Probability of Flop

[Pocket10sMedic]

*I'm new to the whole idea of probability, so don't crucify me if this question has been asked before*

I'm playing 3/6 at the local B&M yesterday and get KK in EP - I 2 Bet and get 2 callers, includng the BB. Flop comes Q Q Q - My question is, can you show me the equation to calculate the probability of this flop even happening and the probability of the other 2 callers having a Q.

TIA

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[AngusThermopyle]

[ QUOTE ]
Flop comes Q Q Q -... and the probability of the other 2 callers having a Q.


[/ QUOTE ]

0, in a normal deck /images/graemlins/shocked.gif

Seriously,
Odds of that flop (specifically Q's):
First card a Q:
4/50 -- you remove your K's
Second card a Q:
3/49
Third card a Q:
2/48
All three, multiply
24/117600 or
0.000204081632653061 or
1 in 4900

Probability that the last Q is in one of your 2 opponents hands is really dependent on what range of hands they would play under the circumstances. You know that they are not random cards, and assuming a Q would be more likely in a hand they played, the odds are higher than mere probablitly would predict.

[Cobra]

The probability that the flop comes three Q's is
(4 choose 3)/(50 choose 3)=.024% or 1 in 4900 hands.

The probability that the flop comes any of the other twelve ranks that you don't hold is 12* above=.24% or 1 in 408 hands.

If you put the two players against you on random hands the probability that one of them has a Q is
=number of opponents * 46/(47 choose 2)=2*4.3%=8.6%

Lets asume that they wouldn't play any Q, assume they would only play a Q paired with a 9 or above that would be
2*1*18/(47 choose 2)=2*1.7%=3.4%

Cobra

[bobbyi]

There are five cards that we know--two in your hand three on the board. So there 47 cards we don't know. Out of these, 4 are in your opponents hands. There is one queen left so it will be in one of their hands 4/47 times, which is pretty close to 1/12. However, that assumes they are equally likely to play any cards, but in practice people call more with high cards than with low cards, so the real chance of running into a queen is higher than that. We can't calculate it exactly because we don't know exactly what hands your opponents play and how often they will play them in this situation.

[housenuts]

[ QUOTE ]
There are five cards that we know--two in your hand three on the board. So there 47 cards we don't know. Out of these, 4 are in your opponents hands. There is one queen left so it will be in one of their hands 4/47 times, which is pretty close to 1/12. However, that assumes they are equally likely to play any cards, but in practice people call more with high cards than with low cards, so the real chance of running into a queen is higher than that. We can't calculate it exactly because we don't know exactly what hands your opponents play and how often they will play them in this situation.

[/ QUOTE ]

i would say the chance of running into a queen is actually alot lower than that. out of all the possible hands that have a queen i wouldn't suspect they'd be playing even half of them. there's 4 ways they could have AQ, 2 ways they could have KQ (assuming you have the other 2 k's), 0 QQ, 4 QJ, 4 QT. depending on the opponents you can add a few possibilities, but really that's not many hands compared to the realm of possible hands.

[MickeyHoldem]

The flop question has been answered by others.

For the other Q... I think the odds are considerably higher than some of the answers that have been given.

The odds you are going to see someone show you that other Q is dependant on your opponents play. You need to figure out the range of hands that are going to be calling your raise from these positions and figure out the ratio: hands with Q/total hands

Example:
Range1: calling 2 bets cold
AA-88: 36
AK: 8
AQ: 4
KQ: 2
AJs: 4
ATs: 4
KJs: 4
QJs: 1
QTs: 1
JTs: 4

# with Q : 8
Total : 68

Range2: calling one bet
all above: 68
77-22: 36
KTs: 4
QTs: 1
Q9s: 1
J9s: 4
T9s: 4
98s: 4
AJ: 16
KQ: 1
ATs: 4
QJ: 3
QT: 3

# with Q: 17
Total: 141

Up against Q = 1 - prob. no Q = 1 - (60/68 * 124/141) = ~.224 or 1 in 4.5

[Pocket10sMedic]

Thanks again for the help...

Had no read on the person but it was a very loose game.. actually only my second hand played.

Luckily enough for me, she cold-called a 2 bet in MP with Q4o... BLAH

TA

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