Axx or Kxx or AKx flops

[HitNRunPoster]

You have 44.

What's the chance of a Axx or Kxx or AKx flop? 1/3?

That seems ridiculously high to me but I'd like ot know. [img]/images/graemlins/frown.gif[/img]

My justification for the 1/3 number, if you're up for something a little funny...

I thought that since the chance of pairing one of your hole cards is about 1/3 (caro reference?), that if I just picked two cards (AK) the chance would have to be higher than 1/3, since I haven't pulled those cards out of the deck.

But when I think about it, I don't know if 1/3 of my flops have contained A or K over the last couple hundred k hands or whatever.

[SNOWBALL]

If you draw three cards it's slightly more than 40% for one of them to be an ace or a king. If you are holding cards that are neither an ace or a king, then it's even more likely still.

[jay_shark]

How many flops do not contain aces when you have pocket 4's ?

This is just (50-4)c3/50c3 = 77.44%

Therefore 1-0.7744 = 22.55 % of the time the flop contains at least an ace .

The same is true for kings (22.55%) .

The probability the flop doesn't contain an ace or a king is
(50-8)C3/ 50C3 = 58.57%

The probability the flop contains either an ace or a king is 1-0.5857= 41.42% .

[Blitzwing]

What do you mean with c3?

[BruceZ]

[ QUOTE ]
What do you mean with c3?

[/ QUOTE ]

xCy = C(x,y)

[HitNRunPoster]

Thanks for your responses, guys.

I guess I've trained myself not to notice the frequency of these flops, but DAMN that's crazy.

I'll have to start actaully looking for it to see how close my observation lines up to the math, although, well, that obviously won't change the math. [img]/images/graemlins/smile.gif[/img]

Thanks for your help, guys.

--Dave.