Please check this formula

[MickeyHoldem]

Just wondering if this formula is correct...

p = your chance of winning
T = number of trials
x = min. wins

x
---
\
/ nCr(T,i) * p^i * (1-p)^(T-i)
---
i=0


A) For a coin flip... what are the chances that heads comes up a min of 8 times out of 20... answer ~87%

B) for pocket pairs vs. 2 overs (roughly 54% - 46%)... what are the chances of losing 100 times out of 200... I calculated this as <12% using the above formula

Someone claimed to have lost 156 out of 200 of these situations <cough...bull<cencored>>... somewhere around 1 in 1.97E+20

[BruceZ]

[ QUOTE ]
Just wondering if this formula is correct...

p = your chance of winning
T = number of trials
x = min. wins

x
---
\
/ nCr(T,i) * p^i * (1-p)^(T-i)
---
i=0


A) For a coin flip... what are the chances that heads comes up a min of 8 times out of 20... answer ~87%

[/ QUOTE ]

87% is correct, but you must sum i from 8 to 20 wins, not 0 to 8.


[ QUOTE ]

B) for pocket pairs vs. 2 overs (roughly 54% - 46%)... what are the chances of losing 100 times out of 200... I calculated this as <12% using the above formula

[/ QUOTE ]

You would sum i from 0 to 100 with p = 0.54 to get the probability of winning 100 or less. I get 14.3% using the equivalent Excel function
=binomdist(100,200,0.54,true).

[MickeyHoldem]

[ QUOTE ]
=binomdist(100,200,0.54,true).

[/ QUOTE ]

WOW... excel has this built in... I'm an idiot! [img]/images/graemlins/wink.gif[/img]