probability of overcards flopping in Hold'em

[jonny quest]

<<I posted this in Probability but have not heard a word, so figured I'd also post here since may apply and hope to find a helpful responder>>

Specifically, I was trying to calculate the probability of overcards flopping to specific Pocket Pairs in Hold'em.

For example, % of time overcards would flop against someone holding pocket 3's.

For the first card of the flop, I calculated the % of an overcard as such:
44/50 = 88%

But how do I extend this for the following two cards to come with an total flop %?

Independently, flop card one is 44/50, two is 44/49, three is 44/48?

And then how would I arrive at the total %?


Thanks.

[Maple Leafs]

Are you looking for the probability of one overcard, or that all three cards will be overs?

All three cards are not overcards = 6/50 * 5/49 * 4/48 = 0.15%

(i.e. you calculate the chances of an overcard not appearing each time and multiply together to get the chance of it happening each time.)

So chances of at least one over = 99.85%

[jonny quest]

[ QUOTE ]
AAll three cards are not overcards = 6/50 * 5/49 * 4/48 = 0.15%


[/ QUOTE ]
When I perform that calculation I get 0.10%??

[James Nl]

Probability of Flopping at least one over card:
(AND you do not hit a set)
KK: .21
QQ: .38
JJ: .52
TT: .63
99: .72
88: .78
77: .82
66: .85
55: .87
44: .88
33: .88
22: .88

[James Nl]

This is obviously when you hold a pocket pair^
Not exactly what you were looking for but close enough.

[jonny quest]

[ QUOTE ]
This is obviously when you hold a pocket pair^
Not exactly what you were looking for but close enough.

[/ QUOTE ]

A player holds a pocket-pair. What are the chances the flop contains at least one overcard to the pair?

As I ran the numbers, I came up with the following:

22 = 100% of at least 1 overcard
33 = 99% at least 1 overcard
44 = 99
55= 98
66=96
77= 92
88 = 86
99 = 79
tt = 69
jj = 56
qq = 41
kk = 22 %
AA = 0%

But I thought my formula was flawed, therefore my calculations were errant.

And I'm still not sure [img]/images/graemlins/confused.gif[/img]

[jonny quest]

[ QUOTE ]

(AND you do not hit a set)


[/ QUOTE ]

Yes [img]/images/graemlins/smile.gif[/img] I see.

[Gullanian]

KK

There is 1 overcard. 4 aces in the deck. 3 hits. =

4/50 + 4/49 + 4/48

QQ

There are two overcards. 4 kings and 4 aces in deck =

8/50 + 8/49 + 8/48

etc etc