Interesting Ace King question in holdem

[fireitup123]

This question relates to Ace King in holdem vs. a pocket pair. What are the chances of both of the following occuring:

An ace or king hits on the flop + other opponent flops a set. It might be easier to assume that your oppoent does not have aces or kings in the hand against the ace king.

As an example, your hand is As Kd. Opponent has 6c6h. What's the chance of flopping tptk or better and opponent flopping a set with you.

[Laddy]

Well.....the chances that you hit when you have AK (shocking to some people) are about 35%.....the chances of someone with 66 flopping a set are about 1 in 8. Therefore the chances of both happening (as they are both mutually exclusive) are approx. (1/8 x 1/3) = 1/24. Not something that an experienced Hold'em player needs to worry about.

Comments?

[SheetWise]

Laddy -- How can you say they are mutually exclusive? They are very dependent. And you have to exclude getting A-A, K-K, and A-K as the question was about getting a pair -- not a pair or better.

SheetWise

[BruceZ]

[ QUOTE ]
Laddy -- How can you say they are mutually exclusive? They are very dependent.

SheetWise

[/ QUOTE ]

Being dependent has nothing to do with whether or not they are mutually exclusive. Mutually exclusive events are never independent unless one of their probabilities is zero. In this case they are not mutually exclusive, and they are not independent. If they were mutually exclusive, the chance of them both happening would be zero. Independence would allow you to multiply the probabilities.

AK vs. 66:

P(one A or K, and one 6) = 6*2*40/C(48,3) =~ 2.78%

P(one A or K, and two 6's) = 6*1/C(48,3) =~ 0.0347%

P(two A or K, and one 6) = C(6,2)*2/C(48,3) =~ 0.173%
-----------
total =~ 3.0% or 32.5-to-1.

[PairTheBoard]

Just an adendum here.

In those cases where you do flop exactly one pair, with your opponent holding a pocket pair less than kings, the probabilty that your One Pair will be up against a set or quads on the flop is:

1 - C(40,2)/C(42,2) = 9.41%
or about 1 in 10.6

Assuming I did that right. I make no guarantees these days.

PairTheBoard

[z80x86]

They are independent events which must be treated seperately. The AK and the 66 can't both pair and set at the same time.