quick odds calculation question

[Goodnews]

If i had two overcards and a flush draw on the flop, how would i go about calculating my odds of hitting one of my outs by the river?

is it 15/47 + 15/46 = 65% ? Or am I calculating these odds incorrectly?

My friend argue that the real percentage is around 50% (through some method through permutations), and I'm not sure how they got this number, as you can probably see, an 15% difference is something to be concerned about.

He mentioned something about HPFAP, but i was quite drunk when we were discussing this.

[TStoneMBD]

if you need to do on the fly calculations, the 4/2 rule is your best bet.

for instance, if you have 8 outs, the odds of connecting in the next 2 cards is about 8x4=32%. if you have 8 outs on the turn, your odds of connecting on the river is about 8x2=16%.

once you get up to around 14 outs though the system doesnt work.

[Balla2hot4u]

i want to fully understand why these out percentages are what they are.. thanks
-Adam

[TStoneMBD]

quite honestly, i have no clue, but they work out pretty well.

[Balla2hot4u]

[ QUOTE ]
if you need to do on the fly calculations, the 4/2 rule is your best bet.

for instance, if you have 8 outs, the odds of connecting in the next 2 cards is about 8x4=32%. if you have 8 outs on the turn, your odds of connecting on the river is about 8x2=16%.

once you get up to around 14 outs though the system doesnt work.

[/ QUOTE ]

ok so why is it 8 X 4 on the turn and 8 X 2 on the river? is it because your outs are automatically multiplied times 2 ( because the math of the amount of outs u have divided by the cards remaining almost always multiplies it by 2?) then times the amount of cards remaining to come.. so u have 8 outs on the flop to hit a straight right.. 8X2(x2 again for the amount of cards still to come) = 34% then now on the river u have 8 outs still but only one card to come so its just 8X2= 16%? im just a little confused and would to clarify to myself thanks

[TStoneMBD]

it should be pretty selfexplanitory why its Xx4 and Xx2 since youre getting half the cards you divide by 2. again, i dont know why this system works, all i know is that it works.

[jimmyd2]

Clonie Gowen wrote a poker tip on computing % on Fulltiltpoker.com. She used the 4X2.
# of outs X number of cards remaining X 2. It is not exact but can help you while in play. The exact site is:
http://www.fulltiltpoker.com/proless...olessons1.html

[Cobra]

The easiest way to figure the probability of getting an out on the turn or the river is 1 - the probability of not getting it on the turn and river. This gives you the probability of one or more of your outs hitting.

In this 15 out example:

= 1 - (32/47*31/46) = 54.11%

Cobra

[jba]

[ QUOTE ]
The easiest way to figure the probability of getting an out on the turn or the river is 1 - the probability of not getting it on the turn and river. This gives you the probability of one or more of your outs hitting.

In this 15 out example:

= 1 - (32/47*31/46) = 54.11%

Cobra

[/ QUOTE ]

this is it. OP's original post is off because it ignores the short circuit case.

The 4x rule is a rough approximation of the function Cobra points out, which is formally:
f(x)=(1-((47-x)/47)*(46-x)/46))*100;

note that this is a quadratic function (x squared is in the house) so the function f(x)=4x can only possibly be an approximation, because it's a linear function. It just so happens to closely approximate the real function for values of x between 0 and 10. Past ten it starts to breaks down - note that with 25 outs you win 100% of the time, which clearly isn't right.

The 2x is actually pretty damn close. the real function here is:

f(x) = (1-(46-x/x))*100

note that there's no x squared in the hizouse, so we have a linear function, so it can be closer. in fact:

(1-(46-x/x))*100 = (46-(46-x))/46*100 = 100x/46 = 2.17x

close enough to 2x.


check out this link, you can graph the functions and see how they relate.

fix up the x/y coordinates to reasonable numbers (0-50x and 0-100y is good) and paste these equations in:
(1-(((47-x)/47)*((46-x)/46)))*100;
4x;
(1-((46-x)/46))*100;
2x;

peace

[CallYNotRaise06]

[ QUOTE ]
The easiest way to figure the probability of getting an out on the turn or the river is 1 - the probability of not getting it on the turn and river. This gives you the probability of one or more of your outs hitting.

In this 15 out example:

= 1 - (32/47*31/46) = 54.11%

Cobra


--------------------------------------------------------------------------------



this is it. OP's original post is off because it ignores the short circuit case.

The 4x rule is a rough approximation of the function Cobra points out, which is formally:
f(x)=(1-((47-x)/47)*(46-x)/46))*100;

note that this is a quadratic function (x squared is in the house) so the function f(x)=4x can only possibly be an approximation, because it's a linear function. It just so happens to closely approximate the real function for values of x between 0 and 10. Past ten it starts to breaks down - note that with 25 outs you win 100% of the time, which clearly isn't right.

The 2x is actually pretty damn close. the real function here is:

f(x) = (1-(46-x/x))*100

note that there's no x squared in the hizouse, so we have a linear function, so it can be closer. in fact:

(1-(46-x/x))*100 = (46-(46-x))/46*100 = 100x/46 = 2.17x

close enough to 2x.


check out this link, you can graph the functions and see how they relate.

fix up the x/y coordinates to reasonable numbers (0-50x and 0-100y is good) and paste these equations in:
(1-(((47-x)/47)*((46-x)/46)))*100;
4x;
(1-((46-x)/46))*100;
2x;

peace


[/ QUOTE ]

just a little highschool algebra