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Holding AQ. What high card has highest prob on flop?

  
 
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Openside
Old 08-21-2010, 07:05 PM     Post subject: Holding AQ. What high card has highest prob on flop? #1 (permalink)  
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 I was talking to spoon on mIRC and was posed this question:
[23:43] <spoonitnow> if you hold AQ
[23:43] <spoonitnow> what's the most likely high card on the flop
01[23:43] <Openside> K
[23:43] <ZwiFTiBAF> buuuuurt
[23:43] <ZwiFTiBAF> wrong
[23:44] <spoonitnow> an ace is still the most likely high card
[23:44] <spoonitnow> isn't that sick


[23:50] <spoonitnow> chance of an a-high flop if we take an a and a q out of the deck is like (3/50)*(47/49)*(46/48)*3
[23:51] <spoonitnow> ok so chance of a k-high flop under the same circumstances is
[23:52] <spoonitnow> actually that's wrong
[23:52] <spoonitnow> it should be
[23:52] <spoonitnow> (3/50)*3, i think
[23:52] <spoonitnow> anyway
[23:52] <spoonitnow> so here comes the K-high flop train
[23:53] <spoonitnow> (4/50)*(46/49)*(45/48)*3 = 0.21
[23:53] <spoonitnow> which should be lower than (3/50)*3 = 0.18

I like to figure things out for myself and hate it when i can't. I am missing something, I cant figure why A has the highest prob.
Here is my logic: we hold AQ
Flop can come Axx, xAx or xxA
Prob. of hitting at least one A on flop = 3/50+3/49+3/48 = 0.18


Now prob of the flop hitting a K and no A is
K, no A, noA + no A, K, no A + no A, no A, K
= (4/50*46/49*45/48)+(47/50*4/49*45/48)+(47/50*46/49*4/48) = 0.21

So to me hitting a K and no A is higher prob. than hitting an A on flop.

Damn it, where am i going wrong?
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celtic123
Old 08-21-2010, 08:14 PM #2 (permalink)  
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 I might be barking up the wrong tree, but It it like a trick question?

Maybe its not to do with maths.


Quote:
Originally Posted by Openside View Post
I was talking to spoon on mIRC and was posed this question:
[23:43] <spoonitnow> if you hold AQ
[23:43] <spoonitnow> what's the most likely high card on the flop

I dont see how the K can be the most likely High card, because the J is equally most likely and this is also a high card.

Its like saying , higher cards have more chance than low cards of landing in the flop.
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Openside
Old 08-21-2010, 08:26 PM #3 (permalink)  
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Quote:
Originally Posted by celtic123 View Post
I might be barking up the wrong tree, but It it like a trick question?

Maybe its not to do with maths.





I dont see how the K can be the most likely High card, because the J is equally most likely and this is also a high card.

Its like saying , higher cards have more chance than low cards of landing in the flop.
No i dont think its a trick question. Think of it as "which has a higher prob. of hitting the flop A or K and being high card?"
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celtic123
Old 08-21-2010, 08:41 PM #4 (permalink)  
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Quote:
Originally Posted by Openside View Post
Think of it as "which has a higher prob. of hitting the flop A or K and being high card?"


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Imthenewfish
Old 08-21-2010, 09:07 PM #5 (permalink)  
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Quote:
Originally Posted by Openside View Post
Now prob of the flop hitting a K and no A is
K, no A, noA + no A, K, no A + no A, no A, K
= (4/50*46/49*45/48)+(47/50*4/49*45/48)+(47/50*46/49*4/48) = 0.21

So to me hitting a K and no A is higher prob. than hitting an A on flop.

Damn it, where am i going wrong?
Why does it matter what order they're in? Just find the probability of a king flopping and then subtract it by the probability of an ace hitting the other two cards. (4/50+4/49+4/48)-[(3/49)+(3/48)]?(0.8+0.816+0.833)-[(0.0612)+(0.0625)=24.5%-12.37%
probability of a king being the high card should be something like 12%
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spoonitnow
Old 08-21-2010, 10:15 PM #6 (permalink)  
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 There are K-high flops and there are A-high flops. Which is most likely if you hold AQ?
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Originally Posted by Ripptyde
I only have 2 simple rules when I am coaching a new student.

Rule # 1: don't ask questions

Rule # 2: don't ask questions

I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.
 
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spoonitnow
Old 08-21-2010, 10:16 PM #7 (permalink)  
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 Btw I f'ed up the original question, K-high flops are the most likely in that scenario. Meant to ask if we hold AK which is most likely, an A-high flop or Q-high flop.

If we hold AQ then A/K-high flops are of similar likelihood.
Quote:
Originally Posted by Ripptyde
I only have 2 simple rules when I am coaching a new student.

Rule # 1: don't ask questions

Rule # 2: don't ask questions

I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.
 
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