odd question about odds

[Tyler Durden]

What are the odds of:

a) flopping a set
b) turning (or rivering) a set
c) flopping a four flush
d) making the flush by the river if you've flopped the four flush
e) flopping a boat when you hold a pocket pair


thanks much.

[Homer]

1) Flopping a set

= 1 - P(no set) = 1 - [(48/50)*(47/49)*(46/48)] = 11.75% or 7.5:1 against


2) Turning or rivering a set

P (turning a set) = 2/47
P (rivering a set) = 2/46

P (turning or rivering a set):

= 1 - P(no set) = 1 - [(45/47)*(44/46)] = 8.42% or 11:1 against


3) Flopping a four-flush

= C(3,2)*(11/50)*(10/49)*(39/48) = 10.95% or 8:1 against

3b) Flopping a four-flush or flush

P(Flopping a flush) = (11/50)*(10/49)*(9/48) = .841%

P(Flopping a four-flush or flush) = .1095 + .00841 = 11.79% or 7.5:1 against


4) Making flush by river if flopped four-flush

= 1 - P(no flush) = 1 - [(38/47)*(37/46)] = 34.97% or 2:1 against


5) Flopping a boat when you hold a pocket pair

I'll assume you mean something like 822 when you hold 88 rather than something like 222. In other words you flop a set and there is a pair.

= C(3,2)*(2/50)*(48/49)*(3/48) = .735% or 135:1 against


I'm not the best at this stuff so there could be some mistakes.

-- Homer

[SoBeDude]

P (turning or rivering a set):

= 1 - P(no set) = 1 - [(45/47)*(44/46)] = 8.42% or 11:1 against

Using these numbers, what do I need to try to stick it out to the river with my little pair?

Lets assume I'm in late position (the only place I volintarily play them) and I feel a flop raise by me will get me a "free" card". Lets also assume the board is uncoordinated enough that I feel if I do make my set it has a decent chance of holding up.

What kind of money in the pot and/or number of players do I need to be facing, for the implied odds to make this late position flop raise correct?

Thanks!

-Scott