[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


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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