, and I wouldn't be surprised if I were wrong in several places. I sincerely appreciate the time it takes you to reply and thank you for your help.
PsychProf
PS. Maybe I should have picked an easier problem to tackle as my first probability calculation in 10 years. LOL