Hold Em probability question

[kongo_totte]

Hello everyone!
I wonder what the exact probability is that the board pairs (or make quads) when flopped a set.
My home made calculation is:
Number of outs for pairing any of the flopped cards: 3+3+1= 7 outs.

(7/48)+(7/47)=29.47695034%

I think that would be correct. I’m less sure about my calculation that a runner runner pair will come though. Does anyone know if this is correct:

I make the calculation: (4/48)x(3/47)x10= 5.31%

29.47695034+5.31=34.7869%

Example:
Lets say I have 33 and the flop comes 2 3 4.
There is a 29.4769% chance that another 2, 3 or 4 will turn or river.

Let’s say a J falls on the turn (4/48). I then have 3 outs to the jack. (3/47). I then multiply this by 10, cause there are13-3 cards this can happen with (A 5 6 7 8 9 T J Q K).

Please, correct me if I’m wrong, probably am (I have only high school math to support this with). I know a number of probability generators can give me the right answer, but I would really like to know the calculation. Thinks it gives me a better understanding of the game.

[BruceZ]

[ QUOTE ]
Hello everyone!
I wonder what the exact probability is that the board pairs (or make quads) when flopped a set.
My home made calculation is:
Number of outs for pairing any of the flopped cards: 3+3+1= 7 outs.

(7/48)+(7/47)=29.47695034%

[/ QUOTE ]

7/47 + (40/47)*(7/46) = 27.8445883%

There are 47 cards remaining after the flop, not 48, and the 7/46 on the river applies only if you miss on the turn, hence the 40/47. This is just for pairing a flop card.


[ QUOTE ]
I think that would be correct. I’m less sure about my calculation that a runner runner pair will come though. Does anyone know if this is correct:

I make the calculation: (4/48)x(3/47)x10= 5.31%


29.47695034+5.31=34.7869%

[/ QUOTE ]

(4/47)*(3/46)*10 = 5.5504163%

27.8445883% + 5.5504163% = 33.3950046%

You can do this all in one step like this:

7/47 + (40/47)*(10/46) = 33.3950046% same as above.

That is, you pick up an extra 3 outs if you miss on the turn, so you have 10 outs on the river.

[kongo_totte]

What? There is 52 cards in a deck? [img]/images/graemlins/laugh.gif[/img]. I really shouldn't be posting before 11:00 AM since my brain works at 7/47 of it's capacity during the first half of the day. Well, there is swedish high school math for ya, or maybe I've just been out of school for too long.

Thanks a bunch anyway